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4549 lines
232 KiB
4549 lines
232 KiB
% !TeX spellcheck = en_US
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% !TeX encoding = UTF-8
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\documentclass{article}
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\usepackage{hyperref}
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\usepackage[parfill]{parskip}
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\usepackage{siunitx}
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\usepackage[style=numeric-comp,backend=biber,eprint=true,url=true]{biblatex}
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%\DeclareFieldFormat[article]{title}{}
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\renewbibmacro{in:}{}
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\addbibresource{mcfm.bib}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{microtype}
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\usepackage{scalefnt}
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\newcommand{\abbrev}{\scalefont{.9}}
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\newcommand{\Qone}{\ensuremath{\mathcal{Q}_{\varphi q}^{(3,33)}}}
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\newcommand{\Qtwo}{\ensuremath{\mathcal{Q}_{\varphi u d }^{33}}}
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\newcommand{\Qthree}{\ensuremath{\mathcal{Q}_{uW}^{33}}}
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\newcommand{\Qfour}{\ensuremath{\mathcal{Q}_{dW}^{33}}}
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\newcommand{\Qsix}{\ensuremath{\mathcal{Q}_{uG}^{33} }}
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\newcommand{\Qseven}{\ensuremath{\mathcal{Q}_{dG}^{33}}}
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\newcommand{\Qeight}{\ensuremath{\mathcal{Q}_{4L}}}
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\newcommand{\Qnine}{\ensuremath{\mathcal{Q}_{4R}}}
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\newcommand{\Qten}{\ensuremath{\mathcal{Q}_{dB}^{33}}}
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\newcommand{\Cone}{\ensuremath{\mathcal{C}_{\varphi q}^{(3,33)}}}
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\newcommand{\Ctwo}{\ensuremath{\mathcal{C}_{\varphi u d }^{33}}}
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\newcommand{\Cthree}{\ensuremath{\mathcal{C}_{uW}^{33}}}
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\newcommand{\Cfour}{\ensuremath{\mathcal{C}_{dW}^{33}}}
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\newcommand{\Csix}{\ensuremath{\mathcal{C}_{uG}^{33} }}
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\newcommand{\Cseven}{\ensuremath{\mathcal{C}_{dG}^{33}}}
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\newcommand{\Ceight}{\ensuremath{\mathcal{C}_{4L}}}
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\newcommand{\Cnine}{\ensuremath{\mathcal{C}_{4R}}}
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\newcommand{\Cten}{\ensuremath{\mathcal{C}_{dB}^{33}}}
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\begin{document}
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\def\GeV{\mbox{GeV}}
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\def\cteqten{\mbox{1007.2241 [hep-ph]}}
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\def\cteqsixsixm{\mbox{0802.0007 [hep-ph]}}
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\def\cteqsixonem{\mbox{hep-ph/0303013}}
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\def\cteqsix{\mbox{hep-ph/0201195}}
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\def\cteqfive{\mbox{hep-ph/9903282}}
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\def\cteqfour{\mbox{hep-ph/9606399}}
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\def\cteqthree{\mbox{MSU-HEP/41024}}
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\def\mrstff{\mbox{hep-ph/0603143}}
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\def\mrstohtwo{\mbox{hep-ph/0211080}}
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\def\mrstohtwofirst{\mbox{hep-ph/0201127}}
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\def\mrstohone{\mbox{hep-ph/0110215}}
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\def\mrsninenine{\mbox{hep-ph/9907231}}
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\def\mrsnineeight{\mbox{hep-ph/9803445}}
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\def\mrsninesix{\mbox{PLB387 (1996) 419}}
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\def\mrsninefive{\mbox{PLB354 (1995) 155}}
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\def\hmrs{\mbox{Durham DTP-90-04}}
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\def\mstwoheight{\mbox{0901.0002 [hep-ph]}}
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\def\MCFM{{\tt MCFM }}
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\def\pow{{\lower.12ex\hbox{\texttt{\char`\^}}}}
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\thispagestyle{empty}
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\vspace*{3cm}
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\begin{center}
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{\Huge MCFM v8.3} \\
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\vspace*{0.5cm}
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\Large{A Monte Carlo for FeMtobarn} \\
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\Large{processes at Hadron Colliders} \\
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\vspace*{1.5cm}
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{\huge Users Guide} \\
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\vspace*{4cm}
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{\it Authors:} \\
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\vspace*{0.2cm}
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John M. Campbell ({\tt johnmc@fnal.gov}) \\
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R. Keith Ellis ({\tt ellis@fnal.gov}) \\
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Walter Giele ({\tt giele@fnal.gov}) \\
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Tobias Neumann ({\tt tneumann@fnal.gov}) \\
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Ciaran Williams ({\tt ciaranwi@buffalo.edu}) \\
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\vspace*{1.5cm}
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{\it \small Updated: \today}
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\end{center}
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\newpage
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\tableofcontents
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\newpage
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\section{Overview}
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\MCFM is a parton-level Monte Carlo program that gives NLO predictions
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for a range of processes at hadron colliders. The program has been
|
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developed over a number of years and results have been presented in
|
|
a number of published papers. The papers describing the original
|
|
code and the most significant developments in the NLO implementation are:
|
|
\begin{itemize}
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\item J.~M.~Campbell and R.~K.~Ellis, \\
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{\it ``An update on vector boson pair production at hadron colliders,''} \\
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Phys.\ Rev.\ D {\bf 60}, 113006 (1999)
|
|
[arXiv:hep-ph/9905386].
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\item J.~M.~Campbell, R.~K.~Ellis and C.~Williams, \\
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{\it ``Vector boson pair production at the LHC,''} \\
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JHEP {\bf 1107}, 018 (2011)
|
|
[arXiv:1105.0020 [hep-ph]].
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\item J.~M.~Campbell, R.~K.~Ellis and W.~Giele, \\
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{\it ``A Multi-Threaded Version of MCFM''}, \\
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EPJ {\bf C75}, 246 (2015)
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[arXiv:1503.06182 [hep-ph]].
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\end{itemize}
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As of v8.0 MCFM can also compute selected color-singlet processes through NNLO in QCD
|
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perturbation theory. The processes available at this precision, as well as
|
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benchmark numbers, are detailed in Section~\ref{sec:NNLO}. When using MCFM 8.0
|
|
for NNLO calculations please refer to:
|
|
\begin{itemize}
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\item
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R.~Boughezal, J.~M.~Campbell, R.~K.~Ellis, \\
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|
C.~Focke, W.~Giele, X.~Liu,~F. Petriello and C.~Williams, \\
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{\it ``Color singlet production at NNLO in MCFM''},
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arXiv:1605.08011.
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|
\end{itemize}
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|
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Other relevant references, corresponding to publications associated with the
|
|
implementation of specific processes at NLO and NNLO, are listed
|
|
in Appendix~\ref{MCFMrefs}. Appendices~\ref{changelog8.1}--\ref{changelog} contain
|
|
a record of changes to the code since v6.0.
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\section{Installation}
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The tar'ed and gzip'ed package may be downloaded from
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the \MCFM home-page at {\tt http://mcfm.fnal.gov}.
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After extracting, the source can be initialized by running the
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{\tt ./Install} command and then compiled with {\tt make}. The
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makefile may be edited prior to running, to include
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the locations of the CERNLIB and LHAPDF libraries, if desired.
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The code requires and only supports the GNU compiler collection with at least
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version 6 and smaller than 8 including the C++11 compiler g++ and the Fortran compiler gfortran.
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If your GNU Fortran and GNU C++ compiler commands are different than gfortran
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and g++ you should export the environment variables FC and CXX to match the
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names of the gfortran and g++ compiler commands before running the Install
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script or the makefile.
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Please ensure that your compiler is working and can produce executable program
|
|
files. For example when your compiler has been installed into a non-standard
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|
location you probably need to append the compiler library path to {\tt
|
|
LD\_LIBRARY\_PATH } ({\tt DYLD\_FALLBACK\_LIBRARY\_PATH} on OS X). This can be
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|
achieved, for example, as follows:
|
|
\begin{verbatim}
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export LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:/home/user/local/lib
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\end{verbatim}
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|
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The directory structure of the installation is as follows:
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\begin{itemize}
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\item {\tt Doc}. The source for this document.
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\item {\tt Bin}. The directory containing the executable {\tt mcfm\_omp},
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and various essential files -- notably the options file {\tt input.DAT}.
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\item {\tt Bin/Pdfdata}. The directory containing the PDF data-files.
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\item {\tt obj}. The object files produced by the compiler.
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\item {\tt src}. The Fortran source files in various subdirectories.
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\item {\tt qcdloop-2.0.2}. The source files to the
|
|
library QCDLoop~\cite{Carrazza:2016gav,Ellis:2007qk}.
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\item {\tt TensorReduction} General tensor reduction code based on the work of Passarino and
|
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Veltman \cite{Passarino:1978jh} and Oldenborgh and Vermaseren \cite{vanOldenborgh:1989wn}.
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\end{itemize}
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%The files which it is most likely that the user will need to modify
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%are located in {\tt src/User}. It is convenient, if one wants to
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%modify one of these files, (or any other file in the subdirectories of the
|
|
%{\tt src} directory),
|
|
%to copy it first to the directory where the user has installed MCFM.
|
|
%The makefile will use this file in preference to the identically named
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|
%file in the sub-directories of {\tt src}.
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\subsection{OpenMP and MPI}
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\MCFM uses OpenMP (Open Multi-Processing) to implement multi-threading and will automatically adjust to the
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number of available cpu threads. The multi-threading is implemented with respect to the integration routine
|
|
Vegas, which distributes the event evaluations over the threads and combines all events at the end of
|
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every iteration.
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Two environment variables are useful when using the OMP version of \MCFM.
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The first, {\tt OMP\_STACKSIZE} may need to be set in order for the program
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to run correctly. On some systems, depending on the OMP implementation,
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the program will crash when calculating some of the more complicated processes,
|
|
for example $W+2$~jet production at NLO. Setting this
|
|
variable to {\tt 16000}, for instance in the Bash shell by using the
|
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command {\tt export OMP\_STACKSIZE=16000}, has been found to be sufficient
|
|
for all processes. The second useful variable {\tt OMP\_NUM\_THREADS}
|
|
may be used to directly control the number of threads used during
|
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OMP execution (the default is the maximum number of threads available
|
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on the system).
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|
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It is also possible to run \MCFM using the MPI (Message Passing Interface).
|
|
To run in this mode, change the flag {\tt USEMPI} in the makefile to {\tt YES} and specify the MPI compiler
|
|
wrappers and compilers in the makefile. By default the OpenMPI compiler wrappers mpifort and mpic++ are set
|
|
to use gfortran and g++.
|
|
|
|
%\subsection{Installation as a library}
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%It is also possible to compile all of \MCFM as a library.
|
|
%This can be of use if the user desires to use routines of \MCFM
|
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%in association with another program. This is achieved by the make command
|
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%{\tt make mcfmlib}. The \MCFM executable can also be compiled using
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%the library with {\tt make mcfmalt}.
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\section{Input parameters}
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\label{Input_parameters}
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\MCFM allows the user to choose between a number of schemes
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for defining the electroweak couplings. These choices are summarized
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in Table~\ref{ewscheme}. The scheme is selected by modifying the
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value of {\tt ewscheme} in {\tt src/User/mdata.f} prior to compilation,
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which also contains
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the values of all input parameters (see also Table~\ref{default}).
|
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|
|
\begin{table}
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\begin{center}
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\begin{tabular}{|c|c|c|c|c|c|c|} \hline
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Parameter & Name & Input Value
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& \multicolumn{4}{c|}{Output Value determined by \tt ewscheme} \\
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\cline{4-7}
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& ({\tt \_inp}) & & {\tt -1} & {\tt 0} & {\tt 1} & {\tt 2} \\ \hline
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$G_F$ & {\tt Gf} & 1.16639$\times$10$^{-5}$
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& input & calculated & input & input \\
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|
$\alpha(M_Z)$ & {\tt aemmz} & 1/128.89
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& input & input & calculated & input \\
|
|
$\sin^2 \theta_w$& {\tt xw} & 0.2223
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& calculated & input & calculated & input \\
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|
$M_W$ & {\tt wmass} & 80.385 GeV
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& input & calculated & input & calculated \\
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|
$M_Z$ & {\tt zmass} & 91.1876 GeV
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& input & input & input & calculated \\
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|
$m_t$ & {\tt mt} & {\tt input.DAT}
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& calculated & input & input & input \\
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\hline
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\end{tabular}
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\caption{Different options for the scheme used to fix the electroweak
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parameters of the Standard Model and the corresponding default input
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values. $M_W$ and $M_Z$ are taken from ref.~\cite{Amsler:2008zzb}.}
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\label{ewscheme}
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|
\end{center}
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\end{table}
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|
|
The default scheme corresponds to {\tt ewscheme=+1}. As described below, this corresponds to a scheme
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in which the top quark mass is an input parameter so that it is
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more suitable for many processes now included in the program.
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|
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The choice of ({\tt ewscheme=-1}) enforces the use of an effective field
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|
theory approach, which is valid for scales below the top mass. In this
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approach there are 4 independent parameters (which we choose to be
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$G_F$, $\alpha(M_Z)$, $M_W$ and $M_Z$). For further details,
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|
see Georgi~\cite{Georgi:1991ci}.
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|
For all the other schemes ({\tt ewscheme=0,1,2}) the top mass is simply
|
|
an additional input parameter and there are 3 other independent
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parameters from the remaining 5. The variable {\tt ewscheme} then performs
|
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exactly the same role as {\tt idef} in MadEvent~\cite{Maltoni:2002qb}.
|
|
{\tt ewscheme=0} is the old MadEvent default and {\tt ewscheme=1} is the
|
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new MadEvent default, which is also the same as that used in
|
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Alpgen~\cite{Alpgen} and LUSIFER~\cite{Lusifer}
|
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For processes in which the top quark is directly produced it is
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preferable to use the schemes ({\tt ewscheme=0,1,2}), since in these schemes
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one can adjust the top mass to its physical value (in the input file,
|
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{\tt input.DAT}).
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|
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\begin{table}
|
|
\begin{center}
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\begin{tabular}{|c|c|c|} \hline
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Parameter & Fortran name & Default value \\
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\hline
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|
$m_\tau$ & {\tt mtau} & 1.777 GeV \\
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$m^2_\tau$& {\tt mtausq} & 3.1577 GeV$^2$ \\
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$\Gamma_\tau$ & {\tt tauwidth}& 2.269$\times$10$^{-12}$~GeV \\
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$\Gamma_W$ & {\tt wwidth} & 2.093 GeV \\
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$\Gamma_Z$ & {\tt zwidth} & 2.4952 GeV \\
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$V_{ud}$ & {\tt Vud} & 0.975 \\
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$V_{us}$ & {\tt Vus} & 0.222 \\
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$V_{ub}$ & {\tt Vub} & 0. \\
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$V_{cd}$ & {\tt Vcd} & 0.222 \\
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$V_{cs}$ & {\tt Vcs} & 0.975 \\
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$V_{cb}$ & {\tt Vcb} & 0. \\
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\hline
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\end{tabular}
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\caption{Default values for the remaining parameters in \MCFM.
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$\Gamma_W$ and $\Gamma_Z$ from ref.~\cite{Amsler:2008zzb}.}
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\label{default}
|
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\end{center}
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\end{table}
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In the same file ({\tt mdata.f}) one can also choose the definition
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|
that the program uses for computing transverse quantities, namely
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|
transverse momentum or transverse energy. These are defined by,
|
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\begin{eqnarray}
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\mbox{transverse momentum:} & \sqrt{p_x^2+p_y^2} \; ,\nonumber \\
|
|
\mbox{transverse energy:} &
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\frac{E \sqrt{p_x^2+p_y^2}}{\sqrt{p_x^2+p_y^2+p_z^2}} \; .
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\end{eqnarray}
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The two definitions of course coincide for massless particles.
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The chosen definition is used for all cuts that are applied to the
|
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process and it is the one that is used in the default set of histograms.
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|
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\subsection{Parton distributions}
|
|
The value of $\alpha_S(M_Z)$ is not adjustable; it is hardwired with the
|
|
parton distribution. In addition, the parton distribution also specifies
|
|
the number of loops that should be used in the running of $\alpha_S$.
|
|
The default mode of operation is to choose from a
|
|
collection of modern parton distribution functions that are included with
|
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\MCFM. The distributions, together with their associated $\alpha_S(M_Z)$
|
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values, are given in Table~\ref{pdlabelrecent}. In addition to these
|
|
choices, a number of historical PDF sets are also available; for details, see
|
|
Appendix~\ref{olderPDFs}. Note that, due to the memory requirements for
|
|
using the NNPDF sets, in OpenMP operation it is usually necessary to increase
|
|
the value of the environment variable {\tt OMP\_STACKSIZE} to avoid
|
|
segmentation faults.
|
|
%
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c|c|}
|
|
\hline
|
|
{\tt pdlabel} & $\alpha_S(M_Z)$ & order & reference \\
|
|
\hline
|
|
{\tt mstw8lo} & 0.1394 & 1 & \cite{Martin:2009iq} \\
|
|
{\tt mstw8nl} & 0.1202 & 2 & \cite{Martin:2009iq} \\
|
|
{\tt mstw8nn} & 0.1171 & 3 & \cite{Martin:2009iq} \\
|
|
{\tt MMHT\_lo} & 0.135 & 1 & \cite{Harland-Lang:2014zoa} \\
|
|
{\tt MMHT\_nl} & 0.120 & 2 & \cite{Harland-Lang:2014zoa} \\
|
|
{\tt MMHT\_nn} & 0.118 & 3 & \cite{Harland-Lang:2014zoa} \\
|
|
\hline
|
|
{\tt CT10.00} & 0.118 & 2 & \cite{Lai:2010vv} \\
|
|
{\tt CT14.LL} & 0.130 & 1 & \cite{Dulat:2015mca} \\
|
|
{\tt CT14.NL} & 0.118 & 2 & \cite{Dulat:2015mca} \\
|
|
{\tt CT14.NN} & 0.118 & 3 & \cite{Dulat:2015mca} \\
|
|
{\tt CT14qed} & 0.118 & 2 & \cite{Schmidt:2015zda} \\
|
|
\hline
|
|
{\tt NN2.3NL} & 0.118 & 2 & \cite{Ball:2012cx} \\
|
|
{\tt NN2.3NN} & 0.118 & 3 & \cite{Ball:2012cx} \\
|
|
{\tt NN3.0LO} & 0.118 & 1 & \cite{Ball:2014uwa} \\
|
|
{\tt NN3.0NL} & 0.118 & 2 & \cite{Ball:2014uwa} \\
|
|
{\tt NN3.0NN} & 0.118 & 3 & \cite{Ball:2014uwa} \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{Modern PDF sets that are available in the code,
|
|
their corresponding values of $\alpha_S(M_Z)$ and order of running,
|
|
and a reference to the paper
|
|
that describes their origin. Further sets, of a more historical nature, are
|
|
listed in Appendix~\ref{olderPDFs}.
|
|
\label{pdlabelrecent}}
|
|
\end{table}
|
|
|
|
By editing the {\tt makefile}, one can switch to the {\tt LHAPDF} parton distribution function
|
|
implementations. This requires setting the flag {\tt PDFROUTINES} to {\tt LHAPDF} in the {\tt makefile}.
|
|
If the library is not in one of the standard include and linker paths one must first set the variable {\tt
|
|
LHAPDFLIB} in the makefile to point to the directory that contains libLHAPDF. This version of \MCFM has been
|
|
explicitly tested against {\tt LHAPDF-6.2.1}.
|
|
|
|
The parameters to choose the pdf set are then provided in {\tt Bin/input.DAT} -
|
|
the name of the group and the integer specifying the set.
|
|
%\MCFM expects to find the LHAPDF grids in a sub-directory of {\tt Bin} called
|
|
%{\tt PDFsets}. It is easiest to simply create a symbolic link of the directory where the
|
|
%grids actually reside to a subdirectory of {\tt Bin} called {\tt PDFsets}.
|
|
|
|
If at the first execution of mcfm the library libLHAPDF cannot be found, you can add your LHAPDF library
|
|
path to the environment variable {\tt LD\_LIBRARY\_PATH} as follows:
|
|
\begin{verbatim}
|
|
export LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:/home/user/newpath/lib
|
|
\end{verbatim}
|
|
|
|
\section{Benchmark results at NNLO }
|
|
\label{sec:NNLO}
|
|
We perform all benchmark calculations with the default set of EW parameters
|
|
and for the LHC operating at $\sqrt s = 14$~TeV. We allow all
|
|
vector bosons to be off-shell ({\tt zerowidth} is {\tt .false.})
|
|
and include their decays ({\tt removebr} is {\tt .false.}).
|
|
For each Higgs boson process we consider the decay $H \to \tau^- \tau^+$.
|
|
For parameters that are set in the input file we use,
|
|
\begin{eqnarray}
|
|
m_H = 125~\mbox{GeV} \,, \quad
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|
m_t = 173.3~\mbox{GeV} \,, \quad
|
|
m_b = 4.66~\mbox{GeV} \,,
|
|
\end{eqnarray}
|
|
and we use the NNLO CT14 pdf set (i.e. {\tt pdlabel} is {\tt CT14.NN}) with
|
|
$\mu_F = \mu_R = Q^2$ (i.e. we set {\tt dynamicscale} equal to
|
|
either {\tt m(34)} or {\tt m(345)} or {\tt m(3456)}, as appropriate).
|
|
Our generic set of cuts is,
|
|
\begin{eqnarray}
|
|
&& p_T(\mbox{lepton}) > 20~\mbox{GeV} \,, \quad
|
|
|\eta(\mbox{lepton})| < 2.4 \,, \quad \nonumber \\
|
|
&& p_T(\mbox{photon 1}) > 40~\mbox{GeV} \,, \quad
|
|
p_T(\mbox{photon 2}) > 25~\mbox{GeV} \,, \quad \nonumber \\
|
|
&&|\eta(\mbox{photon})| < 2.5 \,, \quad
|
|
\Delta R(\mbox{photon 1, photon 2}) > 0.4 \,, \quad \nonumber \\
|
|
&& E_T^{\mbox{miss}} > 30~\mbox{GeV} \,, \quad
|
|
\end{eqnarray}
|
|
For $Z$ production we also impose a minimum $Z^*$ virtuality ({\tt m34min})
|
|
of $40$~GeV.
|
|
|
|
For providing benchmark runs we choose a set of integration parameters
|
|
that provides approximately 1\% (or smaller) Monte Carlo uncertainties for the NLO cross sections.
|
|
These are {\tt itmx1 = 4}, {\tt itmx2 = 10} and {\tt ncall1 = ncall2 = 400000}.
|
|
For the NNLO coefficients we use {\tt itmx1 = 4}, {\tt itmx2 = 10} and {\tt ncall1 = ncall2 = 800000} and
|
|
set {\tt taucut} to {\tt 1\%acc}. This gives the reader an impression of the reached integration uncertainty
|
|
compared to the approx. 1\% error due to neglected power corrections. For the NNLO cross sections the
|
|
required computing time is about one week of CPU-time, depending on the process. Corresponding input files
|
|
for each process number can be found in the directory {\tt Bin/benchmarks}.
|
|
|
|
Our benchmarks are shown in Table~\ref{NNLObenchmarks}. These benchmark cross-sections
|
|
may not be sufficiently accurate for all phenomenological applications but they should
|
|
be able to be reproduced relatively easily, even on a desktop machine.
|
|
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|l|} \hline
|
|
Process & {\tt nproc} & $\sigma_\mathrm{NLO} \pm \delta\sigma_\mathrm{NLO}^\mathrm{MC} $ &
|
|
$\sigma_\mathrm{NNLO} \pm
|
|
\delta\sigma_\mathrm{NNLO}^\mathrm{MC} \pm \delta\sigma_\mathrm{NNLO}^\mathrm{pc}$ \\
|
|
\hline
|
|
$W^+$ & {\tt 1} & $4.220 \pm 0.002$ nb & $4.19 \pm 0.02 \pm 0.043$ nb\\
|
|
$W^-$ & {\tt 6} & $3.315 \pm 0.001$ nb & $3.23 \pm 0.01 \pm 0.033$ nb\\
|
|
$Z $ & {\tt 31} & $885.2 \pm 0.3$ pb & $878 \pm 3 \pm 9$ pb\\
|
|
$H $ & {\tt 112} & $1.395 \pm 0.001$ pb & $1.865 \pm 0.004 \pm 0.019$ pb\\
|
|
$\gamma\gamma $ & {\tt 285} & $27.94 \pm 0.01$ pb & $43.60 \pm 0.06 \pm 0.44$ pb\\
|
|
$W^+H$ & {\tt 91} & $2.208 \pm 0.002$ fb & $2.268 \pm 0.007 \pm 0.023$ fb\\
|
|
$W^-H$ & {\tt 96} & $1.494 \pm 0.001$ fb & $1.519 \pm 0.004 \pm 0.015$ fb\\
|
|
$ZH$ & {\tt 110} & $0.7535 \pm 0.0004$ fb & $0.846 \pm 0.001 \pm 0.0085$ fb\\
|
|
$Z\gamma$ & {\tt 300} & $959 \pm 8$ fb & $1268 \pm 22 $ fb \\
|
|
\hline
|
|
\end{tabular}
|
|
\caption{Benchmark cross-sections at NLO and NNLO, using the parameters
|
|
and settings described in the text. $\delta\sigma^{MC}$ represents the uncertainty
|
|
from Monte Carlo statistics, while $\delta\sigma^{pc}$ is an estimate of the
|
|
uncertainty due to neglected power corrections at NNLO.}
|
|
\label{NNLObenchmarks}
|
|
\end{center}
|
|
\end{table}
|
|
|
|
\section{Runtime options}
|
|
|
|
\MCFM execution is performed in the {\tt Bin/} directory,
|
|
with syntax:
|
|
\begin{center}
|
|
{\tt mcfm\_omp [}{\it mydir}{\tt ] [}{\it myfile}{\tt .DAT]}
|
|
\end{center}
|
|
If no command line options are given, then {\tt mcfm} will default
|
|
to using the file {\tt input.DAT} in the current directory for
|
|
choosing options\footnote{Note that this is very different from
|
|
previous versions of \MCFM. All auxiliary input files from v3.2 and
|
|
earlier have now been incorporated into a single file.}.
|
|
The different possibilities are summarized in Table~\ref{clopts}.
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{l|cl}
|
|
Command executed && Location of input file \\
|
|
\hline
|
|
{\tt mcfm} && {\tt input.DAT} \\
|
|
{\tt mcfm myfile.DAT} && {\tt myfile.DAT} \\
|
|
{\tt mcfm mydir} && {\tt mydir/input.DAT} \\
|
|
{\tt mcfm mydir myfile.DAT} && {\tt mydir/myfile.DAT} \\
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{Summary of command line options for running {\tt mcfm}.}
|
|
\label{clopts}
|
|
\end{table}
|
|
In addition, if a working directory {\it mydir} is specified then
|
|
output files will also be produced in this directory. By using these
|
|
options one may, for instance, keep all input and output files for
|
|
different processes in separate directories.
|
|
|
|
Each parameter in the input file is specified by a line such as
|
|
\begin{displaymath}
|
|
{\tt value} \hspace{3cm} {\tt [parameter]}
|
|
\end{displaymath}
|
|
and we will give a description of all the parameters below, together with
|
|
valid and/or sensible inputs for ${\tt value}$. Groups of parameters
|
|
are separated by a blank line and a description of that section, for
|
|
readability.
|
|
|
|
\begin{itemize}
|
|
\item {\tt file version number}. This should match the version number
|
|
that is printed when {\tt mcfm} is executed.
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Flags to specify the mode in which \MCFM is run] }
|
|
\end{center}
|
|
|
|
\item {\tt nevtrequested}. The default for this parameter is {\tt -1} and for the following three
|
|
parameters it is {\tt .false.}. This corresponds to the usual mode
|
|
of operation where the program produces a cross section and a selection of histograms.
|
|
It is possible to generate n-tuples instead of histograms,
|
|
as well as unweighted events, for some processes. Please refer to
|
|
Section~\ref{subsec:otheroutput} for further details.
|
|
\item {\tt creatent}. {\it See above.}
|
|
\item {\tt dswhisto}. {\it See above.}
|
|
\item {\tt writerefs}. Flag to control whether or not the program writes a list
|
|
of appropriate references to the output at the end of the run.
|
|
\item {\tt writetop}. Flag to control whether or not a Topdrawer histogram output file
|
|
is produced. Please refer to Section~\ref{sec:output} for further details.
|
|
\item {\tt writedat}. Flag to control whether or not the plain histogram output file
|
|
is produced. Please refer to Section~\ref{sec:output} for further details.
|
|
\item {\tt writegnu}. Flag to control whether or not a gnuplot histogram output file
|
|
is produced. Please refer to Section~\ref{sec:output} for further details.
|
|
\item {\tt writeroot}. Flag to control whether or not a ROOT script for plotting
|
|
histograms is produced. Please refer to Section~\ref{sec:output} for further details.
|
|
\item {\tt writepwg}. Flag to control whether a powheg-style analysis file is produced.
|
|
This option is available only for a limited number of processes. As currently implemented it
|
|
should be viewed as a development tool, not yet fully supported for the general user.
|
|
\item {\tt writetxt}. Flag to control whether or not a text file with space-separated columns
|
|
is written for each histogram.
|
|
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [General options to specify the process and execution] }
|
|
\end{center}
|
|
|
|
\item {\tt nproc}.
|
|
The process to be studied is given by
|
|
choosing a process number, according to Table~\ref{nproctable}
|
|
in Appendix~\ref{MCFMprocs}.
|
|
$f(p_i)$ denotes a generic partonic jet. Processes denoted as
|
|
``LO'' may only be calculated in the Born approximation. For photon
|
|
processes, ``NLO+F'' signifies that the calculation may be performed
|
|
both at NLO and also including the effects of photon fragmentation
|
|
and experimental isolation. In contrast, ``NLO'' for a process involving
|
|
photons means that no fragmentation contributions are included and isolation
|
|
is performed according to the procedure of Frixione~\cite{Frixione:1998jh}.
|
|
\item {\tt part}.
|
|
This parameter has 5 possible values, described below:
|
|
\begin{itemize}
|
|
\item {\tt lo} (or {\tt lord}).
|
|
The calculation is performed at leading order only.
|
|
\item {\tt virt}.
|
|
Virtual (loop) contributions to the next-to-leading order result are
|
|
calculated (+counterterms to make them finite), including also the
|
|
lowest order contribution.
|
|
\item {\tt real}.
|
|
In addition to the loop diagrams calculated by {\tt virt}, the full
|
|
next-to-leading order results must include contributions from diagrams
|
|
involving real gluon emission (-counterterms to make them finite).
|
|
Note that only the sum of the {\tt real} and the {\tt virt} contributions
|
|
is physical.
|
|
\item {\tt nlo} (or {\tt tota}).
|
|
For simplicity, the {\tt nlo} option simply runs the {\tt virt} and
|
|
{\tt real} real pieces in series before performing a sum to obtain
|
|
the full next-to-leading order result. In this case, the number of
|
|
points specified by {\tt ncall1} and {\tt ncall2} is automatically
|
|
increased when performing the {\tt real} calculation. Sometimes
|
|
it may be more efficient to do run the pieces separately by hand,
|
|
(c.f. {\tt ncall} below. For photon processes that include fragmentation,
|
|
{\tt nlo} also includes the calculation of the fragmentation ({\tt frag})
|
|
contributions.
|
|
\item {\tt nlocoeff}.
|
|
This computes only the contribution of the NLO coefficient; it is equivalent
|
|
to running {\tt nlo} and then subtracting the result of {\tt lo}.
|
|
\item {\tt todk}
|
|
Processes 114, 161, 166, 171, 176, 181, 186, 141, 146, 149, 233, 238, 501, 511 only, see sections~\ref{subsec:stop} and
|
|
\ref{subsec:wt} below.
|
|
\item {\tt frag}.
|
|
Processes 280, 285, 290, 295, 300-302, 305-307, 820-823 only, see sections~\ref{subsec:gamgam}, \ref{subsec:wgamma} and
|
|
\ref{subsec:zgamma} below.
|
|
\item {\tt nnlo} (and {\tt nnlocoeff}).
|
|
The computation of the NNLO prediction (or the NNLO coefficient in the
|
|
expansion) is described separately below.
|
|
\end{itemize}
|
|
|
|
\item {\tt runstring}.
|
|
When \MCFM is run, it will write output to several files. The
|
|
label {\tt runstring} will be appended to the names of these files.
|
|
|
|
\item {\tt sqrts}. This is the centre-of-mass energy, $\sqrt{s}$ of
|
|
the colliding particles, measured in GeV.
|
|
|
|
\item {\tt ih1}, {\tt ih2}. The identities of the incoming hadrons
|
|
may be set with these parameters, allowing simulations for both
|
|
$p{\bar p}$ (such as the Tevatron) and $pp$ (such as the LHC).
|
|
Setting {\tt ih1} equal to ${\tt +1}$ corresponds to
|
|
a proton, whilst ${\tt -1}$ corresponds to an anti-proton.
|
|
Values greater than {\tt 1000d0} represent a nuclear collision,
|
|
as described in Section~\ref{sec:nucleus}.
|
|
|
|
\item {\tt hmass}. For processes involving the Higgs boson, this
|
|
parameter should be set equal to the value of $M_H$.
|
|
|
|
\item {\tt scale}. This parameter may be used to adjust the value
|
|
of the {\it renormalization} scale. This is the scale
|
|
at which $\alpha_S$ is evaluated and will typically be set to
|
|
a mass scale appropriate to the process ($M_W$, $M_Z$, $M_t$ for
|
|
instance). For processes involving vector bosons, setting this
|
|
scale to {\tt -1d0} chooses a scale equal to the average mass of
|
|
the bosons involved.
|
|
|
|
\item {\tt facscale}. This parameter may be used to adjust the value
|
|
of the {\it factorization} scale and will typically be set to
|
|
a mass scale appropriate to the process ($M_W$, $M_Z$, $M_t$ for
|
|
instance). As above, setting it to {\tt -1d0} will choose an
|
|
appropriate value for certain processes.
|
|
|
|
\item {\tt dynamicscale} This character string is used to specify whether
|
|
the renormalization, factorization and fragmentation scales are dynamic, i.e. recalculated
|
|
on an event-by-event basis. If this string is set to either `{\tt .false.}',
|
|
`{\tt no}' or `{\tt none}' then the scales are fixed for all events at the values
|
|
specified by {\tt scale}, {\tt facscale} and {\tt frag\_scale} in the input file.
|
|
|
|
The type of dynamic scale to be used is selected by using a particular string
|
|
for the variable {\tt dynamicscale}, as indicated in Table~\ref{dynamicscales}.
|
|
Not all scales are defined for each process, with program execution halted if
|
|
an invalid selection is made in the input file.
|
|
The selection chooses a reference scale, $\mu_0$. The actual scales used in
|
|
the code are then,
|
|
\begin{equation}
|
|
\mu_{\rm ren} = {\tt scale} \times \mu_0 \;, \qquad
|
|
\mu_{\rm fac} = {\tt facscale} \times \mu_0 \;, \qquad
|
|
\mu_{\rm frag} = \mu_{\rm ren} \;. \nonumber
|
|
\label{eq:dynscale}
|
|
\end{equation}
|
|
Note that, for simplicity, the fragmentation scale (relevant only for processes
|
|
involving photons) is set equal to the renormalization scale.
|
|
In some cases it is possible for the dynamic scale to become very large. This can cause problems
|
|
with the interpolation of data tables for the PDFs and fragmentation functions. As a result if a dynamic scale
|
|
exceeds a maximum of $60$ TeV (PDF) or $990$ GeV (fragmentation) this value is set by default to the maximum.
|
|
%
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
{\tt dynamic scale} & $\mu_0^2$ & comments\\
|
|
\hline
|
|
{\tt m(34)} & $(p_3+p_4)^2$ & \\
|
|
{\tt m(345)} & $(p_3+p_4+p_5)^2$ & \\
|
|
{\tt m(3456)} & $(p_3+p_4+p_5+p_6)^2$ & \\
|
|
{\tt sqrt(M\pow 2+pt34\pow 2)} & $M^2 + (\vec{p_T}_3 + \vec{p_T}_4)^2$ & $M=$~mass of particle 3+4 \\
|
|
{\tt sqrt(M\pow 2+pt345\pow 2)} & $M^2 + (\vec{p_T}_3 + \vec{p_T}_4 + \vec{p_T}_5)^2$ & $M=$~mass of particle 3+4+5 \\
|
|
{\tt sqrt(M\pow 2+pt5\pow 2)} & $M^2 + \vec{p_T}_5^2$ & $M=$~mass of particle 3+4 \\
|
|
{\tt sqrt(M\pow 2+ptj1\pow 2)} & $M^2 + \vec{p_T}_{j_1}^2$ & $M=$~mass(3+4), $j_1=$ leading $p_T$ jet \\
|
|
{\tt pt(photon)} & $\vec{p_T}_\gamma^2$ & \\
|
|
{\tt pt(j1)} & $\vec{p_T}_{j_1}^2$ & \\
|
|
{\tt HT} & $\sum_{i=1}^n {p_T}_i$ & $n$ particles (partons, not jets) \\
|
|
\hline
|
|
\hline\end{tabular}
|
|
\end{center}
|
|
\caption{Choices of the input parameter {\tt dynamicscale} that result in an event-by-event
|
|
calculation of all relevant scales using the given reference scale-squared $\mu_0^2$.
|
|
\label{dynamicscales}}
|
|
\end{table}
|
|
|
|
Although not really dynamic scales, note that the strings `{\tt MW}', `{\tt MZ}',
|
|
`{\tt MH}' and `{\tt mt}' may be used as shorthand to indicate values of $\mu_0$ equal to
|
|
$M_W$, $M_Z$, $M_H$ and $m_t$.
|
|
|
|
An additional option may be used to compute the effect of scale uncertainty in a process. This is
|
|
achieved by adding the string {\tt +scalevar} to the end of the usual option for {\tt dynamicscale}.
|
|
This performs a variation of the scales used in Eq.~(\ref{eq:dynscale}) by a factor of two, so that it
|
|
surveys the additional possibilities,
|
|
\begin{eqnarray}
|
|
&&
|
|
(2\mu_{\rm ren},2\mu_{\rm fac}),
|
|
(\mu_{\rm ren}/2,\mu_{\rm fac}/2), \nonumber \\ &&
|
|
(2\mu_{\rm ren},\mu_{\rm fac}),
|
|
(\mu_{\rm ren}/2,\mu_{\rm fac}),
|
|
(\mu_{\rm ren},2\mu_{\rm fac}),
|
|
(\mu_{\rm ren},\mu_{\rm fac}/2) \,.
|
|
\label{eq:scalevar}
|
|
\end{eqnarray}
|
|
The histograms corresponding to these different choices are included in the output file, from which an
|
|
envelope of theoretical uncertainty may be constructed by the user. If only a two-point scale
|
|
variation is required, corresponding to the additional scales in the first line of Eq.~(\ref{eq:scalevar}),
|
|
this may be obtained by specifying {\tt +scalevar2}. In addition,
|
|
this option requires a longer running-time than the case of no scale variation, of course.
|
|
|
|
\item {\tt zerowidth}. When set to {\tt .true.} then all vector
|
|
bosons are produced on-shell. This is appropriate for calculations
|
|
of {\it total} cross-sections (such as when using {\tt removebr} equal
|
|
to {\tt .true.}, below). When interested in decay products of the
|
|
bosons this should be set to {\tt .false.}.
|
|
|
|
\item {\tt removebr}. When set to {\tt .true.} the branching ratios are
|
|
removed for unstable particles such as vector bosons or top quarks. See the
|
|
process notes in Section~\ref{sec:specific} below for further details.
|
|
|
|
\item {\tt itmx1}, {\tt itmx2}. The program will perform two runs of
|
|
{\tt VEGAS} - once for pre-conditioning and then the final run to
|
|
collect the total cross-section and fill histograms. The number of
|
|
sweeps for each run is given by {\tt itmx1} (pre-conditioning)
|
|
and {\tt itmx2} (final). The default value for both is {\tt 10}.
|
|
|
|
|
|
\item {\tt ncall1}, {\tt ncall2}. For every sweep of {\tt VEGAS},
|
|
the number of events generated will be {\tt ncall1} in the
|
|
pre-conditioning stage and {\tt ncall2} in the final run. The number
|
|
of events required depends upon a number of factors. The error
|
|
estimate on a total cross-section will often be reasonable for a
|
|
fairly small number of events, whereas accurate histograms will
|
|
require a longer run. As the number of particles in the final state
|
|
increases, so should the number of calls per sweep. Typically one
|
|
might make trial runs with {\tt part} set to {\tt lord} to determine
|
|
reasonable values for {\tt ncall1} and {\tt ncall2}. Such values
|
|
should also be appropriate for the {\tt virt} piece of
|
|
next-to-leading order and should probably be increased by a factor of
|
|
$\sim 5$ for the {\tt real} calculation.
|
|
|
|
\item {\tt taucut}. This sets the value of the jettiness variable
|
|
$T_0$ that separates the resolved and unresolved regions in NNLO
|
|
calculations that use zero-jettiness. Recommended values of this
|
|
parameter that yield results that are affected by power corrections
|
|
at the $1$\% and $0.2$\% level can be obtained by using the
|
|
strings {\tt 1\%acc} and {\tt 0.2\%acc} respectively.
|
|
|
|
\item {\tt seed}. This is the seed for the {\tt VEGAS} integration
|
|
and can be altered to give different results for otherwise identical
|
|
runs. Use 0 for a random seed.
|
|
|
|
\item {\tt dryrun}. The default value of this parameter is
|
|
{\tt .false.}. When set to {\tt .true.} the pre-conditioning sweeps
|
|
in the {\tt VEGAS} integration are skipped, with the reported
|
|
results coming from a single run, (ie {\tt itmx1} iterations of
|
|
{\tt ncall1} points each)
|
|
\item {\tt Qflag}. This only has an effect when running a
|
|
$W+2$~jets or $Z+2$~jets process. Please see section~\ref{subsec:w2jets}
|
|
below.
|
|
|
|
\item {\tt Gflag}. This only has an effect when running a
|
|
$W+2$~jets or $Z+2$~jets process. Please see section~\ref{subsec:w2jets}
|
|
below.
|
|
|
|
\item {\tt ewcorr}. Specifies whether or not to compute EW corrections
|
|
for the process. Default is {\tt none}. May be set to {\tt exact}
|
|
or {\tt sudakov} for processes {\tt 31} (neutral-current DY),
|
|
{\tt 157} (top-pair production) and {\tt 190} (di-jet production).
|
|
For more details see section~\ref{subsec:EW}.
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Heavy quark masses] }
|
|
\end{center}
|
|
\item {\tt top mass}. The top quark pole mass (in GeV).
|
|
\item {\tt bottom mass}. The bottom quark pole mass (in GeV).
|
|
\item {\tt charm mass}. The charm quark pole mass (in GeV).
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Pdf selection] }
|
|
\end{center}
|
|
|
|
\item {\tt pdlabel}. The choice of parton distribution is made by
|
|
inserting the appropriate 7-character code from Table~\ref{pdlabelmrs}
|
|
or~\ref{pdlabelcteq} here.
|
|
As mentioned above, this also sets the value of $\alpha_S(M_Z)$.
|
|
|
|
\item {\tt LHAPDF group, LHAPDF set}. These choose the parton
|
|
distribution functions to be used when using the LHAPDF package --
|
|
the group is specified by a character string and the set by an integer.\footnote{Please see
|
|
\url{https://lhapdf.hepforge.org/} for further details.}
|
|
For appropriate PDF sets choosing a value of -1 for the set number ({\tt LHAPDF set})
|
|
will perform the calculation of the PDF uncertainties (see also
|
|
Section~\ref{sec:histos}, especially the caveat regarding using
|
|
non-grid PDF sets).
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Jet definition and event cuts] }
|
|
\end{center}
|
|
|
|
\item {\tt m34min}, {\tt m34max}, {\tt m56min}, {\tt m56max}, {\tt m3456min}, {\tt m3456max}.
|
|
These parameters represent a basic set of cuts that may be applied
|
|
to the calculated cross-section. The only events that contribute to
|
|
the cross-section will have, for example,
|
|
{\tt m34min} $<$ {\tt m34} $<$ {\tt m34max} where {\tt m34} is the
|
|
invariant mass of particles 3 and 4 that are specified by {\tt nproc}.
|
|
{\tt m34min}~$> 0$ is obligatory for processes which can involve a virtual
|
|
photon, such as {\tt nproc=31}.
|
|
\item {\tt inclusive}. This logical parameter chooses whether the
|
|
calculated cross-section should be inclusive in the number of jets
|
|
found at NLO. An {\em exclusive}
|
|
cross-section contains the same number of jets at next-to-leading
|
|
order as at leading order. An {\em inclusive} cross-section may
|
|
instead contain an extra jet at NLO.
|
|
|
|
\item {\tt algorithm.} This specifies the jet-finding algorithm that
|
|
is used, and can take the values
|
|
{\tt ktal} (for the Run II $k_T$-algorithm), {\tt ankt} (for the
|
|
``anti-$k_T$'' algorithm~\cite{Cacciari:2008gp}), {\tt cone} (for
|
|
a midpoint cone algorithm), {\tt hqrk} (for a simplified cone
|
|
algorithm designed for heavy quark processes) and {\tt none} (to
|
|
specify no jet clustering at all). The latter option is only a
|
|
sensible choice when the leading order cross-section is well-defined
|
|
without any jet definition: e.g. the single top process,
|
|
$q{\bar q^\prime} \to t{\bar b}$, which is finite as
|
|
$p_T({\bar b}) \to 0$.
|
|
|
|
\item {\tt ptjet\_min, |etajet|\_max}. These specify the values
|
|
of $p_{T,{\rm min}}$ and $|\eta|_{\rm max}$ for the
|
|
jets that are found by the algorithm. A comma-separated pair
|
|
may be used on either line to indicate a range of allowed values for
|
|
$p_T$ and $|\eta|$.
|
|
|
|
\item {\tt Rcut\_jet}. If the final state of the chosen process contains
|
|
either quarks or gluons then for each event an attempt will be made
|
|
to form them into jets. For this it is necessary to define the
|
|
jet separation $\Delta R=\sqrt{{\Delta \eta}^2 + {\Delta \phi}^2}$
|
|
so that after jet combination, all jet pairs are separated by
|
|
$\Delta R >$~{\tt Rcut\_jet}.
|
|
|
|
\item {\tt makecuts}. If this parameter is set to {\tt .false.} then
|
|
no additional cuts are applied to the events and the remaining
|
|
parameters in this section are ignored. Otherwise, events will
|
|
be rejected according to a set of cuts that is specified below.
|
|
Further options may be implemented by editing {\tt src/User/gencuts.f}.
|
|
A special setting of this parameter, to {\tt LHCb}, invokes a set of
|
|
cuts tailored to the LHCb experiment. This requires the specification
|
|
of an additional set of parameters, as shown in the file {\tt Bin/lhcb.DAT}.
|
|
The effect of these parameters, as well as the particular LHCb cuts that
|
|
are applied, can be found in the file {\tt src/Need/lhcbcode.f}.\footnote{
|
|
The authors are grateful to Philip Ilten ({\tt philten@cern.ch}) for
|
|
providing this code.}
|
|
|
|
\item {\tt ptlepton\_min, |etalepton|\_max}. These specify the values
|
|
of $p_{T,{\rm min}}$ and $|\eta|_{\rm max}$ for one of the leptons produced
|
|
in the process. A comma-separated pair
|
|
may be used on either line to indicate a range of allowed values for
|
|
$p_T$ and $|\eta|$.
|
|
|
|
\item {\tt etalepton\_veto}. This should be specified as a pair of double
|
|
precision numbers that indicate a rapidity range that should be excluded
|
|
for the lepton that passes the above cuts.
|
|
|
|
\item {\tt ptmin\_missing}. Specifies the minimum missing transverse
|
|
momentum (coming from neutrinos).
|
|
|
|
\item {\tt ptlepton(2nd+)\_min, |etalepton(2nd+)|\_max}. These specify
|
|
the values of $p_{T,{\rm min}}$ and $|\eta|_{\rm max}$ for the remaining
|
|
leptons in the process. This allows for staggered cuts where, for
|
|
instance, only one lepton is required to be hard and central.
|
|
A comma-separated pair
|
|
may be used on either line to indicate a range of allowed values for
|
|
$p_T$ and $|\eta|$.
|
|
|
|
\item {\tt etalepton(2nd+)\_veto}. This should be specified as a pair of double
|
|
precision numbers that indicate a rapidity range that should be excluded
|
|
for the remaining leptons.
|
|
|
|
\item {\tt mtrans34cut}. For general processes, this specifies the
|
|
minimum transverse mass of particles 3 and 4,
|
|
\begin{equation}
|
|
\mbox{general}: \quad 2 p_T(3) p_T(4) \left( 1 - \frac{\vec{p_T}(3) \cdot \vec{p_T}(4)}{p_T(3) p_T(4)} \right)
|
|
> {\tt mtrans34cut}
|
|
\end{equation}
|
|
For the $W(\to \ell \nu)\gamma$ process the role of this cut changes, to become
|
|
instead a cut on the transverse cluster mass of the $(\ell\gamma,\nu)$ system,
|
|
\begin{eqnarray}
|
|
W\gamma: && \left[ \sqrt{m_{\ell\gamma}^2 + |\vec{p_T}(\ell)+\vec{p_T}(\gamma)|^2} + p_T(\nu) \right]^2
|
|
\nonumber \\ &&
|
|
-|\vec{p_T}(\ell)+\vec{p_T}(\gamma)+\vec{p_T}(\nu)|^2 > {\tt mtrans34cut}^2
|
|
\end{eqnarray}
|
|
For the $Z\gamma$ process this parameter specifies a simple invariant mass cut,
|
|
\begin{equation}
|
|
Z\gamma: \quad m_{Z\gamma} > {\tt mtrans34cut}
|
|
\end{equation}
|
|
A final mode of operation applies to the $W\gamma$ process and is triggered by a negative value
|
|
of {\tt mtrans34cut}. This allows simple access to the cut that was employed in v6.0 of the code:
|
|
\begin{eqnarray}
|
|
W\gamma, \mbox{obsolete}: &&
|
|
\left[ p_T(\ell) + p_T(\gamma) + p_T(\nu) \right]^2 \nonumber \\
|
|
&-&|\vec{p_T}(\ell)+\vec{p_T}(\gamma)+\vec{p_T}(\nu)|^2 > |{\tt mtrans34cut}|
|
|
\end{eqnarray}
|
|
In each case the screen output indicates the cut that is applied.
|
|
|
|
\item {\tt R(jet,lept)\_min}. Using the definition of $\Delta R$ above,
|
|
requires that all jet-lepton pairs are separated by
|
|
$\Delta R >$~{\tt R(jet,lept)\_min}.
|
|
|
|
\item {\tt R(lept,lept)\_min}. When non-zero, all lepton-lepton pairs
|
|
must be separated by $\Delta R >$~{\tt R(lept,lept)\_min}.
|
|
|
|
\item {\tt Delta\_eta(jet,jet)\_min}. This enforces a pseudo-rapidity
|
|
gap between the two hardest jets $j_1$ and $j_2$, so that: \\
|
|
$|\eta^{j_1} - \eta^{j_2}| >$~{\tt Delta\_eta(jet,jet)\_min}.
|
|
|
|
\item {\tt jets\_opphem}. If this parameter is set to {\tt .true.},
|
|
then the two hardest jets are required to lie in opposite hemispheres,
|
|
$\eta^{j_1} \cdot \eta^{j_2} < 0$.
|
|
|
|
\item {\tt lepbtwnjets\_scheme}. This integer parameter provides no
|
|
additional cuts when it takes the value {\tt 0}. When equal to
|
|
{\tt 1} or {\tt 2}, leptons are required to lie between the two
|
|
hardest jets. With the ordering $\eta^{j_-} < \eta^{j_+}$ for the
|
|
pseudo-rapidities of jets $j_1$ and $j_2$: \\
|
|
{\tt lepbtwnjets\_scheme = 1} :
|
|
$\eta^{j_-} < \eta^{\rm leptons} < \eta^{j_+}$; \\
|
|
{\tt lepbtwnjets\_scheme = 2} :
|
|
$\eta^{j_-}+{\tt Rcut\_jet} < \eta^{\rm leptons} < \eta^{j_+}-{\tt Rcut\_jet}$.
|
|
|
|
\item {\tt ptmin\_bjet, etamax\_bjet}. If {\tt makecuts} is {\tt .true.}
|
|
and a process involving $b$-quarks is being calculated, then these can
|
|
be used to specify {\em stricter} values of $p_T^{\rm min}$
|
|
and $|\eta|^{\rm max}$ for $b$-jets. A comma-separated pair
|
|
may be used on either line to indicate a range of allowed values for
|
|
$p_T$ and $|\eta|$.
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Settings for photon processes] }
|
|
\end{center}
|
|
\item {\tt frag}. This parameter is a logical variable that determines whether the production of photons by a parton
|
|
fragmentation process is included. If {\tt frag} is set to {\tt .true.} the code uses a a standard cone isolation
|
|
procedure (that includes LO fragmentation contributions in the NLO calculation).
|
|
If {\tt frag} is set to {\tt .false.} the code implements
|
|
a Frixione-style photon cut~\cite{Frixione:1998jh},
|
|
\begin{eqnarray}
|
|
\sum_{i \in R_0} E_{T,i}^j < \epsilon_h E_{T}^{\gamma} \bigg(\frac{1-\cos{R_{i\gamma}}}{1-\cos{R_0}}\bigg)^{n} \;.
|
|
\label{frixeq}
|
|
\end{eqnarray}
|
|
In this equation, $R_0$, $\epsilon_h$ and $n$ are defined by {\tt cone\_ang}, {\tt epsilon\_h}
|
|
and {\tt n\_pow} respectively (see below).
|
|
$E_{T,i}^{j}$ is the transverse energy of a parton, $E_{T}^\gamma$ is the
|
|
transverse energy of the photon and $R_{i\gamma}$ is the separation between the photon and the parton using the usual definition
|
|
$R=\sqrt{\Delta\phi^2+\Delta\eta^2}$. $n$ is an integer parameter which by default is set to 1 but can be changed by editing the
|
|
file {\tt src/User/frix.f}.
|
|
|
|
\item {\tt fragset}. A character*8 variable that is used to choose the particular photon fragmentation set.
|
|
Currently implemented fragmentation functions can be called with `{\tt BFGSet\_I}', `{\tt BFGSetII}'~\cite{Bourhis:1997yu}
|
|
or `{\tt GdRG\_\_LO}'~\cite{GehrmannDeRidder:1998ba}.
|
|
|
|
\item {\tt frag\_scale}. A double precision variable that will be used to choose the scale
|
|
at which the photon fragmentation is evaluated.
|
|
|
|
\item {\tt ptmin\_photon}. This specifies the value
|
|
of $p_T^{\rm min}$ for the photon with the largest transverse momentum.
|
|
Note that this cut, together with all the photon cuts specified in this section
|
|
of the input file, are applied even if {\tt makecuts} is set to {\tt .false.}.
|
|
A comma-separated pair may be used to indicate a range of allowed values for $p_T$.
|
|
|
|
\item {\tt etamax\_photon}. This specifies the value
|
|
of $|y|^{\rm max}$ for any photons produced in the process.
|
|
A comma-separated pair may be used to indicate a range of allowed values for $|\eta|$.
|
|
|
|
\item {\tt ptmin\_photon(2nd)} and {\tt ptmin\_photon(3rd)}. These specify the values
|
|
of $p_T^{\rm min}$ for the second and third photons, ordered by $p_T$.
|
|
|
|
\item {\tt R(photon,lept)\_min}. Using the usual definition of $\Delta R$,
|
|
this requires that all photon-lepton pairs are separated by
|
|
$\Delta R >$~{\tt R(photon,lept)\_min}. This parameter must be non-zero
|
|
for processes in which photon radiation from leptons is included.
|
|
|
|
\item {\tt R(photon,photon)\_min}. Using the usual definition of $\Delta R$,
|
|
this requires that all photon pairs are separated by
|
|
$\Delta R >$~{\tt R(photon,photon)\_min}.
|
|
|
|
\item {\tt R(photon,jet)\_min}. Using the usual definition of $\Delta R$,
|
|
this requires that all photon-jet pairs are separated by
|
|
$\Delta R >$~{\tt R(photon,jet)\_min}.
|
|
|
|
\item {\tt cone\_ang}. A double precision variable that fixes the cone size ($R_0$) for photon isolation.
|
|
This cone is used in both forms of isolation.
|
|
|
|
\item {\tt epsilon\_h}. This cut controls the amount of radiation allowed in cone when {\tt frag} is set to {\tt .true.}. If {\tt epsilon\_h} $ < 1$ then the photon is isolated using
|
|
$\sum_{\in R_0} E_T{\rm{(had)}} < \epsilon_h \, p^{\gamma}_{T}.$ Otherwise {\tt epsilon\_h} $ > 1$ sets $E_T(max)$ in $\sum_{\in R_0} E_T{\rm{(had)}} < E_T(max)$.
|
|
If the user wishes to always use a scaling or fixed isolation cut, independent of the value of {\tt epsilon\_h}, the routine
|
|
{\tt src/User/iso.f} may be edited and the value of the variable {\tt imode} changed according to the comments.
|
|
When {\tt frag} is set to {\tt .false.}, $\epsilon_h$ controls the amount of hadronic energy allowed inside the cone using the
|
|
Frixione isolation prescription (see above, Eq.~(\ref{frixeq})).
|
|
|
|
\item {\tt n\_pow}. When using the Frixione isolation prescription, the exponent $n$ in Eq.~(\ref{frixeq}).
|
|
|
|
%These constitute a photon isolation
|
|
%cut which ensures that the amount of hadronic
|
|
%transverse momentum in a cone around each photon is less than
|
|
%a specified fraction of the photon's $p_T$.
|
|
%\begin{displaymath}
|
|
%\sum_{R < R_0} p_T^{\rm hadronic} < f \times p_T^{photon},
|
|
%\end{displaymath}
|
|
%where $R_0$ and $f$ are specified by {\tt cone\_photon} and
|
|
%{\tt cone\_ptcut} respectively.
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Anomalous couplings of the W and Z] }
|
|
\end{center}
|
|
\item {\tt enable}. Boolean flag to enable anomalous coupling contributions. False has the same effect as
|
|
setting all anomalous couplings to zero, but additionally skips computation of anomalous coupling code parts.
|
|
\item {\tt Delta\_g1(Z)}. {\it See section~\ref{subsec:diboson}.}
|
|
\item {\tt Delta\_K(Z)}. {\it See section~\ref{subsec:diboson}.}
|
|
\item {\tt Delta\_K(gamma)}. {\it See sections~\ref{subsec:diboson} and~\ref{subsec:wgamma}.}
|
|
\item {\tt Lambda(Z)}. {\it See section~\ref{subsec:diboson}.}
|
|
\item {\tt Lambda(gamma)}. {\it See sections~\ref{subsec:diboson} and~\ref{subsec:wgamma}.}
|
|
\item {\tt h1(Z)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt h1(gamma)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt h2(Z)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt h2(gamma)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt h3(Z)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt h3(gamma)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt h4(Z)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt h4(gamma)}. {\it See section~\ref{subsec:zgamma}.}
|
|
\item {\tt Form-factor scale, in TeV}. {\it See section~\ref{subsec:diboson}.} \\
|
|
No form-factors are applied to the anomalous couplings if this value is negative.
|
|
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Anomalous width of the Higgs] }
|
|
\end{center}
|
|
|
|
\item {\tt Gamma\_H/Gamma\_H(SM)}. For processes {\tt 123}--{\tt 126}, {\tt 128}--{\tt 133} only,
|
|
this variable provides a rescaling of the width of the Higgs boson. Couplings are rescaled such that the
|
|
corresponding cross section close to the Higgs boson peak is unchanged. Further details of this procedure are given in
|
|
{\tt arXiv:1311.3589}.
|
|
|
|
\end{itemize}
|
|
|
|
The final section of the input file contains settings for various technical parameters that should not
|
|
normally need to be changed.
|
|
\begin{center}
|
|
\{blank line\} \\
|
|
{\tt [Technical parameters that should not normally be changed]}
|
|
\end{center}
|
|
\begin{itemize}
|
|
\item {\tt debug}.
|
|
A logical variable which can be used during a
|
|
debugging phase to mandate special behaviours.
|
|
Passed by common block \\
|
|
{\tt common/debug/debug}.
|
|
\item {\tt verbose}.
|
|
A logical variable which can be used during a debugging phase to write
|
|
special information. Passed in common block \\
|
|
{\tt common/verbose/verbose}.
|
|
\item {\tt new\_pspace}.
|
|
A logical variable which can be used during a debugging phase to test alternative versions of the phase space.
|
|
Passed in common block {\tt common/new\_pspace/new\_pspace}.
|
|
\item {\tt spira}.
|
|
A logical variable. If {\tt spira} is true, we calculate the
|
|
width of the Higgs boson by interpolating from a table
|
|
calculated using the NLO code of M. Spira.
|
|
Otherwise the LO value valid for low Higgs masses only is used.
|
|
\item {\tt noglue}.
|
|
A logical variable.
|
|
The default value is false. If set to true, no processes
|
|
involving initial gluons are included.
|
|
\item {\tt ggonly}.
|
|
A logical variable.
|
|
The default value is false. If set to true,
|
|
only the processes
|
|
involving initial gluons in both hadrons are included.
|
|
\item {\tt gqonly}.
|
|
The default value is false. If set to true,
|
|
only the processes
|
|
involving an initial gluon in one hadron and an initial quark
|
|
or antiquark in the other hadron (or vice versa) are included.
|
|
\item {\tt omitgg}.
|
|
A logical variable.
|
|
The default value is false. If set to true, the gluon-gluon
|
|
initial state is not included.
|
|
\item {\tt clustering}
|
|
This logical parameter determines whether clustering is performed to yield
|
|
jets. Only during a debugging phase should this variable be set to false.
|
|
\item {\tt realwt}.
|
|
This is a logical parameter that in general should be set to false.
|
|
If set to true, mcfm samples the integral according to the
|
|
unsubtracted real emission weight.
|
|
\item {\tt colourchoice}.
|
|
If colourchoice=0, all colour structure are included ($W,Z+2$~jets).
|
|
If colourchoice=1, only the leading
|
|
colour structure is included ($W,Z+2$~jets).
|
|
\item {\tt rtsmin}.
|
|
A minimum value of $\sqrt{s_{12}}$, which ensures that the invariant mass
|
|
of the incoming partons can never be less than {\tt rtsmin}.
|
|
\item {\tt cutoff}.
|
|
A minimum value of $s_{ij}$, which ensures that the invariant mass squared
|
|
of any pair of partons can never be less than {\tt cutoff}.
|
|
\item {\tt aii}.
|
|
A double precision variable which can be used to
|
|
limit the kinematic range for the subtraction of initial-initial dipoles
|
|
as suggested by Trocsanyi and Nagy~\cite{Nagy:2003tz}.
|
|
The value {\tt aii=1d0} corresponds
|
|
to standard Catani-Seymour subtraction.
|
|
\item {\tt aif}.
|
|
A double precision variable which can be used to
|
|
limit the kinematic range for the subtraction of initial-final dipoles
|
|
as suggested by Trocsanyi and Nagy~\cite{Nagy:2003tz}.
|
|
The value {\tt afi=1d0} corresponds
|
|
to standard Catani-Seymour subtraction.
|
|
\item {\tt afi}.
|
|
A double precision variable which can be used to
|
|
limit the kinematic range for the subtraction of final-initial dipoles
|
|
as suggested by Trocsanyi and Nagy~\cite{Nagy:2003tz}.
|
|
The value {\tt afi=1d0} corresponds
|
|
to standard Catani-Seymour subtraction.
|
|
\item {\tt aff}.
|
|
A double precision variable which can be used to
|
|
limit the kinematic range for the subtraction of final-final dipoles
|
|
as suggested by Trocsanyi and Nagy~\cite{Nagy:2003tz}.
|
|
The value {\tt aff=1d0} corresponds
|
|
to standard Catani-Seymour subtraction.
|
|
\item {\tt bfi}.
|
|
A double precision variable which can be used to
|
|
limit the kinematic range for the subtraction of final-initial dipoles
|
|
in the photon fragmentation case.
|
|
\item {\tt bff}.
|
|
A double precision variable which can be used to
|
|
limit the kinematic range for the subtraction of final-final dipoles
|
|
in the photon fragmentation case.
|
|
\item {\tt mtex}.
|
|
Sets the order $k=0,2,4$ of the $1/m_t^k$ expansion for virtual corrections in the $H+$jet process 200. See
|
|
section \ref{subsec:hjetma}.
|
|
\end{itemize}
|
|
|
|
\section{Nuclear collisions}
|
|
\label{sec:nucleus}
|
|
|
|
It is possible to specify nuclear collisions by choosing values
|
|
of {\tt ih1} and/or {\tt ih2} above {\tt 1000d0}. In that case,
|
|
the identity of the nucleus is specified by the atomic number
|
|
and mass ($Z$ and $A$ respectively) as follows:
|
|
\begin{equation}
|
|
{\tt ih} = 1000Z+A.
|
|
\end{equation}
|
|
For example, to choose an incoming lead beam one would set
|
|
{\tt ih1=+82207d0}, corresponding to $Z=82$ and $A=207$.
|
|
When running the program, the value of {\tt sqrts} should also be
|
|
changed. This must be done by hand and is not automatically taken
|
|
care of by the
|
|
program. The centre-of-mass energy is decreased by a factor of
|
|
$\sqrt{Z/A}$ for each nuclear beam.
|
|
|
|
The nucleon PDF's are calculated by applying the correction
|
|
factors of EKS98~\cite{Eskola:1998df} on top of the PDF set that is selected.
|
|
This construction simply corrects each parton distribution by
|
|
a factor that depends on the value of $(x,\mu)$ in the event.
|
|
This parametrization is limited to the region $\mu < 100$~GeV and
|
|
any value above that threshold will instead default to $100$~GeV.
|
|
|
|
Note that the cross-section reported by the program at the end
|
|
of the run is given per nucleon per beam. Therefore the
|
|
appropriate factors of $A$ should be applied in order to obtain
|
|
the total cross section.
|
|
|
|
\section{Output}
|
|
\label{sec:output}
|
|
|
|
In addition to the direct output of the program to {\tt stdout}, after
|
|
the final sweep of {\tt VEGAS} the program can output additional files
|
|
as specified below.
|
|
If a working directory was specified in the command line, then these
|
|
output files will be written to that directory.
|
|
|
|
The standard output will detail the iteration-by-iteration best estimate
|
|
of the total cross-section, together with the accompanying error estimate.
|
|
After all sweeps have been completed, a final summary line will be printed.
|
|
In the {\tt npart}~$=$~{\tt tota} case, this last line will actually be the
|
|
sum of the two separate real and virtual integrations.
|
|
If the {\tt LHAPDF} package is being used and the value of
|
|
{\tt LHAPDF set} is equal to {\tt -1}, to indicate a calculation using
|
|
PDF uncertainties, then the computed PDF uncertainty is
|
|
supplied in the regular output and also echoed to the file,
|
|
{\tt pdfuncertainty.res}. The appropriate method for computing the PDF
|
|
uncertainties is chosen according to the PDF set that is being used.
|
|
For NNPDF sets the uncertainty is computed according to the so-called
|
|
MC prescription, described in detail in Appendix B of
|
|
Ref.~\cite{Ball:2008by}~\footnote{
|
|
The authors thank M. Ubiali and collaborators for providing their
|
|
implementation of the MC method within the \MCFM framework.}.
|
|
For the sets of Alekhin et al. the uncertainty is computed using the
|
|
symmetric Hessian method. For all other sets -- those from CTEQ and
|
|
MSTW -- the asymmetric Hessian uncertainties are computed using
|
|
the formula given explicitly in
|
|
Eqn. (43) of Ref.~\cite{Campbell:2006wx}.
|
|
|
|
Other output files may be produced containing various histograms associated
|
|
with the calculated process. The write-out of the different output files
|
|
is controlled by logical variables at the top of the input file. The various options are:
|
|
\begin{itemize}
|
|
\item {\tt writetop}: write out the histograms as a {\tt TOPDRAWER} file,
|
|
{\tt outputname.top}.
|
|
\item {\tt writedat}: write out the histograms in a raw format
|
|
which may be read in by a plotting package of the user's choosing,
|
|
{\tt outputname.dat}.
|
|
\item {\tt writegnu}: write out the histograms as a {\tt gnuplot} file\footnote{
|
|
For information on obtaining and using {\tt gnuplot}, visit http://www.gnuplot.info/.},
|
|
{\tt outputname.gnu}. This can be processed by running the command
|
|
`{\tt gnuplot outputname.gnu}', producing a postscript version of the histograms
|
|
in {\tt outputname.ps}.
|
|
\item {\tt writeroot}: write out a script, {\tt outputname.C}, that
|
|
can be executed by ROOT. Opening ROOT and running `{\tt .x outputname.C}'
|
|
produces histograms in the file
|
|
{\tt outputname.root}. The histograms can be subsequently inspected or manipulated
|
|
as usual, e.g. by opening the graphical browser using `{\tt TBrowser b;}'.
|
|
\end{itemize}
|
|
|
|
All of the output files include a summary of the options file ({\tt input.DAT}) in the form of
|
|
comments at the beginning. The structure
|
|
of {\tt outputname} is as follows:
|
|
\begin{displaymath}
|
|
{\tt procname\_part\_pdlabel\_scale\_facscale\_runstring}
|
|
\end{displaymath}
|
|
where {\tt procname} is a label assigned by the program corresponding to
|
|
the calculated process; the remaining labels are as input by the user
|
|
in the file {\tt input.DAT}.
|
|
|
|
The histograms are filled via the file {\tt src/User/nplotter.f}.
|
|
For the convenience of the user a dummy routine {\tt src/User/userplotter.f}
|
|
has been provided. The user may substitute their own routine to do the plotting,
|
|
by writing and compiling a routine of this name. See section \ref{user}.
|
|
|
|
For some processes
|
|
a specific routine has been written to plot relevant kinematic quantities. In that case
|
|
a further routine is called, e.g. {\tt nplotter\_W\_only.f} for inclusive $W$ production.
|
|
In all other cases the filling of the histograms is performed by a routine in
|
|
{\tt src/User/nplotter\_auto.f}. The arguments of the process-specific plotting subroutines
|
|
are { \tt p,wt,wt2,switch}. {\tt p} contains the momenta of all the particles
|
|
(i.e. the four momenta of the leptons and jets). The order of the jets is not
|
|
necessarily the order specified in process.DAT. However in the case that we have a
|
|
$b$-quark or antiquark they are labelled by {\tt bq} and {\tt ba} respectively
|
|
in the array jetlabel. {\tt wt} ({\tt wt2}) is the weight of the event (squared).
|
|
|
|
\subsection{Histograms}
|
|
\label{sec:histos}
|
|
|
|
Extra histograms may be added to the plotting files in
|
|
a fairly straightforward manner. Each histogram is filled by making
|
|
a call to the routine {\tt bookplot} and updating the histogram
|
|
counter {\tt n} by 1. For example, the pseudorapidity of particle $3$
|
|
may be plotted using the following code fragment:
|
|
|
|
\begin{verbatim}
|
|
eta3=etarap(3,p)
|
|
call bookplot(n,tag,'eta3',eta3,wt,wt2,-4d0,4d0,0.1d0,'lin')
|
|
n=n+1
|
|
\end{verbatim}
|
|
The first two arguments of the call should not be changed. The third
|
|
argument is a string which is used as the title of the plot in the
|
|
output files. The fourth argument carries the variable to
|
|
be plotted, which has been previously calculated. The arguments {\tt
|
|
wt} and {\tt wt2} contain information about the phase-space weight and
|
|
should not be changed. The
|
|
last arguments tell the histogramming routine to use bins of size {\tt
|
|
0.1} which run from {\tt -4} to {\tt 4}, and use a linear scale for
|
|
the plot. A logarithmic scale may be used by changing the final
|
|
argument to {\tt 'log'}.
|
|
|
|
If the {\tt LHAPDF} package is being used and the value of
|
|
{\tt LHAPDF set} is equal to {\tt -1}, to indicate a calculation using
|
|
PDF uncertainties, then errors on distributions may also be accumulated.
|
|
Note that, due to limitations within the LHAPDF distribution, calculations
|
|
using error PDF sets are impractical unless the grid versions of the sets
|
|
are used. The grid versions are available in LHAPDF v.3 onwards and may be identified
|
|
by the {\tt .LHgrid} extension in the {\tt PDFsets} directory. To use the
|
|
grid version, simply pass the PDF set name, including this extension, as
|
|
the value of {\tt LHAPDF group} in the input file.
|
|
|
|
To accumulate errors in distributions, add an extra
|
|
line to {\tt nplotter.f} after the
|
|
call to {\tt bookplot} but before the counter is incremented. For
|
|
example, to calculate the PDF uncertainties on the distribution
|
|
of {\tt eta3} one would simply add:
|
|
\begin{verbatim}
|
|
call ebookplot(n,tag,eta3,wt)
|
|
\end{verbatim}
|
|
The third argument contains the variable to plot and the other entries
|
|
should not be changed. The other parameters for the plot are exactly
|
|
those specified on the previous line, in the call to {\tt bookplot}.
|
|
Since each PDF error distribution takes up quite a lot of memory
|
|
during execution, there is a limit of 4 on the number of distributions
|
|
with errors that can be calculated at one time. When calculating
|
|
PDF uncertainties on distributions, the program will produce an
|
|
additional file which contains the results for each PDF error set
|
|
individually. In addition, the main file will include the uncertainty
|
|
limits on the distribution, obtained using the appropriate PDF uncertainty
|
|
prescription as described above, on a bin-by-bin basis. Thus
|
|
the resulting error limits are not simply described by a single PDF
|
|
set.
|
|
|
|
\subsection{Other output modes}
|
|
\label{subsec:otheroutput}
|
|
As noted in the description of the input file, there are a number of other
|
|
output modes which may be useful in certain situations. In particular, the
|
|
ability to output n-tuples can be used to generate a large event record that
|
|
can be subsequently analyzed according to the user's needs. Much of the code
|
|
for generating these outputs can be found in {\tt src/User/dswhbook.f}; some
|
|
additional work may be required, depending on the process under study.
|
|
|
|
The simplest alternative output mode is obtained by changing the flag
|
|
{\tt dswhisto} to {\tt .true.} . In this way, the {\tt TOPDRAWER} output file is
|
|
replaced by the file {\tt outputname.rz} which contains the histograms in {\tt HBOOK}
|
|
format.
|
|
|
|
\subsubsection{Simple n-tuple output}
|
|
To obtain the simplest n-tuple output, the flag {\tt creatent} should be set
|
|
to {\tt .true.} and the parameter {\tt NTUPLES} in the {\tt makefile} should be changed
|
|
to either {\tt YES} or {\tt FROOT}. When changed to {\tt YES}, each event that enters a histogram
|
|
is also recorded as an n-tuple in the file {\tt outputname\_batchno.rz}. The {\tt batchno}
|
|
starts at zero and is incremented by one every one million events. Each event
|
|
is a simple row-wise n-tuple consisting of the 4-momenta of each of the final
|
|
state particles ($p_x$, $p_y$, $p_z$ and $E$, in that order) followed by 5 numbers
|
|
representing the event weight. The first number represents the total event weight
|
|
and the others, the contribution from gluon-gluon, quark-gluon (and antiquark-gluon),
|
|
quark-quark (and antiquark-antiquark) and quark-antiquark initial states. If
|
|
PDF uncertainties are being calculated (using {\tt LHAPDF}) then the total event weight
|
|
corresponding to each of the additional PDF sets is also written out at this stage.
|
|
Single precision is used, for economy. A simple way to analyze
|
|
these n-tuples is to use the {\tt h2root} command and then perform
|
|
manipulations with the ROOT package. Note that these n-tuples contain
|
|
no information about either the flavour or the colour of the initial or final
|
|
state particles. Summation and averaging over these variables has already been
|
|
performed. Furthermore, the `events' are {\it weighted} - so they are not events
|
|
in the traditional event generator sense.
|
|
|
|
\subsubsection{n-tuples using FROOT}
|
|
Output is similar when using the {\tt FROOT} option. In this case, the program will directly
|
|
fill a ROOT n-tuple using the FROOT interface of P. Nadolsky ({\tt nadolsky@pa.msu.edu}, a version
|
|
of which is included with \MCFM (in the directory {\tt src/User/froot.c}). The structure
|
|
of the ntuples is slightly different to that above, with entries:
|
|
\begin{itemize}
|
|
\item {\tt E\_i}, {\tt pxi}, {\tt pyi}, {\tt pzi} to specify the particle momenta, with {\tt i}
|
|
looping over all members of the final state.
|
|
\item {\tt wt\_ALL}, {\tt wt\_gg}, {\tt wt\_gq}, {\tt wt\_qq}, {\tt wt\_qqb} for the total event
|
|
weight and the weights in each of the parton-parton subchannels.
|
|
\item {\tt PDFjj}, where {\tt jj} loops over all the PDF uncertainty sets (only written if
|
|
appropriate).
|
|
\end{itemize}
|
|
|
|
\subsubsection{Unweighted events}
|
|
|
|
In order to obtain {\it unweighted} events, one must change the value of
|
|
{\tt nevtrequested} to an integer greater than zero, corresponding to the
|
|
number of unweighted events that is required. This option is only available at lowest order
|
|
at present and only for a limited number of processes.
|
|
In this mode the program will first perform a run to obtain the
|
|
maximum weight and then perform a simple unweighting procedure against this
|
|
number. As a result this procedure is rather inefficient.
|
|
Identities are assigned to the
|
|
partons in the initial state according to the relative parton-parton
|
|
luminosities. If the warm-up stage of the calculation is not sufficiently long, it
|
|
is possible to find events with a weight greater than the maximum in the unweighting
|
|
phase. In this case a warning message is written to the screen and the events are
|
|
not truly unweighted without further processing by the user.
|
|
|
|
The events are written to a file with the extension {\tt .lhe} using the LHE format.
|
|
The routines that handle most of the processing can be found in {\tt src/Need/mcfm\_writelhe.f}.
|
|
At present this feature is still under development.
|
|
|
|
\section{Electroweak corrections}
|
|
\label{subsec:EW}
|
|
|
|
As of version 8.1, {\tt MCFM} allows the calculation of weak corrections to a
|
|
selection of processes: {\tt 31} (neutral-current DY),
|
|
{\tt 157} (top-pair production) and {\tt 190} (di-jet production).
|
|
This is controlled by the flag {\tt ewcorr} in the input file. A complete description
|
|
of the calculations is provided in Ref.~\cite{Campbell:2016dks}.
|
|
|
|
By setting {\tt ewcorr} to {\tt sudakov}, the program performs a calculation of
|
|
the leading weak corrections to these processes using a Sudakov approximation that
|
|
is appropriate at high energies. The calculation of the weak corrections using the
|
|
exact form of the one-loop amplitudes is obtained by using the flag {\tt exact}.
|
|
A comparison between the two approaches, together with discussions of the validity of
|
|
the Sudakov approximation, may be found in Ref.~\cite{Campbell:2016dks}.
|
|
|
|
For the case of top-pair and di-jet production, the weak one-loop corrections contain
|
|
infrared divergences that must be cancelled against corresponding real radiation
|
|
contributions (in much the same manner as a regular NLO QCD calculation). For this
|
|
reason the screen output will contain two sets of iterations corresponding to the
|
|
virtual and real contributions.
|
|
|
|
For all processes, performing the calculation of weak
|
|
corrections enables a special mode of phase-space integration that is designed to
|
|
better-sample events produced at high-energies. For this reason the VEGAS output that
|
|
appears on the screen does not correspond to a physical cross-section -- and a corresponding
|
|
warning message to this effect will be displayed. In many cases the quantity of most interest
|
|
is the relative correction to the leading order result ($\delta_{\rm wk}$) given by,
|
|
\begin{equation}
|
|
\delta_{\rm wk} = \frac{d\sigma_{\rm wk}^{NLO} - d\sigma^{LO}}{d\sigma^{LO}} \;.
|
|
\end{equation}
|
|
It is straightforward to compute this quantity for a distribution by editing the appropriate
|
|
{\tt nplotter} routine. This is achieved by filling a histogram with the weight corresponding
|
|
to the LO result, another with the weight for the NLO weak result and then an additional placeholder
|
|
histogram that contains the special string {\tt '+RELEW+'}. Examples of the syntax and correct calling
|
|
sequence can be seen in the code.
|
|
|
|
\section{Other user options}
|
|
\label{user}
|
|
There are a number of other user options which are included in the file
|
|
{\tt src/User/usercode\_f77.f}
|
|
\begin{itemize}
|
|
\item {\tt logical function userincludedipole(nd, ppart, mcfm\_result)}
|
|
|
|
Variables passed are
|
|
\begin{itemize}
|
|
\item nd: index of the dipole
|
|
\item ppart: momenta of incoming and outgoing particles
|
|
\item mcfm\_result: the decision that was taken by mcfm about whether to keep this event
|
|
\end{itemize}
|
|
|
|
The program works in such a way that the cuts are applied after the
|
|
phase space point has been generated but before the matrix element has
|
|
been calculated. This true for the real, virtual lord and real pieces
|
|
including the contributions from the subtraction dipoles. This
|
|
operation is performed by the \MCFM logical function {\tt mcfmincludedipole}.
|
|
However the (currently dummy) logical function {\tt userincludedipole}
|
|
is also always called. This allows the user to
|
|
veto events that might otherwise pass the \MCFM cuts. It can be used,
|
|
e.g. to force \MCFM to generate only events that are above some large
|
|
HT threshold, which comes in useful when trying to get precision on
|
|
the tails of some distributions.
|
|
|
|
\item {\tt subroutine userplotter(pjet, wt,wt2, nd)}
|
|
This subroutine is called to allow the user to bin their own
|
|
histograms.
|
|
|
|
Variables passed to this routine:
|
|
|
|
\begin{itemize}
|
|
\item p: 4-momenta of incoming partons(i=1,2), outgoing leptons and
|
|
jets in the format p(i,4) with the particles numbered
|
|
according to the input file and components labelled by
|
|
(px,py,pz,E).
|
|
|
|
\item wt: weight of this event
|
|
|
|
\item wt2: weight$^2$ of this event
|
|
|
|
\item nd: an integer specifying the dipole number of this contribution
|
|
(if applicable), otherwise equal to zero.
|
|
\end{itemize}
|
|
|
|
\item {\tt subroutine userwriteinfo(unitno,comment\_string,xsec,xsec\_err,itno)}
|
|
This (currently dummy) subroutine gets called after \MCFM has written its comments to
|
|
one of the output files. It allows the user to write their own comments
|
|
to that same file.
|
|
|
|
Variables passed to this routine:
|
|
|
|
\begin{itemize}
|
|
\item unitno: the unit number to which output is being sent
|
|
\item comment\_string: a comment character that precedes each line of output
|
|
\item xsec, xsec: the cross section and its error (in case you care!)
|
|
\item itno: the iteration number (0 at the end of the last iteration)
|
|
\end{itemize}
|
|
\end{itemize}
|
|
|
|
A similar set of routines written in fortran90 by Gavin Salam are in the file {\tt usercode.f90}.
|
|
Various C routines that may be of use are included in {\tt cxxusercode.cc}.
|
|
|
|
\section{Notes on specific processes}
|
|
|
|
\label{sec:specific}
|
|
|
|
The processes described in the file {\tt process.DAT} include appropriate boson decays when the parameter
|
|
{\tt removebr} is set to {\tt .false.}. In many cases a more simple calculation can be performed by setting
|
|
this parameter to {\tt .true.}, in which case these decays are not performed.
|
|
Technically the full calculation including the decays
|
|
is still performed but cuts are not performed on the decay products and the
|
|
branching ratio is divided out, thus yielding the cross section before decay.
|
|
In the notes below we indicate the simpler processes thus obtained. When running in
|
|
this mode, the parameter {\tt zerowidth} should be set to {\tt .true.} for consistency. However in certain
|
|
circumstances, for the sake of comparison, it may be useful to run with it set to {\tt .false.}.
|
|
|
|
\subsection{$W$-boson production, processes 1,6}
|
|
\label{subsec:wboson}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically. The calculation may be performed at NLO.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+$~jet production, processes 11,16}
|
|
\label{subsec:w1jet}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically, in association with a single jet.
|
|
The calculation may be performed at NLO.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+b$ production, processes 12,17}
|
|
\label{subsec:wb}
|
|
|
|
These processes represent the production of a $W$ boson which
|
|
subsequently decays leptonically, in association with a single bottom
|
|
quark, exploiting the weak transitions $c \to b$ and $u \to b$.
|
|
This is produced at leading order by an initial state which
|
|
contains a charm quark (or the CKM suppressed $u$ quark) and a
|
|
gluon. The effect of the bottom quark mass is included throughout the
|
|
calculation.
|
|
For this case the CKM matrix elements $V_{cb}$ and $V_{ub}$,
|
|
(if they are equal to zero in the input data file, {\tt mdata.f})
|
|
are set equal to $0.041$ and $0.00347$ respectively.
|
|
Otherwise the non-zero values specified in {\tt mdata.f} are used.
|
|
The calculation of this process may
|
|
be performed at NLO.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+c$ production, processes 13,18}
|
|
\label{subsec:wc}
|
|
|
|
These processes represent the production of a $W$ boson which
|
|
subsequently decays leptonically, in association with a charm
|
|
quark. This is produced at leading order by an initial state which
|
|
contains a strange quark (or Cabibbo suppressed $d$ quark) and a
|
|
gluon. The effect of the charm quark mass is included throughout the
|
|
calculation. As of version 5.2, the calculation of this process may
|
|
be performed at NLO.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+c$ production ($m_c=0$), processes 14,19}
|
|
\label{subsec:wcmassless}
|
|
|
|
These processes are identical to {\tt 13} and {\tt 18} except for the fact
|
|
that the charm quark mass is neglected. The calculation can currently be
|
|
performed at LO only.
|
|
|
|
\subsection{$W+b{\bar b}$ production, processes 20,25}
|
|
\label{subsec:wbb}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically, in association with a $b{\bar b}$ pair. The effect of
|
|
the bottom quark mass is included throughout the calculation.
|
|
Beginning with \MCFM version 6.0 this calculation may be performed at NLO, thanks to
|
|
the incorporation of the virtual corrections from ref.~\cite{Badger:2010mg}.
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
To select final states in which one of the $b$-quarks may be unobserved the
|
|
user can employ processes 401--408 instead (see section~\ref{subsec:wbbfilter}).
|
|
These processes use the same matrix
|
|
elements but make specific requirements on the kinematics of the $b$-quarks
|
|
and QCD radiation.
|
|
|
|
\subsection{$W+b{\bar b}$ production ($m_b=0$), processes 21,26}
|
|
\label{subsec:wbbmassless}
|
|
|
|
These processes are identical to {\tt 20} and {\tt 25} except for the fact
|
|
that the bottom quark mass is neglected. This allows the calculation to be
|
|
performed up to NLO, with currently calculated virtual matrix elements. These
|
|
processes run considerably faster than the corresponding processes with the mass
|
|
for the $b$ quark, (20,25). In circumstances where both $b$ quarks are at large
|
|
transverse momentum, the inclusion of the mass for the $b$-quark is not mandatory
|
|
and a good estimate of the cross section may be obtained by using these processes.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+2$~jets production, processes 22,27}
|
|
\label{subsec:w2jets}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to \break
|
|
hep-ph/0202176 and hep-ph/0308195}]
|
|
\end{center}
|
|
This process represents the production of a $W$ boson and $2$ jets,
|
|
where the $W$ boson decays leptonically. The calculation may be
|
|
performed up to NLO, as detailed below. Virtual amplitudes are
|
|
taken from ref.~\cite{Bern:1997sc}.
|
|
|
|
For these processes (and also for $Z+2$~jet production, {\tt nproc=44,46})
|
|
the next-to-leading order matrix elements are
|
|
particularly complex and so they have been divided into two groups.
|
|
The division is according to the lowest order diagrams from which they
|
|
originate:
|
|
\begin{enumerate}
|
|
\item Diagrams involving two external quark lines and two external gluons,
|
|
the ``{\tt Gflag}'' contribution. The real diagrams in this case thus
|
|
involve three external gluons.
|
|
|
|
\item Diagrams where all four external lines are quarks,
|
|
the ``{\tt Qflag}'' contribution. The real diagrams in this case
|
|
involve only one gluon.
|
|
\end{enumerate}
|
|
|
|
By specifying {\tt Gflag} and {\tt Qflag} in {\tt input.DAT} one may
|
|
select one of these options at a time. The full result may be obtained
|
|
by straightforward addition of the two individual pieces, with no
|
|
meaning attached to either piece separately.
|
|
Both of these may be set to {\tt .true.} simultaneously, however this
|
|
may result in lengthy run-times for sufficient convergence of the integral.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+3$~jets production, processes 23,28}
|
|
\label{subsec:w3jets}
|
|
|
|
This process represents the production of a $W$ boson and $3$ jets,
|
|
where the $W$ boson decays leptonically. The calculation may be
|
|
performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+b{\bar b}+$~jet production ($m_b=0$), processes 24,29}
|
|
\label{subsec:wbbjetmassless}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically, in association with a $b{\bar b}$ pair and an
|
|
additional jet. The effect of the bottom quark mass is neglected throughout
|
|
and the calculation may be performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$Z$-boson production, processes 31--33}
|
|
\label{subsec:zboson}
|
|
|
|
These processes represent the production of a $Z$ boson which subsequently
|
|
decays either into electrons ({\tt nproc=31}), neutrinos ({\tt nproc=32})
|
|
or bottom quarks ({\tt nproc=33}). Where appropriate, the effect of a virtual
|
|
photon is also included. As noted above, in these latter cases {\tt m34min > 0}
|
|
is obligatory. The calculation may be performed at NLO,
|
|
although the NLO calculation of process {\tt 33} does not include radiation
|
|
from the bottom quarks (i.e.\ radiation occurs in the initial state only).
|
|
|
|
When {\tt removebr} is true in process {\tt 31}, the $Z$ boson does not decay.
|
|
|
|
\subsection{$Z$-boson production decaying to jets, processes 34--35}
|
|
Radiation from the final state quarks is not included in this process.
|
|
|
|
\subsection{$t \bar{t}$ production mediated by $Z/\gamma^*$-boson exchange, process 36}
|
|
|
|
These processes represent the production of a virtual $Z$ boson or photon
|
|
which subsequently decays into $t \bar{t}$.
|
|
The leptonic decays of the top quarks are included.
|
|
Switching {\tt zerowidth} from {\tt .true.} to {\tt .false.} only affects
|
|
the $W$ bosons from the top quark decay.
|
|
Note that {\tt m34min > 0} is obligatory due to the inclusion of the
|
|
virtual photon diagrams. The calculation may be only be performed at LO.
|
|
|
|
\subsection{Lepton pair production through photonic initial states, process 310}
|
|
\label{subsec:gg2lep}
|
|
|
|
This process represents the production of a lepton pair through an electroweak
|
|
process involving two photons in the initial state, $\gamma\gamma \to e^- e^+$.
|
|
|
|
|
|
\subsection{$Z+$~jet production, processes 41--43}
|
|
\label{subsec:zjet}
|
|
|
|
These processes represent the production of a $Z$ boson and a single jet,
|
|
where the $Z$ subsequently
|
|
decays either into electrons ({\tt nproc=41}), neutrinos ({\tt nproc=42})
|
|
or bottom quarks ({\tt nproc=43}). Where appropriate, the effect of a virtual
|
|
photon is also included. The calculation may be performed at NLO,
|
|
although the NLO calculation of process {\tt 43} does not include radiation
|
|
from the bottom quarks.
|
|
|
|
When {\tt removebr} is true in process {\tt 41}, the $Z$ boson does not decay.
|
|
|
|
\subsection{$Z+2$~jets production, processes 44, 46}
|
|
\label{subsec:z2jets}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to \break
|
|
hep-ph/0202176 and hep-ph/0308195}]
|
|
\end{center}
|
|
|
|
These processes represents the production of a $Z$ boson and $2$ jets,
|
|
including also the effect of a virtual photon ({\tt nproc=44} only). The $Z/\gamma^*$ decays
|
|
to an $e^+ e^-$ pair ({\tt nproc=44}) or into three species of neutrino ({\tt nproc=46}).
|
|
The calculation may be performed up to NLO --
|
|
please see the earlier Section~\ref{subsec:w2jets} for more details,
|
|
especially the discussion regarding {\tt Qflag} and {\tt Gflag}.
|
|
As of version 6.0, both of these may be set to {\tt .true.} simultaneously but this
|
|
may result in lengthy run-times for sufficient convergence of the integral.
|
|
Virtual amplitudes are taken from ref.~\cite{Bern:1997sc}.
|
|
|
|
When {\tt removebr} is true, the $Z$ boson does not decay.
|
|
|
|
|
|
\subsection{$Z+3$~jets production, processes 45, 47}
|
|
\label{subsec:z3jets}
|
|
|
|
These processes represent the production of a $Z$ boson and $3$ jets,
|
|
including also the effect of a virtual photon ({\tt nproc=45} only). The $Z/\gamma^*$ decays
|
|
to an $e^+ e^-$ pair ({\tt nproc=45}) or into three species of neutrino ({\tt nproc=47}).
|
|
The calculation may be performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $Z$ boson does not decay.
|
|
|
|
\subsection{$Z+b{\bar b}$ production, process 50}
|
|
\label{subsec:zbb}
|
|
|
|
These processes represent the production of a $Z$ boson (or virtual photon)
|
|
which subsequently decays leptonically, in association
|
|
with a $b{\bar b}$ pair. The effect of
|
|
the bottom quark mass is included throughout the calculation.
|
|
The calculation may be performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $Z$ boson does not decay.
|
|
|
|
\subsection{$Z+b{\bar b}$ production ($m_b=0$), processes 51--53}
|
|
\label{subsec:zbbmassless}
|
|
|
|
Process {\tt 51} is identical to {\tt 50} except for the fact
|
|
that the bottom quark mass is neglected. This allows the calculation to be
|
|
performed up to NLO. The other processes account for the decays into
|
|
neutrinos ({\tt nproc=52}) and bottom quarks ({\tt nproc=53}). Note that
|
|
the NLO calculation of process {\tt 53} does not currently
|
|
include radiation from the
|
|
bottom quarks produced in the decay.
|
|
|
|
When {\tt removebr} is true in process {\tt 51}, the $Z$ boson does not decay.
|
|
|
|
\subsection{$Z+b{\bar b}+$~jet production ($m_b=0$), process 54}
|
|
\label{subsec:zbbjetmassless}
|
|
|
|
This process represents the production of a $Z$ boson (and virtual photon)
|
|
which subsequently decays leptonically, in association
|
|
with a $b{\bar b}$ pair and an additional jet.
|
|
The effect of the bottom quark mass is neglected throughout
|
|
and the calculation may be performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $Z$ boson does not decay.
|
|
|
|
\subsection{$Z+c{\bar c}$ production ($m_c=0$), process 56}
|
|
\label{subsec:zccmassless}
|
|
|
|
Process {\tt 56} is the equivalent of {\tt 51}, with the bottom quarks
|
|
replaced by charm. Although the charm mass is neglected, the calculation
|
|
contains diagrams with two gluons in the initial state and a
|
|
$Z$ coupling to the heavy quark line -- hence the dependence upon the quark
|
|
flavour.
|
|
|
|
When {\tt removebr} is true in process {\tt 56}, the $Z$ boson does not decay.
|
|
|
|
\subsection{Di-boson production, processes 61--89}
|
|
\label{subsec:diboson}
|
|
|
|
\begin{center}
|
|
[{\it For more details on these calculations, please refer to hep-ph/9905386
|
|
and arXiv:1105.0020 [hep-ph]}]
|
|
\end{center}
|
|
|
|
These processes represent the production of a diboson pair $V_1 V_2$,
|
|
where $V_1$ and $V_2$ may be either a $W$ or $Z/\gamma^*$.
|
|
All the processes in this section may be calculated at NLO, with the exception
|
|
of {\tt nproc=66,69}. There are various
|
|
possibilities for the subsequent decay of the bosons, as specified in the
|
|
sections below. Amplitudes are taken from ref.~\cite{Dixon:1998py}.
|
|
Where appropriate, these processes include glue-glue initiated box diagrams
|
|
which first contribute at order $\alpha_s^2$ but are included here in the
|
|
NLO calculation. We also include singly resonant diagrams at NLO for all processes
|
|
in the case {\tt zerowidth = .false.}.
|
|
|
|
For processes {\tt 62}, {\tt 63}, {\tt 64}, {\tt 65}, {\tt 74}
|
|
and {\tt 75} the default behaviour is that the hadronic decay products
|
|
of the bosons are clustered into jets using the supplied jet
|
|
algorithm parameters, but no cut is applied on the number of jets.
|
|
This behaviour can be altered by changing the value of the
|
|
variable {\tt notag} in the file {\tt src/User/setnotag.f}.
|
|
|
|
\subsubsection{$WW$ production, processes 61-64, 69}
|
|
|
|
For $WW$ production, both $W$'s can decay leptonically ({\tt nproc=61}) or one
|
|
may decay hadronically ({\tt nproc=62} for $W^-$ and {\tt nproc=64} for $W^+$).
|
|
Corresponding to processes {\tt 62,64}, processes {\tt 63,65} implement radiation in
|
|
decay from the hadronically decaying W's.
|
|
Process {\tt 69} implements the matrix elements for the leptonic decay of
|
|
both $W$'s but where no polarization information is retained. It is included
|
|
for the sake of comparison with other calculations.
|
|
Processes {\tt 62} and {\tt 64} may be run at NLO with the option {\tt todk},
|
|
including radiation in the decay of the hadronically decaying $W$.
|
|
Processes {\tt 63} and {\tt 65} give the effect of radiation in the decay alone
|
|
by making the choices {\tt virt}, {\tt real} or {\tt tota}.
|
|
|
|
Note that, in processes
|
|
{\tt 62} and {\tt 64}, the NLO corrections include radiation from the
|
|
hadronic decays of the $W$.
|
|
|
|
The NLO calculations include contributions from the process $gg \to WW$
|
|
that proceeds through quark loops. The calculation of loops containing the third quark generation
|
|
includes the effect of the top quark mass (but $m_b=0$), while the first two
|
|
generations are considered massless. For numerical stability, a small cut on the
|
|
transverse momentum of the $W$ bosons is applied: $p_T(W)>0.05$~GeV for loops
|
|
containing massless (first or second generation) quarks, $p_T(W)>2$~GeV for $(t,b)$
|
|
loops. This typically removes less than $0.1$\% of the total cross section. The
|
|
values of these cutoffs can be changed by editing ${\tt src/WW/gg\_WW.f}$ and recompiling.
|
|
|
|
When {\tt removebr} is true in processes {\tt 61} and {\tt 69},
|
|
the $W$ bosons do not decay.
|
|
|
|
\subsubsection{$WW$+jet production, process 66}
|
|
|
|
This process is only implemented for the leptonic decay modes of both $W$
|
|
bosons and is currently limited to LO accuracy only. When {\tt removebr} is true,
|
|
the $W$ bosons do not decay.
|
|
|
|
\subsubsection{$WZ$ production, processes 71--80}
|
|
|
|
For $WZ$ production, the $W$ is chosen to decay leptonically. The $Z$ (or
|
|
virtual photon, when appropriate) may decay into electrons
|
|
({\tt nproc=71},{\tt 76}), neutrinos ({\tt nproc=72},{\tt 77}), a
|
|
pair of bottom quarks ({\tt nproc=73},{\tt 78}), three generations of down-type
|
|
quarks ({\tt nproc=74},{\tt 79}) or two generations of up-type quarks ({\tt nproc=75},{\tt 80}).
|
|
In process {\tt 78} the mass of the $b$-quark is neglected.
|
|
These processes will be observed
|
|
in the final state as $W$-boson + two or three jets.
|
|
In processes {\tt 72} and {\tt 77}, a sum is performed over all three species of neutrinos.
|
|
|
|
When {\tt removebr} is true in processes {\tt 71} and {\tt 76},
|
|
neither the $W$ or the $Z$ boson decays.
|
|
|
|
\subsubsection{$ZZ$ production, processes 81--84, 86--90}
|
|
|
|
For $ZZ$ production, there are two sets of processes corresponding to the
|
|
inclusion of a virtual photon when appropriate ({\tt nproc=81}--{\tt 84})
|
|
and the case where it is neglected ({\tt nproc=86}--{\tt 89}).
|
|
Thus {\tt nproc=86}--{\tt 89} are really for diagnostic purposes only.
|
|
|
|
The $Z$'s can either both decay leptonically ({\tt nproc=81},{\tt 86}),
|
|
one can decay leptonically while the other decays into neutrinos
|
|
({\tt nproc=82},{\tt 87}) or bottom quarks ({\tt nproc=83},{\tt 88}), or
|
|
one decays into neutrinos and the other into a bottom quark pair
|
|
({\tt nproc=84},{\tt 89}).
|
|
In process {\tt 83} the mass of the $b$-quark is neglected. Note that, in processes
|
|
{\tt 83}--{\tt 84} and {\tt 88}--{\tt 89}, the NLO corrections do not include
|
|
radiation from the bottom quarks that are produced by the $Z$ decay.
|
|
|
|
The NLO calculations include contributions from the process $gg \to ZZ$
|
|
that proceeds through quark loops. The calculation of loops containing the third quark generation
|
|
includes the effect of both the top and the bottom quark mass ($m_t,m_b \neq 0$), while the first two
|
|
generations are considered massless. For numerical stability, a small cut on the
|
|
transverse momentum of the $Z$ bosons is applied: $p_T(Z)>0.1$~GeV.
|
|
This typically removes less than $0.1$\% of the total cross section. The
|
|
values of these cutoffs can be changed by editing ${\tt src/ZZ/getggZZamps.f}$
|
|
and recompiling.
|
|
|
|
When {\tt removebr} is true in processes {\tt 81} and {\tt 86},
|
|
neither of the $Z$ bosons decays.
|
|
|
|
In process {\tt 90} the two $Z$ bosons decay to identical charged leptons,
|
|
and interference effects between the decay products of the two $Z$ bosons
|
|
are included. This process may be calculated at LO only.
|
|
|
|
\subsubsection{$ZZ$+jet production, process 85}
|
|
|
|
This process is only implemented for the case when one $Z$ boson decays to
|
|
electrons and the other to neutrinos (i.e. the companion of {\tt nproc=82}).
|
|
It may only be calculated at LO. When {\tt removebr} is true, the $Z$ bosons
|
|
do not decay.
|
|
|
|
\subsubsection{Anomalous couplings}
|
|
|
|
\label{sec:anomalous}
|
|
As of version 3.0, it is possible to specify anomalous trilinear
|
|
couplings for the $W^+W^-Z$ and $W^+W^-\gamma$ vertices that are
|
|
relevant for $WW$ and $WZ$ production. To run in this mode, one
|
|
must set {\tt zerowidth} equal to {\tt .true.}
|
|
and modify the appropriate lines for the couplings in {\tt input.DAT}
|
|
(see below). Note that, at present, the effect of anomalous couplings is not included
|
|
in the gluon-gluon initiated contributions to the $WW$ process.
|
|
|
|
The anomalous couplings appear in the Lagrangian,
|
|
${\cal L} = {\cal L}_{SM} + {\cal L}_{anom}$ as follows
|
|
(where ${\cal L}_{SM}$ represents the usual Standard Model Lagrangian and
|
|
${\cal L}_{anom}$ is taken from Ref.~\cite{Dixon:1999di}):
|
|
\begin{eqnarray}
|
|
{\cal L}_{anom} & = & i g_{WWZ} \Biggl[
|
|
\Delta g_1^Z \left( W^*_{\mu\nu}W^\mu Z^\nu - W_{\mu\nu}W^{*\mu} Z^\nu \right)
|
|
+\Delta\kappa^Z W^*_\mu W_\nu Z^{\mu\nu} \nonumber \\
|
|
& &+
|
|
\frac{\lambda^Z}{M_W^2} W^*_{\rho\mu} W^\mu_\nu Z^{\nu\rho} \Biggr]
|
|
+i g_{WW\gamma} \Biggl[
|
|
\Delta\kappa^\gamma W^*_\mu W_\nu \gamma^{\mu\nu}
|
|
+\frac{\lambda^\gamma}{M_W^2} W^*_{\rho\mu} W^\mu_\nu\gamma^{\nu\rho}
|
|
\Biggr], \nonumber
|
|
\end{eqnarray}
|
|
where $X_{\mu\nu} \equiv \partial_\mu X_{\nu} - \partial_\nu X_{\mu}$
|
|
and the overall coupling factors are $g_{WW\gamma}=-e$,
|
|
$g_{WWZ}=-e\cot\theta_w$.
|
|
This is the most general Lagrangian that conserves $C$ and $P$
|
|
separately and electromagnetic gauge invariance requires that there
|
|
is no equivalent of the $\Delta g_1^Z$ term for the photon coupling.
|
|
|
|
In order to avoid a violation of unitarity, these couplings are often
|
|
included only after suppression by dipole form factors,
|
|
\begin{displaymath}
|
|
\Delta g_1^Z \rightarrow \frac{\Delta g_1^Z}{(1+\hat{s}/\Lambda^2)^2}, \qquad
|
|
\Delta \kappa^{Z/\gamma} \rightarrow
|
|
\frac{\Delta \kappa_1^{Z/\gamma}}{(1+\hat{s}/\Lambda^2)^2}, \qquad
|
|
\lambda^{Z/\gamma} \rightarrow
|
|
\frac{\Delta \lambda^{Z/\gamma}}{(1+\hat{s}/\Lambda^2)^2},
|
|
\end{displaymath}
|
|
where $\hat{s}$ is the vector boson pair invariant mass and $\Lambda$
|
|
is an additional parameter giving the scale of new physics, which should
|
|
be in the TeV range.
|
|
These form factors should be produced by the new physics associated with the
|
|
anomalous couplings and this choice is somewhat arbitrary. The use of the form
|
|
factors can be disabled as described below.
|
|
|
|
The file {\tt input.DAT} contains the values of the $6$ parameters
|
|
which specify the anomalous couplings:
|
|
\begin{verbatim}
|
|
0.0d0 [Delta_g1(Z)]
|
|
0.0d0 [Delta_K(Z)]
|
|
0.0d0 [Delta_K(gamma)]
|
|
0.0d0 [Lambda(Z)]
|
|
0.0d0 [Lambda(gamma)]
|
|
2.0d0 [Form-factor scale, in TeV]
|
|
\end{verbatim}
|
|
with the lines representing $\Delta g_1^Z$, $\Delta \kappa^Z$,
|
|
$\Delta \kappa^\gamma$, $\lambda^Z$, $\lambda^\gamma$ and
|
|
$\Lambda$~[TeV] respectively. By setting the first 5 parameters to zero,
|
|
as above, one recovers the Standard Model result.
|
|
If the input file contains a negative value for the form-factor scale
|
|
then the suppression factors described above are not applied.
|
|
|
|
\subsection{$WH$ production, processes 91-94, 96-99}
|
|
\label{subsec:wh}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically, in association with a Standard Model Higgs boson that
|
|
decays into a bottom quark pair ({\tt nproc=91, 96}),
|
|
a pair of $W$ bosons ({\tt nproc=92, 97}),
|
|
a pair of $Z$ bosons ({\tt nproc=93, 98}), or a pair of photons ({\tt nproc=94, 99}).
|
|
Note that in the cases of Higgs decay to $W$,($Z$) pairs,
|
|
below the $W$,($Z$) pair threshold
|
|
one of the $W$,($Z$) bosons is virtual
|
|
and therefore one must set {\tt zerowidth=.false.}.
|
|
The calculation may be performed at NLO.
|
|
Note that the bottom quarks are considered massless and radiation from the
|
|
bottom quarks in the decay is not included.
|
|
|
|
When {\tt removebr} is true, neither the $W$ boson nor the Higgs decays.
|
|
|
|
\subsection{$ZH$ production, processes 101--109}
|
|
\label{subsec:zh}
|
|
|
|
These processes represent the production of a $Z$ boson (or virtual photon)
|
|
in association with a Standard Model Higgs boson that
|
|
decays into a bottom quark pair ({\tt nproc=101-103}),
|
|
or decays into a pair of photons ({\tt nproc=104-105})
|
|
or a pair of $W$ bosons ({\tt nproc=106-108}),
|
|
or a pair of $Z$ bosons ({\tt nproc=109}).
|
|
The $Z$ subsequently decays into
|
|
either an $e^+ e^-$ pair ({\tt nproc=101, 106, 109}), neutrinos ({\tt nproc=102, 107})
|
|
or a bottom quark pair ({\tt nproc=103, 108}).
|
|
The calculation may be performed at NLO, although radiation from the
|
|
bottom quarks in the decay of the Higgs (or the $Z$, for processes
|
|
{\tt 103, 108}) is not included.
|
|
|
|
When {\tt removebr} is true in processes {\tt 101, 106, 109}, neither the $Z$ boson
|
|
nor the Higgs decays.
|
|
|
|
\subsection{Higgs production, processes 111--121}
|
|
\label{subsec:h}
|
|
|
|
These processes represent the production of a Standard Model Higgs
|
|
boson that decays either into a bottom quark
|
|
pair ({\tt nproc=111}), a pair of tau's ({\tt nproc=112}),
|
|
a $W^+W^-$
|
|
pair that further decays leptonically ({\tt nproc=113})
|
|
a $W^+W^-$ pair where the $W^-$ decays hadronically ({\tt nproc=114,115})
|
|
or a $ZZ$ pair ({\tt nproc=116-118}) . In addition, the loop-level decays of the Higgs
|
|
into a pair of photons ({\tt nproc=119}) and the $Z\gamma$ decay are included
|
|
({\tt nproc=120,121}).
|
|
|
|
For the case of $W^+W^-$ process {\tt nproc=115} gives the contribution
|
|
of radiation from the hadronically decaying $W^-$.
|
|
Process {\tt 114} may be run at NLO with the option {\tt todk},
|
|
including radiation in the decay of the hadronically decaying $W^-$.~\footnote{
|
|
We have not included the case of a hadronically decaying $W^+$; it can
|
|
be obtained from processes {\tt nproc=114,115} by performing the
|
|
substitutions $\nu \to e^-$ and $e^+ \to \bar{\nu}$.}
|
|
For the case of a $ZZ$ decay,
|
|
the subsequent decays can either be into a pair of muons and a pair of electrons
|
|
({\tt nproc=116)}, a pair of muons and neutrinos ({\tt nproc=117}) or
|
|
a pair of muons and a pair of bottom quarks ({\tt nproc=118}).
|
|
|
|
At LO the relevant diagram
|
|
is the coupling of two gluons to the Higgs via a top quark loop.
|
|
This calculation is performed in the limit of infinite top quark mass, so that
|
|
the top quark loop is replaced by an effective operator. This corresponds
|
|
to the effective Lagrangian,
|
|
\begin{equation}
|
|
\mathcal{L} = \frac{1}{12\pi v} \, G^a_{\mu\nu} G^{\mu\nu}_a H \;,
|
|
\label{eq:HeffL}
|
|
\end{equation}
|
|
where $v$ is the Higgs vacuum expectation value and $G^a_{\mu\nu}$ the
|
|
gluon field strength tensor.
|
|
The calculation may be performed at NLO, although radiation from the
|
|
bottom quarks in the decay of processes {\tt 111} and {\tt 118} is not yet included.
|
|
|
|
At the end of the output the program will also display the cross section rescaled
|
|
by the constant factor,
|
|
\begin{equation}
|
|
\frac{\sigma_{\rm LO}(gg \to H, \mbox{finite}~m_t)}{\sigma_{\rm LO}(gg \to H, m_t \to \infty)} \;.
|
|
\label{eqn:hrescale}
|
|
\end{equation}
|
|
For the LO calculation this gives the exact result when retaining a finite value for $m_t$,
|
|
but this is only an approximation at NLO. The output histograms are not rescaled in this way.
|
|
|
|
When {\tt removebr} is true in processes {\tt 111,112,113,118},
|
|
the Higgs boson does not decay.
|
|
|
|
Process {\tt 119} implements the decay of the Higgs boson into two photons
|
|
via loops of top quarks and $W$-bosons.
|
|
The decay is implemented using the formula Eq.(11.12) from ref.~\cite{Ellis:1991qj}.
|
|
When {\tt removebr} is true in process {\tt 119} the Higgs boson does not decay.
|
|
|
|
Processes {\tt 120} and {\tt 121} implement the decay of the Higgs boson into an lepton-antilepton
|
|
pair and a photon. As usual the production of a charged lepton-antilepton pair is mediated by a
|
|
$Z/\gamma^*$ (process {\tt 120}) and the production of three types of neutrinos
|
|
$\sum \nu \bar{\nu}$ by a $Z$-boson (process {\tt 121}). These processes are implemented
|
|
using a generalization of the formula of \cite{Djouadi:1996yq}. (Generalization to take into
|
|
account off-shell $Z$-boson and adjustment of the sign of $C_2$ in their Eq.(4)).
|
|
|
|
|
|
\subsection{$H \to W^+W^-$ production, processes 123-126}
|
|
These processes represent the production of a Higgs boson that decays to $W^+ W^-$,
|
|
with subsequent decay into leptons. For process {\tt 123}, the exact form of the triangle
|
|
loop coupling a Higgs boson to two gluons is included, with both top and bottom quarks
|
|
circulating in the loop. This is to be contrasted with process {\tt 113} in which only the
|
|
top quark contribution is included in the effective coupling approach.
|
|
|
|
Process {\tt 124} includes only the effect of the interference of the
|
|
Higgs and $gg \to W^+W^-$ amplitudes, as described in ref.~\cite{Campbell:2011cu}.
|
|
The calculation is available at LO only. LO corresponds to $O(\alpha_s^2)$ in this case.
|
|
The calculation of loops containing the third quark generation
|
|
includes the effect of the top quark mass (but $m_b=0$), while the first two
|
|
generations are considered massless. For numerical stability, a small cut on the
|
|
transverse momentum of the $W$ bosons is applied: $p_T(W)>0.05$~GeV for loops
|
|
containing massless (first or second generation) quarks, $p_T(W)>2$~GeV for $(t,b)$
|
|
loops. This typically removes less than $0.1$\% of the cross section. The
|
|
values of these cutoffs can be changed by editing ${\tt src/HWW/gg\_WW\_int.f}$ and recompiling.
|
|
|
|
Process {\tt 125} includes all $gg$-intitiated diagrams that have a Higgs boson in the $s$-channel,
|
|
namely the square of the $s$-channel Higgs boson production and the interference with the diagrams
|
|
that do not contain a Higgs boson, (i.e. $gg \to W^+W^- \to \nu_e e^+ e^- \bar{\nu_e}$).
|
|
|
|
The result for the square of the box diagrams alone, i.e. the process
|
|
$gg \to W^+W^- \to \nu_e e^+ e^- \bar{\nu_e}$, may be obtained by running process
|
|
{\tt nproc=61} with {\tt part=virt} and {\tt ggonly=.true.}
|
|
|
|
Process {\tt 126} calculates the full result for this process from $gg$-intitiated diagrams.
|
|
This includes diagrams that have a Higgs boson in the $s$-channel, the continuum $W^+W^-$
|
|
diagrams described above and their interference.
|
|
|
|
|
|
\subsection{$H \to ZZ \to e^- e^+ \mu^- \mu^+$ production, processes 128-133}
|
|
These processes represent the production of a Higgs boson that decays to $Z Z$,
|
|
with subsequent decay into charged leptons. For process {\tt 128}, the exact form of the triangle
|
|
loop coupling a Higgs boson to two gluons is included, with both top and bottom quarks
|
|
circulating in the loop. This is to be contrasted with process {\tt 116} in which only the
|
|
top quark contribution is included in the effective coupling approach.
|
|
|
|
Process {\tt 129} includes only the effect of the interference of the
|
|
Higgs and $gg \to ZZ$ amplitudes.
|
|
The calculation is available at LO only. LO corresponds to $O(\alpha_s^2)$ in this case.
|
|
The calculation of loops containing the third quark generation
|
|
includes the effect of both the top quark mass and the bottom quark, while the first two
|
|
generations are considered massless. For numerical stability, a small cut on the
|
|
transverse momentum of the $Z$ bosons is applied: $p_T(Z)>0.05$~GeV.
|
|
This typically removes less than $0.1$\% of the cross section. The
|
|
values of these cutoffs can be changed by editing ${\tt src/ZZ/getggZZamps.f}$ and recompiling.
|
|
|
|
Process {\tt 130} includes all $gg$-intitiated diagrams that have a Higgs boson in the $s$-channel,
|
|
namely the square of the $s$-channel Higgs boson production and the interference with the diagrams
|
|
that do not contain a Higgs boson, (i.e. $gg \to Z/\gamma^*+Z/\gamma^* \to e^- e^+ \mu^- \mu^+$).
|
|
|
|
Process {\tt 131} calculates the full result for this process from $gg$-intitiated diagrams.
|
|
This includes diagrams that have a Higgs boson in the $s$-channel, the continuum $ Z/\gamma^*+Z/\gamma^*$
|
|
diagrams described above and their interference.
|
|
|
|
Process {\tt 132} gives the result for the square of the box diagrams alone, i.e. the process
|
|
$gg \to Z/\gamma^*+Z/\gamma^* \to e^- e^+ \mu^- \mu^+$.
|
|
|
|
Process {\tt 133} calculates the interference for the $qg$ initiated process.
|
|
|
|
For those processes that include contributions from the Higgs boson, the form
|
|
of the Higgs propagator may be changed by editing the file
|
|
{\tt src/Need/sethparams.f}. If the logical variable {\tt CPscheme} is
|
|
changed from the default value {\tt .false.} to {\tt .true.} then the
|
|
Higgs propagator is computed using the ``bar-scheme'' that is
|
|
implemented in the HTO code of G. Passarino~\cite{Goria:2011wa,Passarino:2010qk}.
|
|
The value of the Higgs boson width has been computed with v1.1 of the
|
|
HTO code, for Higgs masses in the interval $50 < m_H< 1500$~GeV. These
|
|
values are tabulated, in $0.5$~GeV increments, in the file
|
|
{\tt Bin/hto\_output.dat}. The widths for other masses in this range
|
|
are obtained by linear interpolation.
|
|
|
|
\subsubsection{Specifying other final states}
|
|
\label{specifyingZdecays}
|
|
As described above, these processes refer to a final state
|
|
$e^- e^+ \mu^- \mu^+$. It is however possible to specify a final state
|
|
that corresponds to a different set of $Z$ boson decays. This is achieved
|
|
by altering the value of {\tt NPROC} in the input file by appending a
|
|
period, followed by two 2-character strings that identify each of the decays.
|
|
Possible values for the strings, and the corresponding decays, are
|
|
shown in the table below.
|
|
\begin{center}
|
|
\begin{tabular}{ll}
|
|
string & $Z$ decay \\
|
|
\hline
|
|
{\tt el,EL} & $(e^-,e^+)$ \\
|
|
{\tt mu,MU,ml,ML} & $(\mu^-,\mu^+)$ \\
|
|
{\tt tl,TL} & $(\tau^-,\tau^+)$ \\
|
|
{\tt nu,NU,nl,NL} & $(\nu,\bar\nu) \times 3$ \\
|
|
{\tt bq,BQ} & $(b,\bar b)$ \\
|
|
\end{tabular}
|
|
\end{center}
|
|
Note that, for the case of neutrino decays, the sum over three flavours of
|
|
neutrino is performed. The labelling of the particles in the output is best
|
|
understood by example. Setting {\tt nproc=132.ELNU} corresponds to the
|
|
process $gg \to Z/\gamma^*+Z/\gamma^* \to e^-(p_3) e^+(p_4) \nu(p_5) \bar\nu(p_6)$.
|
|
Note that the default process corresponds to the string {\tt ELMU} so that,
|
|
for instance {\tt nproc=132.ELMU} is entirely equivalent to
|
|
{\tt nproc=132}.
|
|
The effect of changing the lepton flavour is only seen in the output
|
|
of LHE events, where the correct mass is then used when producing the
|
|
event record.
|
|
|
|
\subsection{$e^- e^+ \nu_e \bar \nu_e$ production, processes 1281, 1311, 1321}
|
|
These processes compute cross sections relevant for the final state
|
|
$e^- e^+ \nu_e \bar \nu_e$, i.e. with charged leptons and neutrinos from the
|
|
same (electron) doublet. As a result they receive contributions from diagrams
|
|
with resonant $ZZ$ propagators and resonant $WW$ propagators. Process
|
|
{\tt 1281} only includes amplitudes containing a Higgs boson {c.f. processes
|
|
{\tt 123} and {\tt 128}. Process
|
|
{\tt 1321} only includes continuum (box-diagram) amplitudes {c.f. processes
|
|
{\tt 127} and {\tt 132}. Process
|
|
{\tt 1311} includes both amplitudes and the effects of the interference
|
|
between them {c.f. processes {\tt 126} and {\tt 131}.
|
|
The effect of the interference between the $WW$ and $ZZ$ diagrams can be assessed
|
|
by, for instance, comparing process {\tt 1281} with the sum of processes
|
|
{\tt 123} and one-third of {\tt 128.ELNU}, where the weighting is to divide out
|
|
the natural sum over three neutrino flavours in process {\tt 128.ELNU}.
|
|
|
|
Event generation is not available for these processes at present.
|
|
|
|
\subsection{$e^- e^+ \nu \bar \nu$ production, processes 1282, 1312, 1322}
|
|
These processes compute cross sections relevant for the final state
|
|
$e^- e^+ \nu \bar \nu$, i.e. an electron pair and a sum over all three
|
|
flavours of neutrino. For muon and tau neutrinos, only $ZZ$ diagrams
|
|
contribute. For electron neutrinos there are contributions from diagrams
|
|
with resonant $ZZ$ propagators and resonant $WW$ propagators. Process
|
|
{\tt 1282} only includes amplitudes containing a Higgs boson {c.f. processes
|
|
{\tt 123} and {\tt 128}. Process
|
|
{\tt 1322} only includes continuum (box-diagram) amplitudes {c.f. processes
|
|
{\tt 127} and {\tt 132}. Process
|
|
{\tt 1312} includes both amplitudes and the effects of the interference
|
|
between them {c.f. processes {\tt 126} and {\tt 131}.
|
|
The effect of the interference between the $WW$ and $ZZ$ diagrams can be assessed
|
|
by, for instance, comparing process {\tt 1282} with the sum of processes
|
|
{\tt 123} and {\tt 128.ELNU}.
|
|
|
|
Event generation is not available for these processes at present.
|
|
|
|
|
|
\subsection{$H+b$ production, processes 136--138}
|
|
\label{subsec:Hb}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to hep-ph/0204093}]
|
|
\end{center}
|
|
|
|
These processes represent the production of a Standard Model Higgs
|
|
boson that decays into a pair of bottom quarks,
|
|
in association with a further bottom quark. The initial state at lowest order
|
|
is a bottom quark and a gluon.
|
|
The calculation may be performed at NLO, although radiation from the
|
|
bottom quarks in the Higgs decay is not included.
|
|
|
|
For this process, the matrix elements are divided up into a number of
|
|
different sub-processes, so the user must sum over these after performing
|
|
more runs than usual. At lowest order one can proceed as normal, using
|
|
{\tt nproc=136}. For a NLO calculation, the sequence of runs is as follows:
|
|
\begin{itemize}
|
|
\item Run {\tt nproc=136} with {\tt part=virt} and {\tt part=real} (or, both
|
|
at the same time using {\tt part=tota});
|
|
\item Run {\tt nproc=137} with {\tt part=real}.
|
|
\end{itemize}
|
|
The sum of these yields the cross-section with one identified $b$-quark in
|
|
the final state. To calculate the contribution with two $b$-quarks in the
|
|
final state, one should use {\tt nproc=138} with {\tt part=real}.
|
|
|
|
When {\tt removebr} is true, the Higgs boson does not decay.
|
|
|
|
\subsection{$t\bar{t}$ production with 2 semi-leptonic decays, processes 141--145}
|
|
\label{subsec:ttbar}
|
|
|
|
These processes describe $t \bar{t}$ production including semi-leptonic
|
|
decays for both the top and the anti-top.
|
|
In version 6.2 we have updated this to use the one-loop amplitudes of
|
|
ref.~\cite{Badger:2011yu}. The code for the virtual amplitudes now runs
|
|
about three times faster than earlier versions where the virtual
|
|
amplitudes of ref.~\cite{Korner:2002hy} were used.
|
|
Switching {\tt zerowidth} from {\tt .true.} to {\tt .false.} only affects
|
|
the $W$ bosons from the top quark decay, because our method of including spin
|
|
correlations requires the top quark to be on shell.
|
|
|
|
Process {\tt 141} includes all corrections, i.e.\ both radiative corrections
|
|
to the decay and to the production. This process is therefore the
|
|
basic process for the description of top production where both quarks
|
|
decay semi-leptonically. When {\tt removebr} is true in process {\tt 141},
|
|
the top quarks do not decay.
|
|
When one wishes to calculate observables related to the decay of the top
|
|
quark, {\tt removebr} should be false in process {\tt 141}.
|
|
The LO calculation proceeds as normal.
|
|
At NLO, there are two options:
|
|
\begin{itemize}
|
|
\item {\tt part=virt, real} or {\tt tota} : final state radiation is included
|
|
in the production stage only
|
|
\item {\tt part = todk} : radiation is included in the decay of the top
|
|
quark also and the final result corresponds to the sum of real and virtual
|
|
diagrams.
|
|
Note that these runs automatically perform an extra integration, so
|
|
will take a little longer.
|
|
\end{itemize}
|
|
|
|
Process {\tt 142} includes only the corrections in
|
|
the semileptonic decay of the top quark. Thus it is of primary
|
|
interest for theoretical studies rather than for physics applications.
|
|
Because of the method that we have used to include the radiation in the decay,
|
|
the inclusion of the corrections in the decay does not change the
|
|
total cross section. This feature is explained in section 6 of ref.~\cite{Campbell:2012uf}.
|
|
|
|
In the case of process {\tt 145}, there are no spin correlations in
|
|
the decay of the top quarks. The calculation is performed by
|
|
multiplying the spin summed top production cross section, by the decay
|
|
matrix element for the decay of the $t$ and the $\bar{t}$. These
|
|
processes may be used as a diagnostic test for the importance of the
|
|
spin correlation.
|
|
|
|
|
|
|
|
\subsection{$t\bar{t}$ production with decay and a gluon, process 143}
|
|
This process describes lowest order $t \bar{t}+g$ production
|
|
including two leptonic decays $t \to b l \nu$.
|
|
When {\tt removebr} is true, the top quarks do not decay.
|
|
This LO process only includes radiation only includes radiation in production.
|
|
|
|
\subsection{$t\bar{t}$ production with one hadronic decay, processes 146--151}
|
|
|
|
These processes describe the hadronic production of a pair of top
|
|
quarks, with one quark decaying hadronically and one quark decaying
|
|
semileptonics. For processes {\tt 146--148}, the top quark decays
|
|
semileptonically whereas the anti-top quark decays hadronically. For
|
|
processes {\tt 149--151}, the top quark decays hadronically whereas the
|
|
anti-top quark decays semi-leptonically. The base processes for
|
|
physics are process {\tt 146} and {\tt 149} which include
|
|
radiative corrections in both production and decay. Switching {\tt zerowidth} from
|
|
{\tt .true.} to {\tt .false.} only affects the $W$ bosons from the top
|
|
quark decay, because our method of including spin correlations
|
|
requires the top quark to be on shell.
|
|
When one wishes to calculate observables related to the decay of the top
|
|
quark, {\tt removebr} should be false in processes {\tt 146} and {\tt 149}.
|
|
The LO calculation proceeds as normal. At NLO, there are two options:
|
|
\begin{itemize}
|
|
\item {\tt part=virt, real} or {\tt tota} : final state radiation is included
|
|
in the production stage only
|
|
\item {\tt part = todk} : radiation is included in the decay of the top
|
|
quark also and the final result corresponds to the sum of real and virtual
|
|
diagrams.
|
|
Note that these runs automatically perform an extra integration, so
|
|
will take a little longer.
|
|
\end{itemize}
|
|
|
|
|
|
Processes {\tt 147} and {\tt 150} include only the radiative
|
|
corrections in the decay of the top quark without including
|
|
the radiative corrections in the hadronic decay of the $W$-boson.
|
|
Because of the method that we have used to include the radiation in the decays,
|
|
the inclusion of the corrections in this stage of the decay does not change the
|
|
total cross section.
|
|
Process {\tt 148} ({\tt 151}) includes only the radiative corrections
|
|
in the hadronic decay of the $W$-boson coming from the anti-top (top).
|
|
The inclusion of the corrections in this stage of the decay increases the
|
|
partial width by the normal $\alpha_s/\pi$ factor.
|
|
|
|
\subsection{$Q\overline{Q}$ production, processes 157--159}
|
|
These processes calculate the production of heavy quarks
|
|
({\tt 157} for top, {\tt 158} for bottom and {\tt 159} for charm) up to NLO
|
|
using the matrix elements of ref.~\cite{Nason:1987xz}. No decays
|
|
are included.
|
|
|
|
\subsection{$t{\bar t}+$~jet production, process 160}
|
|
This process calculates the production of top quarks and a single jet
|
|
at LO, without any decay of the top quarks.
|
|
|
|
\subsection{Single top production, processes 161--177}
|
|
\label{subsec:stop}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to hep-ph/0408158}]
|
|
\end{center}
|
|
|
|
These processes represent single top production and may be calculated up to
|
|
NLO as described below.
|
|
|
|
Single top production is divided as usual into $s$-channel
|
|
(processes {\tt 171-177}) and $t$-channel ({\tt 161-167})
|
|
diagrams. Each channel includes separately the production of a top
|
|
and anti-top quark, which is necessary when calculating rates at the LHC.
|
|
Below we illustrate the different use of these processes by considering
|
|
$t$-channel top production ({\tt 161,162}), although the procedure is the same
|
|
for anti-top production ({\tt 166,167}) and the corresponding $s$-channel
|
|
processes ({\tt 171,172}) and ({\tt 176,177}).
|
|
|
|
|
|
To calculate cross-sections that do not include any decay of the (anti-)top
|
|
quark, one should use process {\tt 161}
|
|
(or, correspondingly, {\tt 166}, {\tt 171} and {\tt 176}) with {\tt removebr}
|
|
true. The procedure is exactly the same
|
|
as for any other process.
|
|
Switching {\tt zerowidth} from {\tt .true.} to {\tt .false.} only affects
|
|
the $W$ boson from the top quark decay.
|
|
|
|
For processes {\tt 161}, {\tt 162}, {\tt 163}, {\tt 166}, {\tt 167}
|
|
and {\tt 168} the default behaviour when {\tt removebr} is true is that
|
|
partons are clustered into jets using the supplied jet
|
|
algorithm parameters, but no cut is applied on the number of jets.
|
|
This behaviour can be altered by changing the value of the
|
|
variable {\tt notag} in the file {\tt src/User/setnotag.f}.
|
|
|
|
When one wishes to calculate observables related to the decay of the top
|
|
quark, {\tt removebr} should be false.
|
|
The LO calculation proceeds as normal. At NLO, there are two options:
|
|
\begin{itemize}
|
|
\item {\tt part=virt, real} or {\tt tota} : final state radiation is included
|
|
in the production stage only
|
|
\item {\tt part = todk} : radiation is included in the decay of the top
|
|
quark also and the final result corresponds to the sum of real and virtual
|
|
diagrams. This process can only be performed at NLO with
|
|
{\tt zerowidth = .true}. This should be set automatically.
|
|
Note that these runs automatically perform an extra integration, so
|
|
will take a little longer.
|
|
\end{itemize}
|
|
|
|
The contribution from radiation in the decay may be calculated separately using
|
|
process {\tt 162}. This process number can be used with {\tt part=virt,real}
|
|
only. To ensure consistency, it is far simpler to use {\tt 161}
|
|
and this is the recommended approach.
|
|
|
|
A further option is provided for the $t-$channel single top process (when no
|
|
top quark decay is considered), relating to NLO real radiation diagrams that
|
|
contain a bottom quark. In the processes above the bottom quark is taken to
|
|
be massless. To include the effect of $m_b > 0$, one can run process
|
|
{\tt 163} ({\tt 168}) in place of {\tt 161} ({\tt 166}) and additionally include
|
|
process $\tt 231$ ({\tt 236}) at leading order.
|
|
The non-zero bottom quark mass has little effect on
|
|
the total cross section, but enables a (LO) study of the bottom quark kinematics.
|
|
Higher order corrections to the bottom quark kinematics can only be studied by running
|
|
process {\tt 231} ({\tt 236}) at NLO.
|
|
|
|
\subsection{Off-shell single top production in SM and SMEFT, processes 164,169}
|
|
\label{subsec:offstop}
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to ref.~\cite{Neumann:2019kvk}}]
|
|
\end{center}
|
|
|
|
The processes 164 and 169 represent off-shell single-top-quark and anti-top-quark production
|
|
in the complex-mass scheme, respectively. Both the SM and contributions from the SMEFT can be calculated.
|
|
|
|
Dynamical double deep inelastic scattering scales can be
|
|
consistently used at NLO by setting \texttt{dynamicscale} to `DDIS'
|
|
and \texttt{scale}$=$\texttt{facscale} to 1d0. In this way the
|
|
momentum transfer along the $W$-boson $Q^2$ is used as the scale for
|
|
the light-quark-line corrections $\mu^2=Q^2$, and $\mu^2=Q^2+m_t^2$ for
|
|
the heavy-quark-line corrections. These scales are also consistently
|
|
used for the non-resonant contributions, with QCD corrections on the
|
|
$ud$-quark line, and separate QCD corrections on the bottom-quark
|
|
line.
|
|
|
|
The new block `Single top SMEFT, nproc=164,169' in the input
|
|
file governs the inclusion of SMEFT operators and corresponding
|
|
orders. The scale of new physics $\Lambda$ can be separately set, and
|
|
has a default value of $\SI{1000}{\GeV}$. The flag \texttt{enable
|
|
1/lambda4} enables the $1/\Lambda^4$ contributions, where operators
|
|
$\Qtwo, \Qfour, \Qseven$ and $\Qnine$ can contribute for the first
|
|
time. For the non-Hermitian operators we allow complex Wilson
|
|
coefficients. We also have a flag to disable the pure SM
|
|
contribution, leaving only contributions from SMEFT operators
|
|
either interfered with the SM amplitudes or as squared
|
|
contributions at $1/\Lambda^4$. This can be used to directly and
|
|
quickly extract kinematical distributions and the magnitudes of
|
|
pure SMEFT contributions.
|
|
|
|
To allow for easier comparisons with previous anomalous couplings
|
|
results, and possibly estimate further higher order effects, we allow
|
|
for an anomalous couplings mode at LO by enabling the corresponding
|
|
flag. The relations between our operators and the anomalous couplings
|
|
are
|
|
|
|
For comparisons with on-shell results one needs to add up the contributions
|
|
from processes 161 at NLO and from the virt and real contributions from 162, see above.
|
|
|
|
\begin{align*}
|
|
\delta V_L &= \Cone \frac{m_t^2}{\Lambda^2} ,\,\text{where } V_L = 1 + \delta V_L\,,\\
|
|
V_R &= \Ctwo{}^* \frac{m_t^2}{\Lambda^2}\,, \\
|
|
g_L &= -4\frac{m_W m_t}{\Lambda^2} \cdot \Cfour\,, \\
|
|
g_R &= -4 \frac{m_W m_t}{\Lambda^2} \cdot \Cthree{}^*\,,
|
|
\end{align*}
|
|
|
|
where $m_W$ is the $W$-boson mass, and $m_W = \frac{1}{2} g_W v$ has
|
|
been used to derive this equivalence. Note that the minus sign for
|
|
$g_L$ and $g_R$ is different from the literature. See also the publication for more information.
|
|
|
|
The analysis/plotting routine is contained in the file
|
|
`\texttt{src/User/nplotter\_ktopanom.f}', where all observables
|
|
presented in this study are implemented, and the $W$-boson/neutrino
|
|
reconstruction is implemented and can be switched on or off.
|
|
|
|
\subsection{$Wt$ production, processes 180--187}
|
|
\label{subsec:wt}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to hep-ph/0506289}]
|
|
\end{center}
|
|
|
|
These processes represent the production of a $W$ boson that decays leptonically
|
|
in association with a top quark. The lowest order diagram involves a gluon and
|
|
a bottom quark from the PDF, with the $b$-quark radiating a $W$ boson and
|
|
becoming a top quark. The calculation can be performed up to NLO.
|
|
|
|
Processes {\tt 180} and {\tt 185} produce a top quark that does not decay,
|
|
whilst in processes {\tt 181} and {\tt 186} the top quark decays leptonically.
|
|
Consistency with
|
|
the simpler processes ({\tt 180,185}) can be demonstrated by running process
|
|
{\tt 181,186} with {\tt removebr} set to true.
|
|
|
|
At next-to-leading order, the calculation includes contributions from diagrams
|
|
with two gluons in the initial state, $gg \rightarrow Wtb$. The $p_T$ of the
|
|
additional $b$ quark is vetoed according to the value of the parameter
|
|
{\tt ptmin\_bjet} which is specified in the input file. The contribution from
|
|
these diagrams when the $p_T$ of the $b$ quark is above {\tt ptmin\_bjet}
|
|
is zero. The values of this parameter and the factorization scale ({\tt facscale})
|
|
set in the input file should be chosen carefully. Appropriate values for both
|
|
(in the range $30$-$100$~GeV) are discussed in the associated paper.
|
|
|
|
When one wishes to calculate observables related to the decay of the top
|
|
quark, {\tt removebr} should be false.
|
|
The LO calculation proceeds as normal. At NLO, there are two options:
|
|
\begin{itemize}
|
|
\item {\tt part=virt, real} or {\tt tota} : final state radiation is included
|
|
in the production stage only
|
|
\item {\tt part = todk} : radiation is included in the decay of the top
|
|
quark also and the final result corresponds to the sum of real and virtual
|
|
diagrams. This process can only be performed at NLO with
|
|
{\tt zerowidth = .true}. This should be set automatically.
|
|
Note that these runs automatically perform an extra integration, so
|
|
will take a little longer.
|
|
\end{itemize}
|
|
|
|
The contribution from radiation in the decay may be calculated separately using
|
|
processes {\tt 182,187}. These process numbers can be used with {\tt part=virt,real}
|
|
only. To ensure consistency, it is far simpler to use {\tt 181,186}
|
|
and this is the recommended approach.
|
|
|
|
\subsection{$H+$~jet production with finite top-mass effects,\\ process 200}
|
|
\label{subsec:hjetma}
|
|
This process represents the production of a Higgs boson in association with a single jet based on ref.~ \cite{Neumann:2016dny}. Decay modes are currently unsupported/untested. The top-quark mass is taken into account exactly for the born and real-emission parts, as well as for the singular part of the virtual corrections.
|
|
|
|
The finite part of the two-loop virtual corrections can be computed in different ways.
|
|
\begin{itemize}
|
|
\item In a low energy asymptotic expansion in $1/m_t^k$ up to order $k=2,4$ by setting mtex to $2$ or $4$ in the input file. This is recommended for transverse momenta up to $\simeq\SI{225}{\GeV}$.
|
|
\item In a high energy expansion by setting mtex=100 in the input file. This is recommended for transverse momenta beyond \SI{450}{\GeV}.
|
|
\item In a rescaling approach where the finite part of the two-loop virtual amplitude in the effective field theory ($m_t=\infty$) is rescaled pointwise by the ratio of the one-loop amplitude computed with full $m_t$ dependence to the one-loop amplitude for $m_t=\infty$. This mode is the default mode and enabled with mtex=0 in the input file. This is the recommended approach for the intermediate energy region and for estimating top-mass uncertainties in the transition regions between these approaches.
|
|
\end{itemize}
|
|
|
|
\subsection{Di-jet production, processes 190--191}
|
|
\label{subsec:dijet}
|
|
|
|
Process {\tt 190} represents di-jet production through strong interactions.
|
|
It may be calculated to LO only.
|
|
|
|
Process {\tt 191} is an ancillary process that is used in the calculation of
|
|
weak one-loop corrections to di-jet production. When computed at LO it gives the
|
|
contribution of weak (${\cal O}(\alpha^2)$) and mixed weak-strong (${\cal O}(\alpha\alpha_s)$)
|
|
mediated processes to di-jet production. Please refer to Ref.~\cite{Campbell:2016dks} for details.
|
|
|
|
\subsection{$H+$~jet production, processes 201--210}
|
|
\label{subsec:hjet}
|
|
|
|
These processes represent the production of a Higgs boson in association
|
|
with a single jet, with the subsequent decay of the Higgs to either
|
|
a pair of bottom quarks (processes {\tt 201,203,206})
|
|
or to a pair of tau's ({\tt 202,204,207}),
|
|
or to a pair of $W$'s which decay leptonically ({\tt 208}),
|
|
or to a pair of $Z$'s which decay leptonically ({\tt 209}),
|
|
or to a pair of photons ({\tt 210}).
|
|
|
|
The Higgs boson couples to a pair of gluons via a loop of heavy fermions
|
|
which, in the Standard Model, is accounted for almost entirely by including
|
|
the effect of the top quark alone. For processes {\tt 201,202,206,207}, the
|
|
matrix elements include the full dependence on the top quark mass.
|
|
The calculation can only be performed at LO.
|
|
However, the Higgs boson can either be the Standard Model one
|
|
(processes {\tt 201,202}) or a pseudoscalar ({\tt 206,207}).
|
|
Note that the pseudoscalar case corresponds, in the heavy top limit, to the effective Lagrangian,
|
|
\begin{equation}
|
|
\mathcal{L} = \frac{1}{8\pi v} \, G^a_{\mu\nu} \widetilde G^{\mu\nu}_a A \;,
|
|
\end{equation}
|
|
where $\widetilde G^{\mu\nu}_a = i\epsilon^{\mu\nu\alpha\beta}
|
|
G_{\alpha\beta}^a$.
|
|
The interaction differs from the scalar case in Eq.~{\ref{eq:HeffL}} by a factor of $3/2$
|
|
and hence the rate is increased by a factor of $(3/2)^2$.
|
|
|
|
|
|
For processes {\tt 203,204,208,209,210}, the calculation is performed in the
|
|
limit of infinite top quark mass, so that NLO results can be obtained.
|
|
The virtual matrix elements have been implemented from
|
|
refs~\cite{Ravindran:2002dc} and~\cite{Schmidt:1997wr}.
|
|
Phenomenological results have previously been
|
|
given in refs.~\cite{deFlorian:1999zd},\cite{Ravindran:2002dc}
|
|
and \cite{Glosser:2002gm}.
|
|
Note that the effect of radiation from the bottom quarks in process {\tt 203}
|
|
is not included.
|
|
|
|
When {\tt removebr} is true in processes {\tt 201}, {\tt 203}, {\tt 206}, {\tt 208}, {\tt 209}
|
|
and {\tt 210}, the Higgs boson does not decay.
|
|
|
|
\subsection{Higgs production via WBF, processes 211--217}
|
|
\label{subsec:wbf}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to hep-ph/0403194}]
|
|
\end{center}
|
|
|
|
These processes provide predictions for the production of a Higgs boson in
|
|
association with two jets via weak-boson fusion (WBF). The Higgs boson
|
|
subsequently decays to either a pair of bottom quarks
|
|
(processes {\tt 211, 216}), to a pair of tau's ({\tt 212, 217}),
|
|
to a pair of $W$ bosons ({\tt 213}),
|
|
to a pair of $Z$ bosons ({\tt 214}),
|
|
or to a pair of photons ({\tt 215}).
|
|
|
|
Calculations can be performed up to NLO for processes {\tt 211}--{\tt 215}.
|
|
In addition to this, processes {\tt 216} and {\tt 217} provide the lowest
|
|
order calculation of the WBF reaction which radiates an additional jet.
|
|
|
|
When {\tt removebr} is true, the Higgs boson does not decay.
|
|
|
|
\subsection{$\tau^+\tau^-$ production, process 221}
|
|
\label{subsec:tautau}
|
|
|
|
This process provides predictions for the production of a tau lepton
|
|
pair mediated by $\gamma^*/Z$, with subsequent leptonic decays. The calculation is available at LO
|
|
only. The relevant matrix elements are adapted from the ones in
|
|
ref.~\cite{Kleiss:1988xr}.
|
|
|
|
When {\tt removebr} is true, the tau leptons do not decay.
|
|
|
|
|
|
%
|
|
\subsection{$e^-e^+ \nu_{\mu} \bar\nu_{\mu} $-pair production via WBF, processes 222}
|
|
The {\it weak} processes occur in $O(\alpha^6)$, whereas the {\it strong} processes occur in $O(\alpha^4 \alpha_S^2)$.
|
|
These processes can currently only be calculated at lowest order.
|
|
\begin{eqnarray}
|
|
&222 & f(p_1)+f(p_2) \to Z(e^-(p_3),e^+(p_4))Z(\nu_\mu(p_5),\bar{\nu}_\mu(p_6)))+f(p_7)+f(p_8) [WBF] \nonumber \\
|
|
&2201 & f(p_1)+f(p_2) \to Z(e^-(p_3),e^+(p_4))Z(\mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) [strong] \nonumber \\
|
|
&2221 & f(p_1)+f(p_2) \to Z(e^-(p_3),e^+(p_4))Z(\nu_\mu(p_5),\bar{\nu}_\mu(p_6)))+f(p_7)+f(p_8) [strong] \nonumber
|
|
\end{eqnarray}
|
|
%
|
|
\subsection{$\nu_e e^+ \mu^- \mu^+$-pair production via WBF, processes 223,2231}
|
|
The {\it weak} processes occur in $O(\alpha^6)$, whereas the {\it strong} processes occur in $O(\alpha^4 \alpha_S^2)$.
|
|
These processes can currently only be calculated at lowest order.
|
|
\begin{eqnarray}
|
|
& 223 & f(p_1)+f(p_2) \to W^+(\nu_e(p_3),e^+(p_4))Z(\mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) [weak] \nonumber \\
|
|
& 2231 & f(p_1)+f(p_2) \to W^+(\nu_e(p_3),e^+(p_4))Z(\mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) [strong] \nonumber
|
|
\end{eqnarray}
|
|
|
|
\subsection{$e^- \bar\nu_{e} \nu_{\mu} \mu^+$-pair production via WBF, processes 224,2241}
|
|
The {\it weak} processes occur in $O(\alpha^6)$, whereas the {\it strong} processes occur in $O(\alpha^4 \alpha_S^2)$.
|
|
These processes can currently only be calculated at lowest order.
|
|
\begin{eqnarray}
|
|
&224 & f(p_1)+f(p_2) \to W^-(e^-(p_3),\bar{\nu}_e(p_6)))W^+(\nu_\mu(p_5),\mu^+(p_4))+f(p_7)+f(p_8) [WBF] \nonumber \\
|
|
&2241 & f(p_1)+f(p_2) \to W^-(e^-(p_3),\bar{\nu}_e(p_6)))W^+(\nu_\mu(p_5),\mu^+(p_4))+f(p_7)+f(p_8) [strong] \nonumber
|
|
\end{eqnarray}
|
|
%
|
|
\subsection{$e^- \bar\nu_{e} \mu^- \mu^+$-pair production via WBF, processes 225,2251}
|
|
The {\it weak} processes occur in $O(\alpha^6)$, whereas the {\it strong} processes occur in $O(\alpha^4 \alpha_S^2)$.
|
|
These processes can currently only be calculated at lowest order.
|
|
\begin{eqnarray}
|
|
&225 & f(p_1)+f(p_2) \to W^-(e^-(p_3),\bar{\nu}_e(p_4))Z(\mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) [weak] \nonumber \\
|
|
&2251 & f(p_1)+f(p_2) \to W^-(e^-(p_3),\bar{\nu}_e(p_4))Z(\mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) [strong] \nonumber
|
|
\end{eqnarray}
|
|
|
|
|
|
\subsection{$e^- e^+ \bar\nu_{e} \nu_{e}$-pair production via WBF, processes 226}
|
|
The {\it weak} processes occur in $O(\alpha^6)$, whereas the {\it strong} processes occur in $O(\alpha^4 \alpha_S^2)$.
|
|
This process can currently only be calculated at lowest order.
|
|
\begin{eqnarray}
|
|
&226 & f(p_1)+f(p_2) \to e-(p_3)+e^+(p_4)+\nu_e(p_5)+\bar{\nu}_e(p_6)+f(p_7)+f(p_8) [WBF] \nonumber
|
|
\end{eqnarray}
|
|
|
|
\subsection{$\nu_{e} e^+ \nu_{\mu} \mu^+ $-pair production via WBF, processes 228,2281}
|
|
This is pure electroweak process, occuring in $O(\alpha^6)$.
|
|
These processes can currently only be calculated at lowest order.
|
|
\begin{eqnarray}
|
|
&228 & f(p_1)+f(p_2) \to W^+(\nu_e(p_3),e^+(p_4)))W^+(\nu_\mu(p_5),\mu^+(p_6))+f(p_7)+f(p_8) [WBF] \nonumber \\
|
|
&2281 & f(p_1)+f(p_2) \to W^+(\nu_e(p_3),e^+(p_4)))W^+(\nu_\mu(p_5),\mu^+(p_6))+f(p_7)+f(p_8) [strong] \nonumber
|
|
\end{eqnarray}
|
|
\subsection{$e^- \bar{\nu}_{e} \mu^- \bar{\nu}_{\mu} $-pair production via WBF, processes 229,2291}
|
|
This is pure electroweak process, occuring in $O(\alpha^6)$.
|
|
These processes can currently only be calculated at lowest order.
|
|
\begin{eqnarray}
|
|
& 229 & f(p_1)+f(p_2) \to W^-(e^-(p_3),\bar{\nu}_e(p_4)))W^+(\mu^-(p_5),\bar{\nu}_\mu(p_6))+f(p_7)+f(p_8) [WBF] \nonumber \\
|
|
&2291 & f(p_1)+f(p_2) \to W^-(e^-(p_3),\bar{\nu}_e(p_4)))W^-(\mu^-(p_5),\bar{\nu}_\mu(p_6))+f(p_7)+f(p_8) [strong] \nonumber
|
|
\end{eqnarray}
|
|
|
|
\subsection{$t$-channel single top with an explicit $b$-quark, processes 231--240}
|
|
\label{subsec:stopb}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to arXiv:0903.0005~[hep-ph]}]
|
|
\end{center}
|
|
|
|
These represent calculations of the $t$-channel single top~({\tt 231}) and anti-top~({\tt 231})
|
|
processes in a scheme with four flavours of quark in the proton, so that $b$-quarks are not present in the proton.
|
|
The $b$-quark is instead explicitly included in the final state.
|
|
|
|
Processes {\tt 232} and {\tt 236} represent $t$-channel single top production in association
|
|
with a further jet and may be calculated at LO only.
|
|
|
|
Processes {\tt 233} and {\tt 238} are the complete four-flavour scheme $t$-channel single top production processes.
|
|
These are therefore the processes that should be used for most physics applications.
|
|
When one wishes to calculate observables related to the decay of the top
|
|
quark, {\tt removebr} should be false in processes {\tt 233} and {\tt 236}.
|
|
The LO calculation proceeds as normal. At NLO, there are two options:
|
|
\begin{itemize}
|
|
\item {\tt part=virt, real} or {\tt tota} : final state radiation is included
|
|
in the production stage only
|
|
\item {\tt part = todk} : radiation is included in the decay of the top
|
|
quark also and the final result corresponds to the sum of real and virtual
|
|
diagrams.
|
|
Note that these runs automatically perform an extra integration, so
|
|
will take a little longer.
|
|
\end{itemize}
|
|
|
|
|
|
Processes {\tt 234} and {\tt 239} give the extra contribution due to radiation
|
|
in top decay. These processes are mainly of theoretical interest.
|
|
|
|
Processes {\tt 235} and {\tt 240} are the leading order single top processes with an
|
|
extra radiated parton. These processes do not includes jets produced in the decay process.
|
|
|
|
\subsection{$W^+W^++$jets production, processes 251,252}
|
|
These processes represent the production of two $W^+$
|
|
bosons in association with two (process {\tt 251}) or three (process {\tt 252})
|
|
jets. The lowest order at which two positively charged $W$ bosons
|
|
can be produced is with two jets.
|
|
This process is only implemented for leptonic decays of the
|
|
$W$ particles. The calculation is available at LO only.
|
|
The calculation and code are from ref.~\cite{Melia:2010bm}.
|
|
{\tt removebr} is not implemented and has no effect.
|
|
|
|
\subsection{$Z+Q$ production, processes 261--267}
|
|
\label{subsec:ZQ}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to hep-ph/0312024}]
|
|
\end{center}
|
|
|
|
These processes represent the production of a $Z$
|
|
boson that decays into a pair of electrons,
|
|
in association with a heavy quark, $Q$.
|
|
|
|
For processes {\tt 261}, {\tt 262}, {\tt 266} and {\tt 267} the initial
|
|
state at lowest order is the heavy quark and a gluon and
|
|
the calculation may be performed at NLO.
|
|
As for $H+b$ production, the matrix elements are divided into two
|
|
sub-processes at NLO. Thus the user must sum over these after performing
|
|
more runs than usual. At lowest order one can proceed as normal, using
|
|
{\tt nproc=261} (for $Z+b$) or {\tt nproc=262} (for $Z+c$).
|
|
For a NLO calculation, the sequence of runs is as follows:
|
|
\begin{itemize}
|
|
\item Run {\tt nproc=261} (or {\tt 262}) with {\tt part=virt} and
|
|
{\tt part=real} (or, both at the same time using {\tt part=tota});
|
|
\item Run {\tt nproc=266} (or {\tt 267}) with {\tt part=real}.
|
|
\end{itemize}
|
|
The sum of these yields the cross-section with one identified heavy quark in
|
|
the final state when {\tt inclusive} is set to {\tt .false.} . To calculate the
|
|
rate for at least one heavy quark, {\tt inclusive} should be {\tt .true.}.
|
|
|
|
For processes {\tt 263} and
|
|
{\tt 264}, the calculation uses the matrix elements for the production
|
|
of a $Z$ and a heavy quark pair and demands that one of the heavy quarks
|
|
is not observed. It may either lie outside the range of $p_T$ and $\eta$
|
|
required for a jet, or both quarks may be contained in the same jet.
|
|
Due to the extra complexity (the calculation must retain the full
|
|
dependence on the heavy quark mass), this can only be computed at LO.
|
|
|
|
When {\tt removebr} is true, the $Z$ boson does not decay.
|
|
|
|
\subsection{$H + 2$~jet production, processes 270--274}
|
|
|
|
These processes represent the production of a Standard Model Higgs boson
|
|
in association with two jets. The Higgs boson
|
|
subsequently decays to either a pair of photons ({\tt nproc=270}), a bottom quark pair ({\tt nproc=271}),
|
|
a pair of tau's ({\tt nproc=272}), a pair of leptonically decaying $W$'s ({\tt nproc=273})
|
|
or a pair of leptonically decaying $Z$'s ({\tt nproc=274}).
|
|
|
|
The matrix elements are included in the infinite top mass limit
|
|
using the effective Lagrangian approach.
|
|
|
|
When {\tt removebr} is true, the Higgs boson does not decay.
|
|
|
|
\subsection{$H + 3$~jet production, processes 275-278}
|
|
|
|
These processes represent the production of a Standard Model Higgs boson
|
|
in association with three jets. The Higgs boson
|
|
subsequently decays to either a bottom quark pair ({\tt nproc=275}),
|
|
or a pair of tau's ({\tt nproc=276})
|
|
or a pair of $W$'s that decay leptonically into a single generation of leptons ({\tt nproc=278})
|
|
or a pair of $Z$'s that decay leptonically into a single generation of leptons ({\tt nproc=279}).
|
|
The matrix elements are included in the infinite top mass limit
|
|
using an effective Lagrangian approach. These calculations can be
|
|
performed at LO only.
|
|
|
|
When {\tt removebr} is true, the Higgs boson does not decay.
|
|
|
|
\subsection{Direct $\gamma$ production, processes 280--282}
|
|
\label{subsec:dirphot}
|
|
|
|
These processes represent the production a real photon.
|
|
Since this process includes a real photon, the cross section diverges
|
|
when the photon is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. This will ensure that
|
|
the cross section is well-defined.
|
|
|
|
The calculation of process {\tt 282} is only available at leading order.
|
|
|
|
\subsection{Direct $\gamma$ + heavy flavour production, processes 283--284}
|
|
\label{subsec:heavyfl}
|
|
|
|
These processes represent the production a real photon with a $b$ quark
|
|
or a charm quark
|
|
Since this process includes a real photon, the cross section diverges
|
|
when the photon is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. This will ensure that
|
|
the cross section is well-defined.
|
|
|
|
The calculation of process {\tt 283}--{\tt 284} is only available at leading order.
|
|
|
|
\subsection{$\gamma\gamma$ production, processes 285-286}
|
|
\label{subsec:gamgam}
|
|
|
|
Process {\tt 285} represents the production of a pair of real photons.
|
|
Since this process includes two real photons, the cross section diverges
|
|
when one of the photons is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. This will ensure that
|
|
the cross section is well-defined.
|
|
|
|
The calculation of process {\tt 285} may be performed at NLO using either the
|
|
Frixione algorithm~\cite{Frixione:1998jh} or standard cone isolation. This process also includes
|
|
the one-loop gluon-gluon contribution as given in
|
|
ref.~\cite{Bern:2002jx}. The production of a photon via parton fragmentation is included at NLO and
|
|
can be run separately by using the {\tt frag} option in {\tt part}. This option includes the contributions from the integrated
|
|
photon dipole subtraction terms and the LO QCD matrix element multiplied by the fragmentation function.
|
|
|
|
%Process {\tt 285} can be run using different cuts for each photon. Setting the first 9 characters of the runstring to
|
|
%{\tt Stag\_phot} will apply the following default cuts:
|
|
%\begin{eqnarray*}
|
|
%p_T^{\gamma_1} > 40~\mbox{GeV}, \; p_T^{\gamma_2} > {\tt ptmin\_photon}~\mbox{GeV}, \; |\eta^{\gamma_i}| < {\tt etamax\_photon}
|
|
%\end{eqnarray*}
|
|
%These values can be changed by editing the file photon\_cuts.f in src/User.
|
|
|
|
The phase space cuts for the final state photons are defined in {\tt{input.DAT}}, for multiple photon processes such
|
|
as {\tt 285 - 287} the $p_T$'s of the individual photons (hardest, second hardest and third hardest or softer) can be controlled independently.
|
|
The remaining cuts on $R_{\gamma j}$, $\eta_{\gamma}$ etc. are applied universally to all photons. Users wishing to alter
|
|
this feature should edit the file {\tt{photon\_cuts.f}} in the directory {\tt{src/User}}.
|
|
|
|
|
|
Process {\tt 286}, corresponding to $\gamma\gamma+$jet production, can be computed at leading order only.
|
|
|
|
\subsection{$\gamma\gamma\gamma$ production, process 287}
|
|
\label{subsec:trigam}
|
|
|
|
Process {\tt 287} represents the production of three real photons.
|
|
The cross section diverges
|
|
when one of the photons is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. This will ensure that
|
|
the cross section is well-defined.
|
|
|
|
The calculation of process {\tt 285} may be performed at NLO using either the
|
|
Frixione algorithm~\cite{Frixione:1998jh} or standard cone isolation. The production of a photon via parton fragmentation is included at NLO and
|
|
can be run separately by using the {\tt frag} option in {\tt part}. This option includes the contributions from the integrated
|
|
photon dipole subtraction terms and the LO QCD matrix element multiplied by the fragmentation function.
|
|
The phase space cuts for the final state photons are defined in {\tt{input.DAT}}, for multiple photon processes such
|
|
as {\tt 285 - 287} the $p_T$'s of the individual photons (hardest, next-to hardest and softest) can be controlled independently.
|
|
The remaining cut on $R_{\gamma j}$, $\eta_{\gamma}$ etc. are applied universally to all photons. Users wishing to alter
|
|
this feature should edit the file {\tt{photon\_cuts.f}} in the directory {\tt{src/User}}.
|
|
|
|
|
|
\subsection{$\gamma\gamma\gamma\gamma$ production, process 289}
|
|
\label{subsec:fourgam}
|
|
|
|
Process {\tt 289} represents the production of four real photons.
|
|
The cross section diverges
|
|
when one of the photons is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. This will ensure that
|
|
the cross section is well-defined.
|
|
|
|
The calculation of process {\tt 289} may be performed at NLO using either the
|
|
Frixione algorithm~\cite{Frixione:1998jh} or standard cone isolation. The production of a photon via parton fragmentation is included at NLO and
|
|
can be run separately by using the {\tt frag} option in {\tt part}. This option includes the contributions from the integrated
|
|
photon dipole subtraction terms and the LO QCD matrix element multiplied by the fragmentation function.
|
|
The phase space cuts for the final state photons are defined in {\tt{input.DAT}}, for multiple photon processes such
|
|
as {\tt 285 - 289} the $p_T$'s of the individual photons (hardest, next-to hardest and softest) can be controlled independently.
|
|
The remaining cut on $R_{\gamma j}$, $\eta_{\gamma}$ etc. are applied universally to all photons. Users wishing to alter
|
|
this feature should edit the file {\tt{photon\_cuts.f}} in the directory {\tt{src/User}}.
|
|
|
|
Note that for this process the second softest and softest photons are forced to have equal minimum $p_T$, defined
|
|
by the {\tt{[ptmin\_photon(3rd)]}} variable in the input file.
|
|
|
|
|
|
\subsection{$W\gamma$ production, processes 290-297}
|
|
\label{subsec:wgamma}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically, in association with a real photon.
|
|
Since this process includes a real photon, the cross section diverges
|
|
when the photon is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. Moreover, when the parameters {\tt zerowidth}
|
|
and {\tt removebr} are set to {\tt .false.} the decay $W \to \ell \nu$ will include
|
|
photon radiation from the lepton, so that a non-zero {\tt R(photon,lept)\_min} should
|
|
also be supplied. This will ensure that the cross section is well-defined.
|
|
Virtual amplitudes are taken from ref.~\cite{Dixon:1998py}.
|
|
|
|
The calculation of processes {\tt 290} and {\tt 295} may be performed
|
|
at NLO using the Frixione algorithm~\cite{Frixione:1998jh} or standard isolation.
|
|
|
|
For processes {\tt 290} and {\tt 295} the role of {\tt mtrans34cut} changes to become a cut
|
|
on the transverse mass on the $M_{345}$ system, i.e. the photon is included with the leptons in the cut.
|
|
|
|
\subsubsection{Anomalous $WW\gamma$ couplings}
|
|
Processes {\tt 290}-{\tt 297} may also be computed including the effect of anomalous $WW\gamma$ couplings, making
|
|
use of the amplitudes calculated in Ref.~\cite{DeFlorian:2000sg}. Including only dimension 6 operators
|
|
or less and demanding gauge, $C$ and $CP$ invariance gives the general form of the anomalous vertex~\cite{DeFlorian:2000sg},
|
|
\begin{eqnarray}
|
|
\Gamma^{\alpha \beta \mu}_{W W \gamma}(q, \bar q, p) &=&
|
|
{\bar q}^\alpha g^{\beta \mu}
|
|
\biggl( 2 + \Delta\kappa^\gamma + \lambda^\gamma {q^2\over M_W^2} \biggr)
|
|
- q^\beta g^{\alpha \mu}
|
|
\biggl( 2 + \Delta\kappa^\gamma + \lambda^\gamma {{\bar q}^2\over M_W^2}
|
|
\biggr) \nonumber \\
|
|
&& \hskip 1 cm
|
|
+ \bigl( {\bar q}^\mu - q^\mu \bigr)
|
|
\Biggl[ - g^{\alpha \beta} \biggl(
|
|
1 + {1\over2} p^2 \frac{\lambda^\gamma}{M_W^2} \biggr)
|
|
+\frac{\lambda^\gamma}{M_W^2} p^\alpha p^\beta \Biggr] \,,
|
|
\end{eqnarray}
|
|
where the overall coupling has been chosen to be $-|e|$. The parameters that
|
|
specify the anomalous couplings, $\Delta\kappa^\gamma$ and $\lambda^\gamma$, are
|
|
specified in the input file as already discussed in Section~\ref{subsec:diboson}.
|
|
If the input file contains a negative value for the form-factor scale $\Lambda$
|
|
then no suppression factors are applied to the anomalous couplings.
|
|
Otherwise, the couplings are included
|
|
in \MCFM only after suppression by dipole form factors,
|
|
\begin{displaymath}
|
|
\Delta \kappa^{\gamma} \rightarrow
|
|
\frac{\Delta \kappa_1^{\gamma}}{(1+\hat{s}/\Lambda^2)^2}, \qquad
|
|
\lambda^{\gamma} \rightarrow
|
|
\frac{\Delta \lambda^{\gamma}}{(1+\hat{s}/\Lambda^2)^2} \;,
|
|
\end{displaymath}
|
|
where $\hat{s}$ is the $W\gamma$ pair invariant mass.
|
|
|
|
The Standard Model cross section is obtained by setting $\Delta\kappa^\gamma = \lambda^\gamma = 0$.
|
|
|
|
\subsection{$Z\gamma$, production, processes 300, 305}
|
|
\label{subsec:zgamma}
|
|
|
|
|
|
Processes {\tt 300} and {\tt 305} represent the production of a $Z$ boson (or virtual photon for process {\tt 300})
|
|
in association with a real photon based on ref.~\cite{Campbell:2017aul}. The $Z/\gamma^*$ subsequently decays into
|
|
either an $e^+ e^-$ pair ({\tt nproc=300}) or neutrinos ({\tt nproc=305}).
|
|
Since these processes include a real photon, the cross section diverges
|
|
when the photon is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. Moreover, when the parameters {\tt zerowidth}
|
|
and {\tt removebr} are set to {\tt .false.} the decay $Z \to e^- e^+$ ({\tt nproc=300})
|
|
will include photon radiation from both leptons, so that a non-zero {\tt R(photon,lept)\_min}
|
|
should also be supplied. This will ensure that the cross section is well-defined.
|
|
The calculation of processes {\tt 300} may be performed
|
|
at NNLO using the Frixione algorithm~\cite{Frixione:1998jh} or standard isolation.
|
|
%Processes {\tt 302} and {\tt 307} represents the production of a $Z$ boson (or virtual photon)
|
|
%in association with a real photon and an additional jet. These processes are also available at NLO including
|
|
%the full fragmentation processes. Anomalous couplings are not available for these processes.
|
|
%Processes {\tt 304} and {\tt 309} represents the production of a $Z$ boson (or virtual photon)
|
|
%in association with a real photon and and two additional jets. These processes are available at leading order only.
|
|
%When {\tt removebr} is true in process {\tt 300} or {\tt 302} the $Z$ boson does not decay.
|
|
|
|
For the process {\tt 300} the role of {\tt mtrans34cut} changes to become a cut
|
|
on the invariant mass on the $M_{345}$ system, i.e. the photon is included with the leptons in the cut.
|
|
|
|
\subsubsection{Anomalous $ZZ\gamma$ and $Z\gamma\gamma$ couplings}
|
|
Processes {\tt 300}-{\tt 305} may also be computed including the effect of anomalous couplings between $Z$ bosons and photons.
|
|
Note that, at present, the effect of anomalous couplings is not included in the gluon-gluon
|
|
initiated contributions.
|
|
|
|
The anomalous $Z\gamma Z$ vertex (not present at all in the Standard Model),
|
|
considering operators up to dimension 8, is given by~\cite{DeFlorian:2000sg},
|
|
\begin{eqnarray}
|
|
&& \Gamma^{\alpha \beta \mu}_{Z \gamma Z}(q_1, q_2, p) =
|
|
\frac{i(p^2-q_1^2)}{M_Z^2} \Biggl(
|
|
h_1^Z \bigl( q_2^\mu g^{\alpha\beta} - q_2^\alpha g^{\mu \beta}
|
|
\bigr)
|
|
\nonumber \\ && + \frac{h_2^Z}{M_Z^2} p^\alpha \Bigl( p\cdot q_2\ g^{\mu\beta} -
|
|
q_2^\mu p^\beta \Bigr)
|
|
- h_3^Z \varepsilon^{\mu\alpha\beta\nu} q_{2\, \nu}
|
|
- \frac{h_4^Z}{M_Z^2} \varepsilon^{\mu\beta\nu\sigma} p^\alpha
|
|
p_\nu q_{2\, \sigma} \Biggl)
|
|
\end{eqnarray}
|
|
where the overall coupling has been chosen to be $|e|$ (and
|
|
$\epsilon^{0123}=+1$). The non-standard $Z_\alpha(q_1) \gamma_\beta(q_2)
|
|
\gamma_\mu(p)$ momentum-space vertex can be obtained from
|
|
this equation by setting $q_1^2 \to 0$ and replacing $h_i^Z \to
|
|
h_i^\gamma$.
|
|
The parameters that
|
|
specify the anomalous couplings, $h_i^Z$ and $h_i^\gamma$ (for $i=1\ldots 4$), are
|
|
specified in the input file as, e.g. {\tt h1(Z)} and {\tt h1(gamma)}.
|
|
If the input file contains a negative value for the form-factor scale $\Lambda$
|
|
then no suppression factors are applied to these anomalous couplings.
|
|
Otherwise, the couplings are included
|
|
in \MCFM only after suppression by dipole form factors,
|
|
\begin{displaymath}
|
|
h_{1,3}^{Z/\gamma} \rightarrow
|
|
\frac{h_{1,3}^{Z/\gamma}}{(1+\hat{s}/\Lambda^2)^3}, \qquad
|
|
h_{2,4}^{Z/\gamma} \rightarrow
|
|
\frac{h_{2,4}^{Z/\gamma}}{(1+\hat{s}/\Lambda^2)^4}, \qquad
|
|
\end{displaymath}
|
|
where $\hat{s}$ is the $Z\gamma$ pair invariant mass. Note that these form factors are slightly
|
|
different from those discussed in Sections~\ref{subsec:diboson} and~\ref{subsec:wgamma}. The
|
|
form factors can be modified in {\ttfamily src/Need/set\_anomcoup.f}.
|
|
|
|
The Standard Model cross section is obtained by setting $h_i^Z = h_i^\gamma = 0$ for $i=1\ldots 4$.
|
|
|
|
\subsection{$Z\gamma\gamma$ production processes, 301, 306}
|
|
|
|
Processes {\tt{301}} and {\tt{306}} represent the production of a $Z$ boson
|
|
(or virtual photon for process {\tt 301}) in association with two photons. The $Z/\gamma^*$ subsequently decays into
|
|
either an $e^+ e^-$ pair ({\tt nproc=301}) or neutrinos ({\tt nproc=306}).
|
|
Since these processes include real photons, the cross section diverges
|
|
when either of the photons is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. Moreover, when the parameters {\tt zerowidth}
|
|
and {\tt removebr} are set to {\tt .false.} the decay $Z \to e^- e^+$ ({\tt nproc=301})
|
|
will include photon radiation from both leptons, so that a non-zero {\tt R(photon,lept)\_min}
|
|
should also be supplied. This will ensure that the cross section is well-defined.
|
|
Anomalous couplings are not currently implemented for these processes.
|
|
|
|
\subsection{$Z\gamma j$, production, processes 302, 307}
|
|
\label{subsec:zgammajet}
|
|
Processes {\tt 302} and {\tt 307} represent the production of a $Z$ boson (or virtual photon)
|
|
in association with a real photon and at least one jet.
|
|
The $Z/\gamma^*$ subsequently decays into
|
|
either an $e^+ e^-$ pair ({\tt nproc=302}) or neutrinos ({\tt nproc=307}).
|
|
Since these processes include a real photon and a jet, the cross section diverges
|
|
when the photon or jet is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}, and {\tt ptjet\_min} and {\tt etajet\_max}.
|
|
Moreover, when the parameters {\tt zerowidth}
|
|
and {\tt removebr} are set to {\tt .false.} the decay $Z \to e^- e^+$ ({\tt nproc=302})
|
|
will include photon radiation from both leptons, so that a non-zero {\tt R(photon,lept)\_min}
|
|
should also be supplied. This will ensure that the cross section is well-defined.
|
|
The calculation of processes {\tt 302} and {\tt 307} may be performed
|
|
at NLO using the Frixione algorithm~\cite{Frixione:1998jh} or standard isolation.
|
|
Anomalous couplings are not currently implemented for these processes.
|
|
|
|
|
|
\subsection{$Z\gamma\gamma j$ and $Z\gamma j j $, 303, 304, 308 and 309}
|
|
|
|
These processes are available at LO only. The $Z/\gamma^*$ subsequently decays into
|
|
either an $e^+ e^-$ pair ({\tt nproc=303,304}) or neutrinos ({\tt nproc=308,309}).
|
|
Since these processes include a real photon and a jet, the cross section diverges
|
|
when a photon or a jet is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}, and {\tt ptjet\_min} and {\tt etajet\_max}.
|
|
Moreover, when the parameters {\tt zerowidth}
|
|
and {\tt removebr} are set to {\tt .false.} the decay $Z \to e^- e^+$ ({\tt nproc=303, 304})
|
|
will include photon radiation from both leptons, so that a non-zero {\tt R(photon,lept)\_min}
|
|
should also be supplied. This will ensure that the cross section is well-defined.
|
|
Anomalous couplings are not currently implemented for these processes.
|
|
|
|
|
|
|
|
%Processes {\tt 303} and {\tt 308} represents the production of a $Z$ boson (or virtual photon)
|
|
%in association with a two photons and and an additional jet. These processes are available at leading order only.
|
|
%These processes do not currently have anomalous couplings implemented.
|
|
|
|
\subsection{$W+Q+$~jet production processes 311--326}
|
|
\label{subsec:wQj}
|
|
|
|
These processes represent the production of a $W$
|
|
boson that decays leptonically,
|
|
in association with a heavy quark, $Q$ and an additional light jet. In
|
|
processes {\tt 311} and {\tt 316} $Q$ is a bottom quark, whilst
|
|
processes {\tt 321} and {\tt 326} involve a charm quark.
|
|
In these processes the quark $Q$ occurs as parton PDF in the initial state.
|
|
The initial state in these processes consists of a light quark and a heavy
|
|
quark, with the light quark radiating the $W$ boson. These calculations may
|
|
be performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+c+$~jet production, processes 331, 336}
|
|
\label{subsec:wcj}
|
|
|
|
These processes represent the production of a $W$
|
|
boson that decays leptonically,
|
|
in association with a charm quark and an additional light jet.
|
|
|
|
In contrast to processes {\tt 321} and {\tt 326} described above, the initial
|
|
state in this case consists of two light quarks, one of which is a
|
|
strange quark which radiates the $W$ boson. The calculation may
|
|
be performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$Z+Q+$jet production, processes 341--357}
|
|
\label{subsec:ZQj}
|
|
|
|
\begin{center}
|
|
[{\it For more details on this calculation, please refer to hep-ph/0510362}]
|
|
\end{center}
|
|
|
|
These processes represent the production of a $Z$
|
|
boson that decays into a pair of electrons,
|
|
in association with a heavy quark, $Q$ and an untagged jet.
|
|
|
|
For processes {\tt 341} and {\tt 351} the initial state at lowest
|
|
order is the heavy quark and a gluon and the calculation may be
|
|
performed at NLO. Thus in these processes the quark $Q$ occurs as
|
|
parton PDF in the initial state. As for $H+b$ and $Z+Q$ production,
|
|
the matrix elements are divided into two sub-processes at NLO. Thus
|
|
the user must sum over these after performing more runs than usual. At
|
|
lowest order one can proceed as normal, using {\tt nproc=341} (for
|
|
$Zbj$) or {\tt nproc=351} (for $Zcj$). For a NLO calculation, the
|
|
sequence of runs is as follows:
|
|
\begin{itemize}
|
|
\item Run {\tt nproc=341} (or {\tt 351}) with {\tt part=virt} and
|
|
{\tt part=real} (or, both at the same time using {\tt part=tota});
|
|
\item Run {\tt nproc=342} (or {\tt 352}) with {\tt part=real}.
|
|
\end{itemize}
|
|
The sum of these yields the cross-section with one identified heavy
|
|
quark and one untagged jet in the final state when {\tt inclusive} is
|
|
set to {\tt .false.} . To calculate the rate for at least one heavy
|
|
quark and one jet (the remaining jet may be a heavy quark, or
|
|
untagged), {\tt inclusive} should be {\tt .true.}.
|
|
|
|
Processes {\tt 346,347} and {\tt 356,357} are the lowest order processes that enter
|
|
the above calculation in the real contribution. They can be computed only at LO.
|
|
|
|
When {\tt removebr} is true, the $Z$ boson does not decay.
|
|
|
|
\subsection{$c \overline s \to W^+$, processes 361--363}
|
|
\label{subsec:csbar}
|
|
These processes represent the production of a $W^+$ from a charm and anti-strange
|
|
quark at LO. The $W^+$ boson decays into a neutrino and a positron.
|
|
|
|
The NLO corrections to this LO process include a contribution of the form,
|
|
$g\overline s \to W^+ \overline c$. For process {\tt 361} this contribution is
|
|
calculated in the approximation $m_c=0$ at NLO. In order to perform the NLO calculation
|
|
for a non-zero value of $m_c$, one must instead sum the results of processes {\tt 362}
|
|
and {\tt 363} for {\tt part=tota}.
|
|
|
|
\subsection{$W\gamma\gamma$ production, processes 370-371}
|
|
\label{subsec:wgamgam}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically, in association with two real photons.
|
|
Since this process includes real photons, the cross section diverges
|
|
when the photon is very soft or in the direction of the beam.
|
|
Thus in order to produce sensible results, the input file must supply values for both
|
|
{\tt ptmin\_photon} and {\tt etamax\_photon}. Moreover, when the parameters {\tt zerowidth}
|
|
and {\tt removebr} are set to {\tt .false.} the decay $W \to \ell \nu$ will include
|
|
photon radiation from the lepton, so that a non-zero {\tt R(photon,lept)\_min} should
|
|
also be supplied. This will ensure that the cross section is well-defined.
|
|
|
|
These processes may be computed at leading order only.
|
|
|
|
\subsection{$W+Q$ production in the 4FNS, processes 401--408}
|
|
\label{subsec:wbbfilter}
|
|
These processes represent the production of a $W$ boson and one or more jets,
|
|
at least one of which is a $b$-quark, calculated in the 4-flavour number scheme (4FNS).
|
|
This implies that contributions that explicitly contain a $b$-quark in the initial state
|
|
are not included.
|
|
These processes all use the same matrix
|
|
elements as processes 20 and 25 (see section~\ref{subsec:wbb}), but make different
|
|
cuts on the final state. The final state is specified by the process number and
|
|
the value of the flag {\tt inclusive}, as shown in Table~\ref{table:wbbfilter}.
|
|
An additional flag is hard-coded into the file {\tt src/User/filterWbbmas.f} to control
|
|
the inclusion of the 3-jet configuration, $(b,\overline b,j)$ when {\tt inclusive} is set to {\tt .true.}.
|
|
By default this is included, {\tt veto3jets = .false.}. If this flag is set to {\tt .true.}
|
|
then the $(b,\overline b,j)$ contribution
|
|
is not included in processes 401, 402, 406, 407.
|
|
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c|} \hline
|
|
Process ($W^+$/$W^-$) & {\tt inclusive=.false.} & {\tt inclusive=.true.} \\
|
|
\hline
|
|
{\tt 401}/{\tt 406} & $(b)$ or $(\overline b)$ & + ($b,\overline b$) or ($b,j$) or ($\overline b,j$) \\
|
|
{\tt 402}/{\tt 407} & $(B)$ & + ($B,j$) \\
|
|
{\tt 403}/{\tt 408} & $(b,\overline b)$ & \mbox{(no extra configurations)} \\
|
|
\hline
|
|
\end{tabular}
|
|
\caption{The different final states allowed in the calculation of processes 401--408. A jet containing
|
|
both $b$ and $\overline b$ quarks is denoted by $B$ and a light (quark or gluon) jet by $j$. The inclusive
|
|
(right-hand) column also allows the final states in the exclusive (middle) column.}
|
|
\label{table:wbbfilter}
|
|
\end{center}
|
|
\end{table}
|
|
|
|
As usual, jets may be unobserved as a result of them falling outside the $p_T$
|
|
and rapidity ranges specified in the input file. In addition, the number of jets
|
|
may be different from the number of partons in the matrix element calculation as
|
|
a result of merging in the jet algorithm.
|
|
|
|
\subsection{$W+Q$ production in the 5FNS, processes 411, 416}
|
|
\label{subsec:wb5FNS}
|
|
|
|
These processes represent production of a $W$ boson in association with a
|
|
$b$-jet, computed in the 5-flavour number scheme, i.e. a $b$-quark is present in
|
|
the initial state. The lowest order processes are the same as in processes {\tt 311}, {\tt 316}.
|
|
The results at NLO are not physical cross sections since part of the corrections
|
|
are not included in order to avoid double-counting with the 4FNS process (processes
|
|
{\tt 401} and {\tt 406}). To obtain combined 4FNS+5FNS predictions, the user
|
|
should select process {\tt 421} ($W^+$) or {\tt 426} ($W^-$).
|
|
|
|
\subsection{$W+Q$ production in the combined 4FNS/5FNS, processes 421, 426}
|
|
\label{subsec:wbcombined}
|
|
These processes represent the production of a $W$ boson and one or more jets,
|
|
at least one of which is a $b$-quark, calculated by combining the 4- and 5-flavour results
|
|
of processes {\tt 401}, {\tt 411} (for {\tt 421}) and {\tt 406}, {\tt 416} (for {\tt 426}).
|
|
The selection of the final state is the same as for processes {\tt 401} and {\tt 406}, as
|
|
described in Section~\ref{subsec:wbbfilter}. The procedure for combining the two
|
|
calculations is described in refs.~\cite{Campbell:2008hh,Caola:2011pz}.
|
|
|
|
\subsection{$W+b{\bar b}+$~jet production, processes 431,436}
|
|
\label{subsec:wbbjetmassive}
|
|
|
|
These processes represent the production of a $W$ boson which subsequently
|
|
decays leptonically, in association with a $b{\bar b}$ pair and an
|
|
additional jet. The effect of the bottom quark mass is included (c.f. the massless approximation
|
|
used in processes {\tt 24}, {\tt 29})
|
|
and the calculation may be performed at LO only.
|
|
|
|
When {\tt removebr} is true, the $W$ boson does not decay.
|
|
|
|
\subsection{$W+t{\bar t}$ processes 500--516}
|
|
\label{subsec:wttdecay}
|
|
|
|
These processes represent the production of a $W^\pm$ boson which subsequently
|
|
decays leptonically, in association with a $t{\bar t}$ pair. In all except processes
|
|
{\tt 500} and {\tt 510} the decays of the top and anti-top quark are included.
|
|
Processes {\tt 501,502} and {\tt 511,512} refer to the semileptonic decay of the top and antitop quarks,
|
|
with the latter process in each pair giving the radiation in the decay of the top and antitop.
|
|
Process {\tt 503} ({\tt 513}) refers to the semileptonic decay of the top (antitop)
|
|
and the hadronic decay of the antitop (top). Processes {\tt 506}({\tt 516}) gives the semileptonic
|
|
decay of the antitop(top) and the hadronic decay of the top(antitop). Processes {\tt 506}({\tt 516})
|
|
do not give same sign lepton events, so they may be of less phenomenological importance. For this reason
|
|
we have not yet included radiation in the decay for these processes.
|
|
|
|
For processes {\tt 503}, {\tt 506}, {\tt 513}
|
|
and {\tt 516} the default behaviour is that the hadronic decay products
|
|
are clustered into jets using the supplied jet
|
|
algorithm parameters, but no cut is applied on the number of jets.
|
|
This behaviour can be altered by changing the value of the
|
|
variable {\tt notag} in the file {\tt src/User/setnotag.f}.
|
|
|
|
The top quarks are always
|
|
produced on-shell, which is a necessity for a gauge invariant result
|
|
from this limited set of diagrams, but all spin correlations are included.
|
|
Switching {\tt zerowidth} from {\tt .true.} to {\tt .false.} only affects
|
|
the $W$ bosons (both the directly produced one and from the top quark decay).
|
|
Processes {\tt 501} and {\tt 511} may be run at NLO with the option {\tt todk},
|
|
including radiation in the decay of the top quark, see section \ref{subsec:ttbar}.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\subsection{$Zt{\bar t}$ production, processes 529-533}
|
|
\label{subsec:ztt}
|
|
|
|
These processes represent the production of a $Z$ boson in association
|
|
with a pair of top quarks.
|
|
For process {\tt 529}, neither the top quarks nor the $Z$-boson
|
|
decays.
|
|
In processes {\tt 530-533}, the top quarks are always
|
|
produced on-shell, which is a necessity for a gauge invariant result
|
|
from this limited set of diagrams.
|
|
Switching {\tt zerowidth} from {\tt .true.} to {\tt .false.} only affects
|
|
the $Z$ and the $W$ bosons from the top quark decay.
|
|
In process {\tt 530} the $Z$ boson decays into an electron pair, whilst
|
|
in {\tt 531} the decay is into a massless bottom quark pair.
|
|
In process {\tt 532--533} the $Z$ boson decays into an electron pair, whilst
|
|
on or other of the top quark or top anti-quark decays hadronically.
|
|
The calculations can be performed at LO only.
|
|
|
|
For processes {\tt 532} and {\tt 533} the default behaviour is that the hadronic decay products
|
|
are clustered into jets using the supplied jet
|
|
algorithm parameters, but no cut is applied on the number of jets.
|
|
This behaviour can be altered by changing the value of the
|
|
variable {\tt notag} in the file {\tt src/User/setnotag.f}.
|
|
|
|
When {\tt removebr} is true in process {\tt 530}, the top quarks and the $Z$ boson do not decay.
|
|
|
|
\subsection{$Ht$ and $H\bar{t}$ production, processes 540--557}
|
|
[{\it For more details on this calculation, please refer to arXiv:1302.3856}]
|
|
|
|
\label{subsec:Ht}
|
|
These processes describe the production of a single top quark ({\tt 540}, {\tt 544}, {\tt 550},
|
|
{\tt 554}) or antiquark ({\tt 541}, {\tt 547}, {\tt 551}, {\tt 557}) by $W$ exchange in the
|
|
$t$-channel, in association with a Higgs boson. These processes can be performed at NLO.
|
|
For processes {\tt 540}, {\tt 541}, {\tt 550},
|
|
{\tt 551}, the top quark does not decay, but the
|
|
Higgs boson decays to $b\bar{b}$, ({\tt 540}, {\tt 541}), or to $\gamma \gamma$, ({\tt 550}, {\tt 551}).
|
|
Processes {\tt 544}, {\tt 547} and {\tt 554}, {\tt 557} include the decay of the top quark and antiquark
|
|
in the approximation in which the top quark is taken to be on shell allowing a clean separation
|
|
between production and decay.
|
|
|
|
It is possible to study the effects of anomalous couplings of the Higgs boson to the top quark and $W$ bosons. These are parametrized by $c_{t\bar{t}H} = g_{t\bar{t}H}/g_{t\bar{t}H}^{SM}$ and $c_{WWH} = g_{WWH}/g_{WWH}^{SM}$ respectively, so that $c_{t\bar{t}H}=c_{WWH}=1$ in the SM. Different couplings may be chosen by modifying the variables {\tt cttH} and {\tt cWWH} in {\tt src/Need/reader$\_$input.f} and recompiling.
|
|
|
|
\subsection{$Zt$ and $Z\bar{t}$ production, processes 560--569}\
|
|
[{\it For more details on this calculation, please refer to arXiv:1302.3856}]
|
|
|
|
\label{subsec:Zt}
|
|
These processes describe the production of a single top quark (or antiquark) by $W$ exchange in the
|
|
$t$-channel, in association with a $Z$ boson. Processes {\tt 560}, {\tt 561},
|
|
{\tt 564}, {\tt 567} can be performed at NLO.
|
|
Processes {\tt 560}-{\tt 563} are for stable top quarks, whereas processes {\tt 564}-{\tt 569}
|
|
include the decay of the top quark and antiquark
|
|
in the approximation inwhich the top quark is taken to
|
|
be on shell allowing a clean separation
|
|
between production and decay.
|
|
|
|
For processes {\tt 564} and {\tt 567} the default behaviour is that the hadronic decay products
|
|
are clustered into jets using the supplied jet
|
|
algorithm parameters, but no cut is applied on the number of jets.
|
|
This behaviour can be altered by changing the value of the
|
|
variable {\tt notag} in the file {\tt src/User/setnotag.f}.
|
|
|
|
\subsection{$HH$ production, processes 601--602}
|
|
These processes represent the production of a pair of Higgs bosons.
|
|
The production proceeds through gluon-fusion one-loop diagrams involving loops
|
|
of top quarks. The formulae implemented in the code are taken from ref.~\cite{Glover:1987nx},
|
|
where the two Higgs bosons are treated as being on-shell. To enforce this
|
|
condition, the code sets zerowidth to true, overriding the value set in the input file.
|
|
The calculation can be performed at LO only, (i.e.\ one-loop order only).
|
|
Two decays of the Higgs bosons are currently foreseen, although other decays can easily be implemented.
|
|
In process {\tt 601}, one Higgs boson decays to
|
|
a pair of $b$-quarks, and the other decays to a pair of $\tau$'s.
|
|
In process {\tt 602}, one Higgs boson decays to
|
|
a pair of $b$-quarks, and the other decays to a pair of photons.
|
|
|
|
\subsection{$Ht{\bar t}$ production, processes 640--660}
|
|
\label{subsec:htt}
|
|
|
|
These processes represent the production of a Higgs boson in association
|
|
with a pair of top quarks. The calculation can be performed at LO only.
|
|
|
|
For process {\tt 640}, neither the top quarks nor the Higgs boson
|
|
decays.
|
|
In processes {\tt 641-647}, the top quarks are always
|
|
produced on-shell, which is a necessity for a gauge invariant result
|
|
from this limited set of diagrams.
|
|
Switching {\tt zerowidth} from {\tt .true.} to {\tt .false.} only affects
|
|
the Higgs and the $W$ bosons from the top quark decay.
|
|
In process {\tt 641} both the top quarks decay leptonically
|
|
and the Higgs boson decays into a pair of bottom quarks.
|
|
Consistency with
|
|
the simpler process ({\tt 640}) can be demonstrated by running process
|
|
{\tt 641} with {\tt removebr} set to true.
|
|
In process {\tt 644} the top quark decays leptonically
|
|
and the anti-top quark decays hadronically and the Higgs boson decays into a pair of bottom quarks.
|
|
In process {\tt 647} the anti-top quark decays leptonically
|
|
and the top quark decays hadronically and the Higgs boson decays into a pair of bottom quarks.
|
|
|
|
Processes {\tt 651}--{\tt 657} correspond to processes {\tt 641}--{\tt 647} but with the Higgs decaying
|
|
to two photons.
|
|
Processes {\tt 661}--{\tt 667} correspond to processes {\tt 641}--{\tt 647} but with the Higgs decaying
|
|
to two $W$-bosons which subsequently decay leptonically.
|
|
|
|
\subsection{Dark Matter Processes Mono-jet and Mono-photon 800-848}
|
|
[{\it For more details on this calculation, please refer to arXiv:1211.6390}]
|
|
|
|
This section provides an overview of the Dark Matter (DM) processes
|
|
available in \MCFM. Since these processes are quite different in the
|
|
range of possible input parameters (reflecting the range of potential
|
|
BSM operators) the majority of the new features are controlled by the
|
|
file {\tt dm\_parameters.DAT} located in the {\tt Bin} directory. We
|
|
begin this section by describing the inputs in this file. Note that
|
|
these processes are still controlled, as usual by {\tt input.DAT}
|
|
which is responsible for selecting the process, order in perturbation
|
|
theory, PDFs and phase space cuts etc. The new file controls only the
|
|
new BSM parameters in the code.
|
|
|
|
\begin{itemize}
|
|
\item
|
|
{\tt [dm mass]} This parameter sets the mass of the dark matter particle $m_{\chi}$.
|
|
\item
|
|
{\tt [Lambda]} Controls the mass scale associated with the suppression of the higher dimensional operator in the effective theory approach. Note that each
|
|
operator has a well defined scaling with respect to Lambda, so cross sections and distributions obtained with one particular value can be readily extended to
|
|
determine those with different $\Lambda$.
|
|
\item
|
|
{\tt [effective theory] } Is a logical variable which controls whether or not the effective field theory is used in the calculation of the DM process. If this value is set to
|
|
{\tt .false.} then one must specify the mass of the light mediator and its width (see below for more details).
|
|
\item
|
|
{\tt [Yukawa Scalar couplings]} Is a logical variable which determines if the scalar and pseudo scalar operators scale with the factor $m_{q}/\Lambda$ ( {\tt. .true.})
|
|
or 1 ({\tt .false.}).
|
|
\item
|
|
{ \tt [Left handed DM couplings] } and { \tt [Right handed DM couplings] }
|
|
These variables determine the coupling of the
|
|
various flavours of quarks to the DM operators. The default value is 1.
|
|
Note that the code uses the fact that vector operators scale as
|
|
$(L+R)$ and axial operators scale as $(L-R)$ in constructing cross
|
|
sections. Therefore you should be careful if modifying these
|
|
parameters. For the axial and pseudo scalar operators the code will
|
|
set the right-handed couplings to be the negative of the left handed
|
|
input couplings (if this is not already the case from the setup) and
|
|
inform the user it has done so. The most likely reason to want to
|
|
change these values is to inspect individual flavour operators
|
|
separately, i.e.\ to investigate an operator which only couples to up
|
|
quarks one would set all couplings to 0d0 apart from {\tt [up type]}
|
|
which would be left as 1d0.
|
|
\item
|
|
{\tt [mediator mass]} If {\tt [effective theory]} is set to {\tt .false.} this variable controls the mass of the mediating particle.
|
|
\item
|
|
{\tt [mediator width]} If {\tt [effective theory]} is set to {\tt .false.} this variable controls the width of the mediating particle
|
|
\item
|
|
{\tt [g\_x]} If {\tt [effective theory]} is set to {\tt .false.} this variable controls the coupling of the mediating particle to the DM.
|
|
\item
|
|
{\tt [g\_q]} If {\tt [effective theory]} is set to {\tt .false.} this variable controls the coupling of the mediating particle to the quarks.
|
|
\end{itemize}
|
|
|
|
We now discuss some details of the specific DM process.
|
|
|
|
\begin{itemize}
|
|
\item
|
|
Processes 800 and 820 produce the
|
|
mono-jet or mono-photon signature through the following vector operator,
|
|
\begin{eqnarray}
|
|
\mathcal{O}_V&=&\frac{(\overline{\chi}\gamma_{\mu}\chi)(\overline{q}\gamma^{\mu}q)}{\Lambda^2}~,\label{eq:OV}
|
|
\end{eqnarray}
|
|
These processes are available at NLO and include the usual treatment of photons. See for instance the $V\gamma$ processes ($\sim$ 300) in this
|
|
manual for more details on photon setup in \MCFM. As discussed above the code will calculate left and right-handed helicity amplitudes and build the
|
|
vector operators from $(L+R)$. Therefore you should ensure that the Left and right-handed couplings are equal in {\tt dm\_parameters.DAT}.
|
|
Processes 840 and 845 represent the production of DM plus two jets or DM plus one jet and one photon and are available at LO.
|
|
\item
|
|
Processes 801 and 821 produce the
|
|
mono-jet or mono-photon signature through the following axial-vector operator,
|
|
\begin{eqnarray}
|
|
\mathcal{O}_A&=&\frac{(\overline{\chi}\gamma_{\mu}\gamma_5\chi)(\overline{q}\gamma^{\mu}\gamma_5q)}{\Lambda^2}~,\label{eq:OA}
|
|
\end{eqnarray}
|
|
These processes are available at NLO and include the usual treatment
|
|
of photons. See for instance the $V\gamma$ processes ($\sim$ 300) in
|
|
this manual for more details on photon setup in \MCFM. As discussed
|
|
above the code will calculate left and right-handed helicity
|
|
amplitudes and build the axial vector operators from $(L-R)$. By
|
|
default the code will enforce the right handed couplings to equal to
|
|
the negative of the left handed couplings, if this is not
|
|
already the case in {\tt dm\_parameters.DAT}. Therefore the user does
|
|
not have to change this file when switching between vector and axial
|
|
vector operators. Processes 841 and 846 represent the production of
|
|
DM plus two jets or DM plus one jet and one photon and are available
|
|
at LO.
|
|
\item
|
|
Processes 802 and 822 produce the
|
|
mono-jet or mono-photon signature through the following scalar operator,
|
|
\begin{eqnarray}
|
|
\mathcal{O}_S&=&\frac{\Delta(\overline{\chi}\chi)(\overline{q}q)}{\Lambda^2}~,
|
|
\end{eqnarray}
|
|
These processes are available at NLO and include the usual treatment
|
|
of photons. See for instance the $V\gamma$ processes ($\sim$ 300) in
|
|
this manual for more details on photon setup in \MCFM. As discussed
|
|
above the code will calculate left and right-handed helicity
|
|
amplitudes and build the vector operators from $(L+R)$. Therefore you
|
|
should ensure that the Left and right-handed couplings are equal in
|
|
{\tt dm\_parameters.DAT}. For these processes $\Delta$ is fixed from
|
|
the value of {\tt [Yukawa Scalar Couplings] } if this is {\tt .true.}
|
|
then $\Delta=m_q/\Lambda$ else $\Delta=1$.
|
|
|
|
Processes 842 and 847 represent the production of DM plus two jets or DM plus one jet and one photon and are available at LO.
|
|
\item
|
|
Processes 803 and 823 produce the
|
|
mono-jet or mono-photon signature through the following pseudo-scalar operator,
|
|
\begin{eqnarray}
|
|
\mathcal{O}_{PS}&=&\frac{m_q(\overline{\chi}\gamma_5\chi)(\overline{q}\gamma_5q)}{\Lambda^3}\label{eq:OPS}~.
|
|
\end{eqnarray}
|
|
These processes are available at NLO and include the usual treatment
|
|
of photons. See for instance the $V\gamma$ processes ($\sim$ 300) in
|
|
this manual for more details on photon setup in \MCFM. As discussed
|
|
above the code will calculate left and right-handed helicity
|
|
amplitudes and build the pseudo scalar operators from $(L-R)$. By
|
|
default the code will enforce the right handed couplings to equal to
|
|
the negative of the left handed couplings, if this is not
|
|
already the case in {\tt dm\_parameters.DAT}. Therefore the user does
|
|
not have to change this file when switching between scalar and pseudo
|
|
scalar operators. Processes 841 and 846 represent the production of
|
|
DM plus two jets or DM plus one jet and one photon and are available
|
|
at LO. For these processes $\Delta$ is fixed from the value of {\tt
|
|
[Yukawa Scalar Couplings] } if this is {\tt .true.} then
|
|
$\Delta=m_q/\Lambda$ else $\Delta=1$.
|
|
|
|
Processes 843 and 848 represent the production of DM plus two jets or DM plus one jet and one photon and are available at LO.
|
|
|
|
\item
|
|
Process 804 produces the
|
|
mono-jet signature through the following gluon induced operator,
|
|
\begin{eqnarray}
|
|
\mathcal{O}_g&=&\alpha_s\frac{(\chi\overline{\chi})(G^{\mu\nu}_aG_{a,\mu\nu})}{\Lambda^3}~,
|
|
\end{eqnarray}
|
|
This process is available at NLO. Process 844 represents the
|
|
production of DM plus two jets and is available at LO. Since this
|
|
operator is higher dimensional, extensions to a theory in which there
|
|
is a light mediator requires the definition of two new scales (one for
|
|
the EFT in the loop defining the operator). In this version we
|
|
therefore do not consider in a theory with a light mediator.
|
|
\item
|
|
Process 805 is a separate case of the scalar operator for top quarks
|
|
\begin{eqnarray}
|
|
\mathcal{O}^{m_t}_S&=&\frac{m_t(\overline{\chi}\chi)(\overline{q}q)}{\Lambda^3}~,
|
|
\end{eqnarray}
|
|
This process is available at LO and proceeds through a gluon loop.
|
|
\end{itemize}
|
|
|
|
\section*{Acknowledgments}
|
|
We are happy to acknowledge Fabrizio Caola, Heribertus Hartanto, Fabio
|
|
Maltoni, Raoul R{\"o}ntsch, Gavin Salam, Francesco Tramontano and
|
|
Giulia Zanderighi for their contributions to the code.
|
|
|
|
The original histogramming package mbook.f included in the code is due
|
|
to Michelangelo Mangano. The integration routine vegas.f is due to
|
|
Peter Lepage. The routine XLUDecomp is taken from looptools and is
|
|
adapted from Michael Rauch.
|
|
|
|
|
|
|
|
\appendix
|
|
\section{\MCFM references}
|
|
\label{MCFMrefs}
|
|
|
|
As general references for NLO computations with MCFM, please use:
|
|
\begin{itemize}
|
|
\item J.~M.~Campbell and R.~K.~Ellis, \\
|
|
{\it ``An update on vector boson pair production at hadron colliders,''} \\
|
|
Phys.\ Rev.\ D {\bf 60}, 113006 (1999)
|
|
[arXiv:hep-ph/9905386].
|
|
\item J.~M.~Campbell, R.~K.~Ellis and C.~Williams, \\
|
|
{\it ``Vector boson pair production at the LHC,''} \\
|
|
JHEP {\bf 1107}, 018 (2011)
|
|
[arXiv:1105.0020 [hep-ph]].
|
|
\item J.~M.~Campbell, R.~K.~Ellis and W.~Giele, \\
|
|
{\it ``A Multi-Threaded Version of MCFM''}, \\
|
|
EPJ {\bf C75}, 246 (2015)
|
|
[arXiv:1503.06182 [hep-ph]].
|
|
|
|
\end{itemize}
|
|
|
|
When using MCFM 8.0, or later versions, for NNLO calculations of color-singlet
|
|
processes please refer to:
|
|
\begin{itemize}
|
|
\item
|
|
R.~Boughezal, J.~M.~Campbell, R.~K.~Ellis, \\
|
|
C.~Focke, W.~Giele, X.~Liu,~F. Petriello and C.~Williams, \\
|
|
{\it ``Color singlet production at NNLO in MCFM''},
|
|
arXiv:1605.08011.
|
|
\end{itemize}
|
|
|
|
For calculations of electroweak corrections please refer to:
|
|
\begin{itemize}
|
|
\item
|
|
J.~M.~Campbell, D.~Wackeroth and J.~Zhou, \\
|
|
{\it ``A Study of Weak Corrections to Drell-Yan, Top-quark pair and Di-jet
|
|
Production at High Energies with MCFM''},
|
|
arXiv:1608.03356.
|
|
\end{itemize}
|
|
|
|
Additional references to the program may be used depending on the process under study. The relevant papers are:
|
|
\begin{itemize}
|
|
\item J.~M.~Campbell and R.~K.~Ellis, \\
|
|
{\it ``Radiative corrections to Z b anti-b production,''} \\
|
|
Phys.\ Rev.\ D {\bf 62}, 114012 (2000)
|
|
[arXiv:hep-ph/0006304].
|
|
\item J.~Campbell and R.~K.~Ellis, \\
|
|
{\it ``Next-to-leading order corrections to W + 2jet and Z + 2jet production at
|
|
hadron colliders,''} \\
|
|
Phys.\ Rev.\ D {\bf 65}, 113007 (2002)
|
|
[arXiv:hep-ph/0202176].
|
|
\item J.~Campbell, R.~K.~Ellis, F.~Maltoni and S.~Willenbrock, \\
|
|
{\it ``Higgs boson production in association with a single bottom quark,''} \\
|
|
Phys.\ Rev.\ D {\bf 67}, 095002 (2003)
|
|
[arXiv:hep-ph/0204093].
|
|
\item J.~Campbell, R.~K.~Ellis and D.~L.~Rainwater, \\
|
|
{\it ``Next-to-leading order QCD predictions for W + 2jet and Z + 2jet production
|
|
at the CERN LHC,''} \\
|
|
Phys.\ Rev.\ D {\bf 68}, 094021 (2003)
|
|
[arXiv:hep-ph/0308195].
|
|
\item J.~Campbell, R.~K.~Ellis, F.~Maltoni and S.~Willenbrock, \\
|
|
{\it ``Associated production of a Z boson and a single heavy-quark jet,''} \\
|
|
Phys.\ Rev.\ D {\bf 69}, 074021 (2004)
|
|
[arXiv:hep-ph/0312024].
|
|
\item E.~L.~Berger and J.~Campbell, \\
|
|
{\it ``Higgs boson production in weak boson fusion at next-to-leading order,''} \\
|
|
Phys.\ Rev.\ D {\bf 70}, 073011 (2004)
|
|
[arXiv:hep-ph/0403194].
|
|
\item J.~Campbell, R.~K.~Ellis and F.~Tramontano, \\
|
|
{\it ``Single top production and decay at next-to-leading order,''} \\
|
|
Phys.\ Rev.\ D {\bf 70}, 094012 (2004)
|
|
[arXiv:hep-ph/0408158].
|
|
\item J.~Campbell and F.~Tramontano, \\
|
|
{\it ``Next-to-leading order corrections to Wt production and
|
|
decay,''} \\
|
|
Nucl.\ Phys.\ B {\bf 726}, 109 (2005)
|
|
[arXiv:hep-ph/0506289].
|
|
\item J.~Campbell, R.K.~Ellis, F.~Maltoni and S.~Willenbrock, \\
|
|
{\it ``Production of a $Z$ boson and two jets with one heavy quark tag,''} \\
|
|
Phys.\ Rev.\ D {\bf 73}, 054007 (2006)
|
|
[arXiv:hep-ph/0510362].
|
|
\item J.~M.~Campbell, R.~Frederix, F.~Maltoni and F.~Tramontano,\\
|
|
{\it ``$t$-channel single top production at hadron colliders,''} \\
|
|
Phys. Rev. Lett. {\bf 102} (2009) 182003,
|
|
[arXiv:0903.0005 [hep-ph]].
|
|
\item J.~M.~Campbell, R.~K.~Ellis and G.~Zanderighi, \\
|
|
{\it ``Next-to-leading order Higgs~$+~2$~jet production via gluon fusion,''} \\
|
|
JHEP {\bf 0610}, 028 (2006)
|
|
[arXiv:hep-ph/0608194].
|
|
\item J.~Campbell, R.K.~Ellis, F.~Maltoni and S.~Willenbrock, \\
|
|
{\it ``Production of a $W$ boson and two jets with one $b$-quark
|
|
tag,''} \\
|
|
Phys.\ Rev.\ D {\bf 75}, 054015 (2007)
|
|
[arXiv:hep-ph/0611348].
|
|
\item J.~M.~Campbell, R.~K.~Ellis, F.~Febres Cordero, F.~Maltoni, L.~Reina, D.~Wackeroth and S.~Willenbrock, \\
|
|
{\it ``Associated Production of a $W$ Boson and One $b$ Jet,''} \\
|
|
Phys.\ Rev.\ D {\bf 79}, 034023 (2009)
|
|
[arXiv:0809.3003 [hep-ph]].
|
|
\item J.~M.~Campbell, R.~K.~Ellis and C.~Williams, \\
|
|
{\it ``Hadronic production of a Higgs boson and two jets at next-to-leading order,''} \\
|
|
Phys.\ Rev.\ D {\bf 81} 074023 (2010),
|
|
[arXiv:1001.4495 [hep-ph]].
|
|
\item S.~Badger, J.~M.~Campbell and R.~K.~Ellis, \\
|
|
{\it ``QCD corrections to the hadronic production of a heavy quark pair and a W-boson including decay correlations,''} \\
|
|
JHEP {\bf 1103}, 027 (2011)
|
|
[arXiv:1011.6647 [hep-ph]].
|
|
\item F.~Caola, J.~M.~Campbell, F.~Febres Cordero, L.~Reina and D.~Wackeroth, \\
|
|
{\it ``NLO QCD predictions for $W+1$ jet and $W+2$ jet production with at least one b jet at the 7 TeV LHC,''} \\
|
|
arXiv:1107.3714 [hep-ph].
|
|
\item J.~M.~Campbell, R.~K.~Ellis and C.~Williams, \\
|
|
{\it ``Gluon-gluon contributions to W+ W- production and Higgs interference effects,''} \\
|
|
JHEP {\bf 1110}, 005 (2011),
|
|
arXiv:1107.5569 [hep-ph].
|
|
\item J.~M.~Campbell and R.~K.~Ellis, \\
|
|
{\it ``Top-quark processes at NLO in production and decay,''} \\
|
|
arXiv:1204.1513 [hep-ph], FERMILAB-PUB-12-078-T.
|
|
%\cite{Campbell:2012dh}
|
|
\item J.~M.~Campbell and R.~K.~Ellis, \\
|
|
{\it ``$t \bar{t} W^{\pm}$ production and decay at NLO,''} \\
|
|
JHEP {\bf 1207}, 052 (2012), [arXiv:1204.5678 [hep-ph]].
|
|
\item
|
|
J.~M.~Campbell, H.~B.~Hartanto and C.~Williams\\
|
|
{\it {``Next-to-leading order predictions for $Z \gamma$+jet and
|
|
Z $\gamma \gamma$ final states at the LHC"}}
|
|
JHEP {\bf 1211}, 162 (2012), [arXiv:1208.0566 [hep-ph]].
|
|
\item
|
|
P.~J.~Fox and C.~Williams\\
|
|
{\it {``Next-to-leading order predictions for Dark Matter Production at Hadron Colliders"}}
|
|
[arXiv:1211.6390 [hep-ph]].
|
|
\item
|
|
J.~M.~Campbell, R.~K.~Ellis and R.~R{\"o}ntsch,
|
|
{\it ``Single top production in association with a Z boson at the LHC,''}
|
|
arXiv:1302.3856 [hep-ph].
|
|
|
|
\item
|
|
J.~M.~Campbell, R.~K.~Ellis and C.~Williams,
|
|
{\it ``Associated Production of a Higgs Boson at NNLO''},
|
|
arXiv:1601.00658 [hep-ph].
|
|
|
|
\item
|
|
J.~M.~Campbell, R.~K.~Ellis, Ye~Li and C.~Williams,
|
|
{\it ``Predictions for Diphoton Production at the LHC through NNLO in QCD''},
|
|
arXiv:1603.02663 [hep-ph].
|
|
|
|
\item \fullcite{Neumann:2016dny}
|
|
|
|
\item \fullcite{Campbell:2017aul}
|
|
|
|
\item \fullcite{Neumann:2018bsx}
|
|
|
|
\item \fullcite{Neumann:2019kvk}
|
|
|
|
\end{itemize}
|
|
|
|
The following publications have also made use of calculations
|
|
implemented in MCFM, but the corresponding code has not yet been made
|
|
public. Versions of the code that contain these calculations will be
|
|
released in the future.
|
|
|
|
\begin{itemize}
|
|
\item J.~Campbell, F.~Maltoni and F.~Tramontano, \\
|
|
{\it ``QCD corrections to $J/\psi$ and $\Upsilon$ production
|
|
at hadron colliders,''} \\
|
|
Phys. Rev. Lett. {\bf 98}, 252002 (2007)
|
|
[arXiv:hep-ph/0703113].
|
|
\item R.~K.~Ellis, K.~Melnikov and G.~Zanderighi,\\
|
|
{\it ``Generalized unitarity at work: first NLO QCD results for hadronic $W+$~3 jet production,''}
|
|
arXiv:0901.4101 [hep-ph].
|
|
\end{itemize}
|
|
|
|
\clearpage
|
|
\section{Processes included in MCFM}
|
|
\label{MCFMprocs}
|
|
\begin{table}
|
|
\begin{center}
|
|
\hspace*{-1.5cm}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
{\tt nproc} & $f(p_1)+f(p_2) \to \ldots $& Order \\
|
|
\hline
|
|
%
|
|
1 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))$ & NNLO \\
|
|
6 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))$ & NNLO \\
|
|
\hline
|
|
11 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+f(p_{5})$ & NLO \\
|
|
12 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\bar{b}(p_{5})$ & NLO \\
|
|
13 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\bar{c}(p_{5})$ & NLO \\
|
|
14 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\bar{c}(p_{5}) [\mbox{massless}]$ & LO \\
|
|
16 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+f(p_{5})$ & NLO \\
|
|
17 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+b(p_{5})$ & NLO \\
|
|
18 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+c(p_{5})$ & NLO \\
|
|
19 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+c(p_{5}) [\mbox{massless}]$ & LO \\
|
|
\hline
|
|
20 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +b(p_{5})+\bar{b}(p_{6}) [\mbox{massive}]$ & NLO \\
|
|
21 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +b(p_{5})+\bar{b}(p_{6})$ & NLO \\
|
|
22 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +f(p_{5})+f(p_{6})$ & NLO \\
|
|
23 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +f(p_{5})+f(p_{6})+f(p_{7})$ & LO \\
|
|
24 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +b(p_{5})+\bar{b}(p_{6})+f(p_{7})$ & LO \\
|
|
25 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) +b(p_{5})+\bar{b}(p_{6}) [\mbox{massive}]$ & NLO \\
|
|
26 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) +b(p_{5})+\bar{b}(p_{6})$ & NLO \\
|
|
27 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) +f(p_{5})+f(p_{6})$ & NLO \\
|
|
28 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) +f(p_{5})+f(p_{6})+f(p_{7})$ & LO \\
|
|
29 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) +b(p_{5})+\bar{b}(p_{6})+f(p_{7})$ & LO \\
|
|
\hline
|
|
31 & $ Z(\to e^-(p_{3})+e^+(p_{4}))$ & NNLO \\
|
|
310 & $ Z(\to e^-(p_{3})+e^+(p_{4}))$ [photon induced] & LO \\
|
|
32 & $ Z(\to 3\times(\nu(p_{3})+\bar{\nu}(p_{4})))$ & NNLO \\
|
|
33 & $ Z(\to b(p_{3})+\bar{b}(p_{4}))$ & NLO \\
|
|
34 & $ Z(\to 3\times(d(p_{5})+\bar{d}(p_{6})))$ & NLO \\
|
|
35 & $ Z(\to 2\times(u(p_{5})+\bar{u}(p_{6})))$ & NLO \\
|
|
36 & $ Z \to t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to \bar{b}(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8}))$ & LO \\
|
|
\hline
|
|
41 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+f(p_{5})$ & NLO \\
|
|
42 & $ Z_0(\to 3\times(\nu(p_{3})+\bar{\nu}(p_{4})))+f(p_{5})$ & NLO \\
|
|
43 & $ Z(\to b(p_{3})+\bar{b}(p_{4}))+f(p_{5})$ & NLO \\
|
|
\hline
|
|
44 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+f(p_{5})+f(p_{6})$ & NLO \\
|
|
45 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+f(p_{5})+f(p_{6})+f(p_{7})$ & LO \\
|
|
46 & $ Z(\to 3\times(\nu(p_{3})+\bar{\nu}(p_{4}))+f(p_{5})+f(p_{6})$ & NLO \\
|
|
47 & $ Z(\to 3\times(\nu(p_{3})+\bar{\nu}(p_{4}))+f(p_{5})+f(p_{6})+f(p_{7})$ & LO \\
|
|
\hline
|
|
50 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+\bar{b}(p_{5})+b(p_{6}) [\mbox{massive}]$ & LO \\
|
|
51 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})+\bar{b}(p_{6})$ & NLO \\
|
|
52 & $ Z_0(\to 3\times(\nu(p_{3})+\bar{\nu}(p_{4})))+b(p_{5})+\bar{b}(p_{6})$ & NLO \\
|
|
53 & $ Z(\to b(p_{3})+\bar{b}(p_{4}))+b(p_{5})+\bar{b}(p_{6})$ & NLO \\
|
|
54 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})+\bar{b}(p_{6})+f(p_{7})$ & LO \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
56 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+c(p_{5})+\bar{c}(p_{6})$ & NLO \\
|
|
\hline
|
|
61 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +W^-(\to e^-(p_{5})+\bar{\nu}(p_{6}))$ & NLO \\
|
|
62 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +W^-(\to q(p_{5})+\bar{q}(p_{6}))$ & NLO \\
|
|
63 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +W^-(\to q(p_{5})+\bar{q}(p_{6}))[\mbox{rad.in.dk}]$ & NLO \\
|
|
64 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) W^+(\to q(p_{5})+ \bar{q}(p_{6}))$ & NLO \\
|
|
65 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) W^+(\to q(p_{5})+ \bar{q}(p_{6}))[\mbox{rad.in.dk}]$ & NLO \\
|
|
66 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +W^-(\to e^-(p_{5})+\bar{\nu}(p_{6}))+f(p_{7})$ & LO \\
|
|
69 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +W^-(\to e^-(p_{5})+\bar{\nu}(p_{6})) [\mbox{no pol}]$ & LO \\
|
|
\hline
|
|
71 & $ W^+(\to \nu(p_{3})+\mu^+(p_{4}))+Z(\to e^-(p_{5})+e^+(p_{6}))$ & NLO \\
|
|
72 & $ W^+(\to \nu(p_{3})+\mu^+(p_{4}))+Z(\to 3\times(\nu_e(p_{5})+\bar{\nu}_e(p_{6})))$ & NLO \\
|
|
73 & $ W^+(\to \nu(p_{3})+\mu^+(p_{4}))+Z(\to b(p_{5})+\bar{b}(p_{6}))$ & NLO \\
|
|
74 & $ W^+(\to \nu(p_{3})+\mu^+(p_{4}))+Z(\to 3\times(d(p_{5})+\bar{d}(p_{6})))$ & NLO \\
|
|
75 & $ W^+(\to \nu(p_{3})+\mu^+(p_{4}))+Z(\to 2\times(u(p_{5})+\bar{u}(p_{6})))$ & NLO \\
|
|
\hline
|
|
76 & $ W^-(\to \mu^-(p_{3})+\bar{\nu}(p_{4}))+Z(\to e^-(p_{5})+e^+(p_{6}))$ & NLO \\
|
|
77 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+Z(\to 3\times(\nu_e(p_{5})+\bar{\nu}_e(p_{6})))$ & NLO \\
|
|
78 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+Z(\to b(p_{5})+\bar{b}(p_{6}))$ & NLO \\
|
|
79 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+Z(\to 3\times(d(p_{5})+\bar{d}(p_{6})))$ & NLO \\
|
|
80 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+Z(\to 2\times(u(p_{5})+\bar{u}(p_{6})))$ & NLO \\
|
|
\hline
|
|
81 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + Z(\to \mu^-(p_{5})+\mu^+(p_{6}))$ & NLO \\
|
|
82 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + Z(\to 3\times(\nu(p_{5})+\bar{\nu}(p_{6})))$ & NLO \\
|
|
83 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + Z(\to b(p_{5})+\bar{b}(p_{6}))$ & NLO \\
|
|
84 & $ Z(\to b(p_{3})+\bar{b}(p_{4})) + Z(\to 3\times(\nu(p_{5})+\bar{\nu}(p_{6})))$ & NLO \\
|
|
85 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + Z(\to 3\times(\nu(p_{5})+\bar{\nu}(p_{6})))+f(p_{7})$ & LO \\
|
|
\hline
|
|
86 & $ Z(\to \mu^-(p_{3})+\mu^+(p_{4}))+Z(\to e^-(p_{5})+e^+(p_{6}))[\mbox{no gamma*}]$ & NLO \\
|
|
87 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + Z(\to 3\times(\nu(p_{5})+\bar{\nu}(p_{6}))) [\mbox{no gamma*}]$ & NLO \\
|
|
88 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+Z(\to b(p_{5})+\bar{b}(p_{6})) [\mbox{no gamma*}]$ & NLO \\
|
|
89 & $ Z(\to b(p_{3})+\bar{b}(p_{4})) + Z(\to 3\times(\nu(p_{5})+\bar{\nu}(p_{6}))) [\mbox{no gamma*}]$ & NLO \\
|
|
90 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + Z(\to e^-(p_{5})+e^+(p_{6}))$ & NLO \\
|
|
\hline
|
|
91 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) + H(\to b(p_{5})+\bar{b}(p_{6}))$ & NNLO \\
|
|
92 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) + H(\to W^+(\nu(p_{5}),e^+(p_{6}))W^-(e^-(p_{7}),\bar{\nu}(p_{8})))$ & NNLO \\
|
|
93 & $ W^+(\to \nu(p_3)+e^+(p_{4})) + H(\to Z(e^-(p_{5}),e^+(p_{6}))+Z(\mu^-(p_{7}),\mu(p_{8})))$ & NNLO \\
|
|
94 & $ W^+(\to \nu(p_3)+e^+(p_{4})) + H(\to \gamma(p_{5})+\gamma(p_{6})$ & NNLO \\
|
|
96 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) + H(\to b(p_{5})+\bar{b}(p_{6}))$ & NNLO \\
|
|
97 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4})) + H(\to W^+(\nu(p_{5}),e^+(p_{6}))W^-(e^-(p_{7}),\bar{\nu}(p_{8})))$ & NNLO \\
|
|
98 & $ W^-(\to e^-(p_3)+\bar{\nu}(p_{4})) + H(\to Z(e^-(p_{5}),e^+(p_{6}))+Z(\mu^-(p_{7}),\mu^+(p_{8})))$ & NNLO \\
|
|
99 & $ W^-(\to e^-(p_3)+\bar{\nu}(p_{4})) + H(\to \gamma(p_{5})+\gamma(p_{6}))$ & NNLO \\
|
|
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
101 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + H(\to b(p_{5})+\bar{b}(p_{6}))$ & NNLO \\
|
|
102 & $ Z(\to 3\times(\nu(p_{3})+\bar{\nu}(p_{4}))) + H(\to b(p_{5})+\bar{b}(p_{6}))$ & NLO \\
|
|
103 & $ Z(\to b(p_{3})+\bar{b}(p_{4})) + H(\to b(p_{5})+\bar{b}(p_{6}))$ & NLO \\
|
|
104 & $ Z(\to e^-(p_3)+e^+(p_{4})) + H(\to \gamma(p_{5})+\gamma(p_{6}))$ & NNLO \\
|
|
105 & $ Z(\to \to 3\times(\nu(p_3)+\bar{\nu}(p_{4}))) + H(\to \gamma(p_{5})+\gamma(p_{6}))$ & NLO \\
|
|
106 & $ Z(\to e^-(p_{3})+e^+(p_{4})) + H(\to W^+(\nu(p_{5}),e^+(p_{6}))W^-(e^-(p_{7}),\bar{\nu}(p_{8})))$ & NNLO \\
|
|
107 & $ Z(\to 3\times(\nu(p_{3})+\bar{\nu}(p_{4}))) + H(\to W^+(\nu(p_{5}),e^+(p_{6}))W^-(e^-(p_{7}),\bar{\nu}(p_{8})))$ & NLO \\
|
|
108 & $ Z(\to b(p_{3})+\bar{b}(p_{4})) + H(\to W^+(\nu(p_{5}),e^+(p_{6}))W^-(e^-(p_{7}),\bar{\nu}(p_{8})))$ & NLO \\
|
|
109 & $ Z(\to e^-(p_3)+e^+(p_{4})) + H(\to Z(e^-(p_{5}),e^+(p_{6}))+Z(\to\mu^-(p_{7}),\mu^+(p_{8})))$ & NLO \\
|
|
110 & $ Z(\to e^-(p_3)+e^+(p_{4})) + H(\to \tau^-(p_5) \tau^+_(p_6)))$ & NNLO \\
|
|
\hline
|
|
111 & $ H(\to b(p_{3})+\bar{b}(p_{4}))$ & NNLO \\
|
|
112 & $ H(\to \tau^-(p_{3})+\tau^+(p_{4}))$ & NNLO \\
|
|
113 & $ H(\to W^+(\nu(p_{3})+e^+(p_{4})) + W^-(e^-(p_{5})+\bar{\nu}(p_{6})))$ & NLO \\
|
|
114 & $ H(\to W^+(\nu(p_{3})+e^+(p_{4})) + W^-(q(p_{5})+\bar{q}(p_{6})))$ & NLO \\
|
|
115 & $ H(\to W^+(\nu(p_{3})+e^+(p_{4})) + W^-(q(p_{5})+\bar{q}(p_{6}))) [rad.in.dk]$ & NLO \\
|
|
116 & $ H(\to Z(\to e^-(p_{3})+e^+(p_{4})) + Z(\to\mu^-(p_{5})+\mu^+(p_{6}))$ & NLO \\
|
|
117 & $ H(\to Z(\to3\times(\nu(p_{3})+\bar{\nu}(p_{4})))+ Z(\to\mu^-(p_{5})+\mu^+(p_{6}))$ & NLO \\
|
|
118 & $ H(\to Z(\to\mu^-(p_{3})+\mu^+(p_{4})) + Z(\to b(p_{5})+\bar{b}(p_{6}))$ & NLO \\
|
|
119 & $ H(\to \gamma(p_{3})+\gamma(p_{4}))$ & NNLO \\
|
|
120 & $ H(\to Z(\to\mu^-(p_{3})+\mu^+(p_{4})) + \gamma(p_{5}))$ & NLO \\
|
|
121 & $ H(\to Z(\to3\times(\nu(p_{3})+\bar{\nu}(p_{4})))) + \gamma(p_{5}))$ & NLO \\
|
|
\hline
|
|
123 & $ H(\to W^+(\nu(p_3)+e^+(p_{4})) + W^-(e^-(p_{5})+\bar{\nu}(p_{6})))$ [t, b loops, exact] & LO \\
|
|
124 & $ H(\to W^+(\nu(p_3)+e^+(p_{4})) + W^-(e^-(p_{5})+\bar{\nu}(p_{6})))$ [only H, gg$\rightarrow$WW int & LO \\
|
|
125 & $ H(\to W^+(\nu(p_3)+e^+(p_{4})) + W^-(e^-(p_{5})+\bar{\nu}(p_{6})))$ [$|H|^2$ and H,gg$\rightarrow$WW int] & LO \\
|
|
126 & $ W^+(\nu(p_3)+e^+(p_{4})) + W^-(e^-(p_{5})+\bar{\nu}(p_{6}))$ [gg only, (H + gg$\rightarrow$WW) squared] & LO \\
|
|
\hline
|
|
128 & $ H(\to Z(\to \to e^-(p3)+e^+(p4)) + Z(\to \mu^-(p5)+\mu^+(p6))$ [t, b loops, exact]& LO \\
|
|
129 & $ H(\to Z(\to e^-(p3)+e^+(p4)) + Z(\to \mu^-(p5)+\mu^+(p6))$ [only H, gg$\rightarrow$ZZ int] & LO \\
|
|
130 & $ H(\to Z(\to e^-(p3)+e^+(p4)) + Z(\to \mu^-(p5)+\mu^+(p6))$ [$|H|^2$ and H,gg$\rightarrow$ZZ int]& LO \\
|
|
131 & $ Z(\to e^-(p3)+e^+(p4)) + Z(\to \mu^-(p5)+\mu^+(p6)$ [gg only, $|H + gg \rightarrow ZZ|^2$]& LO \\
|
|
132 & $ Z(\to e^-(p3)+e^+(p4)) + Z(\to \mu^-(p5)+\mu^+(p6)$ [(gg$\rightarrow$ZZ) squared]& LO \\
|
|
\hline
|
|
1281 & $ H(\to e^-(p3)+e^+(p4) \nu_e(p5)+\bar\nu_e(p6)$ [top, bottom loops, exact]& LO \\
|
|
1311 & $ e^-(p3)+e^+(p4)+\nu_e(p5)+\bar\nu_e(p6)$ [gg only, (H + gg$\rightarrow$ZZ) squared]& LO \\
|
|
1321 & $ e^-(p3)+e^+(p4)+\nu_e(p5)+\bar\nu_e(p6)$ [(gg$\rightarrow$ZZ) squared]& LO \\
|
|
\hline
|
|
1282 & $ H(\to e^-(p3)+e^+(p4)+\nu(p5)+\bar\nu(p6)$ [top, bottom loops, exact]& LO \\
|
|
1312 & $ e^-(p3)+e^+(p4)+\nu(p5)+\bar\nu(p6)$ [gg only, (H + gg$\rightarrow$ZZ) squared]& LO \\
|
|
1322 & $ e^-(p3)+e^+(p4)+\nu(p5)+\bar\nu(p6)$ [(gg$\rightarrow$ZZ) squared]& LO \\
|
|
\hline
|
|
133 & $ H(\to Z(\to e^-(p3)+e^+(p4)) + Z(\to \mu^-(p5)+\mu^+(p6) + f(p7))$ [intf,no $p_7$ cut]& LO \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
136 & $ H(\to b(p_{3})+\bar{b}(p_{4})) + b(p_{5}) (+g(p_{6}))$ & NLO \\
|
|
137 & $ H(\to b(p_{3})+\bar{b}(p_{4})) + \bar{b}(p_{5}) (+b(p_{6}))$ & (REAL) \\
|
|
138 & $ H(\to b(p_{3})+\bar{b}(p_{4})) + b(p_{5}) + \bar{b}(p_{6}) [\mbox{both observed}]$ & (REAL) \\
|
|
\hline
|
|
141 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8}))$ & NLO \\
|
|
142 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8}))$ \mbox{\small [rad.in.dk]}& NLO \\
|
|
143 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8}))+f(p_{9})$ & LO \\
|
|
144 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8}))$ \mbox{(uncorr)} & NLO \\
|
|
145 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8}))$ \mbox{\small [rad.in.dk],uncorr} & NLO \\
|
|
146 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+q(p_{7})+\bar{q}(p_{8})) $ & NLO \\
|
|
147 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+q(p_{7})+\bar{q}(p_{8})) $ \mbox{\small [rad.in.top.dk]}& NLO \\
|
|
148 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+q(p_{7})+\bar{q}(p_{8})) $ \mbox{\small [rad.in.$W$.dk]}& NLO \\
|
|
149 & $ t(\to q(p_{3})+\bar{q}(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8})) $ & NLO \\
|
|
150 & $ t(\to q(p_{3})+\bar{q}(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8})) $ \mbox{\small [rad.in.top.dk]}& NLO \\
|
|
151 & $ t(\to q(p_{3})+\bar{q}(p_{4})+b(p_{5}))+\bar{t}(\to b~(p_{6})+e^-(p_{7})+\bar{\nu}(p_{8})) $ \mbox{\small [rad.in.$W$.dk]}& NLO \\
|
|
\hline
|
|
157 & $ t \bar{t} [\mbox{for total Xsect}]$ & NLO \\
|
|
158 & $ b \bar{b} [\mbox{for total Xsect}]$ & NLO \\
|
|
159 & $ c \bar{c} [\mbox{for total Xsect}]$ & NLO \\
|
|
160 & $ t \bar{t} + g [\mbox{for total Xsect}]$ & LO \\
|
|
\hline
|
|
161 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+q(p_{6}) [\mbox{t-channel}]$ & NLO \\
|
|
162 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+q(p_{6}) [\mbox{decay}]$ & NLO \\
|
|
163 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+q(p_{6}) [\mbox{t-channel}] mb>0$ & NLO \\
|
|
164 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+q(p_{6}) [\mbox{full off-shell t-channel}] mb=0$ & NLO \\
|
|
166 & $ \bar{t}(\to e^-(p_{3})+\bar{\nu}(p_{4})+\bar{b}(p_{5}))+q(p_{6}) [\mbox{t-channel}]$ & NLO \\
|
|
167 & $ \bar{t}(\to e^-(p_{3})+\bar{\nu}(p_{4})+\bar{b}(p_{5}))+q(p_{6}) [\mbox{rad.in.dk}]$ & NLO \\
|
|
168 & $ \bar{t}(\to e^-(p_{3})+\bar{\nu}(p_{4})+\bar{b}(p_{5}))+q(p_{6}) [\mbox{t-channel}] mb>0$ & NLO \\
|
|
169 & $ \bar{t}(\to e^-(p_{3})+\bar{\nu}(p_{4})+\bar{b}(p_{5}))+q(p_{6}) [\mbox{full off-shell t-channel}] mb=0$ &
|
|
NLO \\
|
|
\hline
|
|
171 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{b}(p_{6})) [\mbox{s-channel}]$ & NLO \\
|
|
172 & $ t(\to \nu(p_{3})+e^+(p_{4})+b(p_{5}))+\bar{b}(p_{6})) [\mbox{decay}]$ & NLO \\
|
|
176 & $ \bar{t}(\to e^-(p_{3})+\bar{\nu}(p_{4})+\bar{b}(p_{5}))+b(p_{6})) [\mbox{s-channel}]$ & NLO \\
|
|
177 & $ \bar{t}(\to e^-(p_{3})+\bar{\nu}(p_{4})+\bar{b}(p_{5}))+b(p_{6})) [\mbox{rad.in.dk}]$ & NLO \\
|
|
\hline
|
|
180 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+t(p_{5})$ & NLO \\
|
|
181 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+t(\nu(p_{5})+e^+(p_{6})+b(p_{7}))$ & NLO \\
|
|
182 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+t(\nu(p_{5})+e^+(p_{6})+b(p_{7})) [\mbox{rad.in.dk}]$ & NLO \\
|
|
183 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+t(\nu(p_{5})+e^+(p_{6})+b(p_{7}))+b(p_{8})$ & LO \\
|
|
184 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+t(p_{5})+b(p_{6}) [\mbox{massive b}]$ & LO \\
|
|
185 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\bar{t}(p_{5})$ & NLO \\
|
|
186 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\bar{t}(e^-(p_{5})+\bar{\nu}(p_{6})+\bar{b}(p_{7})$ & NLO \\
|
|
187 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\bar{t}(e^-(p_{5})+\bar{\nu}(p_{6})+\bar{b}(p_{7}) [\mbox{rad.in.dk}]$ & NLO \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
190 & $ f(p_{3})+f(p_{4})$ & LO \\
|
|
191 & $ f(p_{3})+f(p_{4})$ [mixed QCD/EW] & NLO \\
|
|
\hline
|
|
200 & $ H + f(p_5)$, see section \ref{subsec:hjetma} & NLO \\
|
|
201 & $ H(\to b(p_{3})+\bar{b}(p_{4})) + f(p_{5}) [\mbox{full mt dep.}]$ & LO \\
|
|
202 & $ H(\to \tau^-(p_{3})+\tau^+(p_{4})) + f(p_{5}) [\mbox{full mt dep.}]$ & LO \\
|
|
203 & $ H(\to b(p_{3})+\bar{b}(p_{4})) + f(p_{5})$ & NNLO \\
|
|
204 & $ H(\to \tau^-(p_{3})+\tau^+(p_{4})) + f(p_{5})$ & NNLO \\
|
|
205 & $ H(\to Z(\mu^-(p_3) + \mu^+(p_4)) + \gamma(p_5)) + f(p_5)$ & NLO \\
|
|
206 & $ A(\to b(p_{3})+\bar{b}(p_{4})) + f(p_{5}) [\mbox{full mt dep.}]$ & LO \\
|
|
207 & $ A(\to \tau^-(p_{3})+\tau^+(p_{4})) + f(p_{5}) [\mbox{full mt dep.}]$ & LO \\
|
|
208 & $ H(\to W^+(\nu(p_{3}),e^+(p_{4}))W^-(e^-(p_{5}),\bar{\nu}(p_{6})))+f(p_{7})$ & NLO \\
|
|
209 & $ H(\to Z(\to e^-(p_{3}),e^+(p_{4}))Z(\to \mu^-(p_{5}),\mu^+(p_{6})))+f(p_{7})$ & NLO \\
|
|
210 & $ H(\to \gamma(p_{3})+\gamma(p_{4})) + f(p_{5})$ & NNLO \\
|
|
\hline
|
|
211 & $ H(\to b(p_{3})+\bar{b}(p_{4}))+f(p_{5})+f(p_{6}) [\mbox{WBF}]$ & NLO \\
|
|
212 & $ H(\to \tau^-(p_{3})+\tau^+(p_{4}))+f(p_{5})+f(p_{6}) [\mbox{WBF}]$ & NLO \\
|
|
213 & $ H(\to W^+(\nu(p_{3}),e^+(p_{4}))W^-(e^-(p_{5}),\bar{\nu}(p_{6})))+f(p_{7})+f(p_{8}) [\mbox{WBF}]$ & NLO \\
|
|
214 & $ H(\to Z(\to e^-(p_3),e^+(p_{4}))+Z(\to \mu^-(p_{5}),\mu^+(p_{6})))+f(p_{7})+f(p_{8}) [\mbox{WBF}]$ & NLO \\
|
|
215 & $ H(\to \gamma(p_3)+\gamma(p_{4}))+f(p_{5})+f(p_{6}) [\mbox{WBF}]$ & NLO \\
|
|
216 & $ H(\to b(p_{3})+\bar{b}(p_{4}))+f(p_{5})+f(p_{6})+f(p_{7}) [\mbox{WBF+jet}]$ & LO \\
|
|
217 & $ H(\to \tau^-(p_{3})+\tau^+(p_{4}))+f(p_{5})+f(p_{6})+f(p_{7}) [\mbox{WBF+jet}]$ & LO \\
|
|
\hline
|
|
221 & $ \tau^-(\to e^-(p_{3})+\bar{\nu}_e(p_{4})+\nu_\tau(p_{5}))+\tau^+(\to \bar{\nu}_\tau(p_{6})+\nu_e(p_{7})+e^+(p_{8}))$ & LO \\
|
|
\hline
|
|
220 & $ Z(\to e^-(p_3),e^+(p_4))Z(\to \mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
2201 & $ Z(\to e^-(p_3),e^+(p_4))Z(\to \mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) $ [strong]' & LO \\
|
|
222 & $ Z(\to e^-(p_3),e^+(p_4))Z(\to \nu_{\mu}(p_5),\bar{\nu}_{\mu}(p_6)))+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
2221 & $ Z(\to e^-(p_3),e^+(p_4))Z(\to \nu_{\mu}(p_5),\bar{\nu}_{\mu}(p_6)))+f(p_7)+f(p_8) $ [strong]' & LO \\
|
|
224 & $ W^-(e^-(p_3),\bar{\nu}_e(p_6)))W^+(\nu_{\mu}(p_5),mu^+(p_4))+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
2241 & $ W^-(e^-(p_3),\bar{\nu}_e(p_6)))W^+(\nu_{\mu}(p_5),mu^+(p_4))+f(p_7)+f(p_8) $ [strong]' & LO \\
|
|
226 & $ e^-(p_3)+e^+(p_4)+\nu_e(p_5)+\bar{\nu}_e(p_6)+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
228 & $ W^+(\nu_e(p_3),e^+(p_4)))W^+(\nu_{\mu}(p_5),mu^+(p_6))+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
2281 & $ W^+(\nu_e(p_3),e^+(p_4)))W^+(\nu_{\mu}(p_5),mu^+(p_6))+f(p_7)+f(p_8) $ [strong]' & LO \\
|
|
229 & $ W^-(e^-(p_3),\bar{\nu}_e(p_4)))W^-(mu^-(p_5),\bar{\nu}_{\mu}(p_6))+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
2291 & $ W^-(e^-(p_3),\bar{\nu}_e(p_4)))W^-(mu^-(p_5),\bar{\nu}_{\mu}(p_6))+f(p_7)+f(p_8) $ [strong]' & LO \\
|
|
223 & $ W^+(\nu_e(p_3),e^+(p_4))Z(\to \mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
2231 & $ W^+(\nu_e(p_3),e^+(p_4))Z(\to \mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) $ [strong]' & LO \\
|
|
225 & $ W^-(e^-(p_3),\bar{\nu}_e(p_4))Z(\to \mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) $ [weak]' & LO \\
|
|
2251 & $ W^-(e^-(p_3),\bar{\nu}_e(p_4))Z(\to \mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8) $ [strong]' & LO \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
231 & $t(p_3)+\bar{b}(p_4)+q(p_5)$ [\mbox{t-channel]} & NLO \\
|
|
232 & $t(p_3)+\bar{b}(p_4)+q(p_5)+q(p_6)$ [\mbox{t-channel]} & LO \\
|
|
233 & $t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{b}(p_6)+q(p_7)$ [\mbox{t-channel]} & NLO \\
|
|
234 & $t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{b}(p_6)+q(p_7)$ [\mbox{t-channel, rad.in.dk]} & NLO \\
|
|
235 & $t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{b}(p_6)+q(p_7)+f(p_8)$ [\mbox{t-channel]} & LO \\
|
|
236 & $\bar{t}(p_3)+b(p_4)+q(p_5)$ [\mbox{t-channel]} & NLO \\
|
|
237 & $\bar{t}(p_3)+b(p_4)+q(p_5)+q(p_6)$ [\mbox{t-channel]} & LO \\
|
|
238 & $\bar{t}(\to e^-(p_3)+\bar{\nu}(p_4)+\bar{b}(p_5))+b(p_6)+q(p_7)$ [\mbox{t-channel]} & NLO \\
|
|
239 & $\bar{t}(\to e^-(p_3)+\bar{\nu}(p_4)+\bar{b}(p_5))+b(p_6)+q(p_7)$ [\mbox{t-channel, rad.in.dk]} & NLO \\
|
|
240 & $\bar{t}(\to e^-(p_3)+\bar{\nu}(p_4)+\bar{b}(p_5))+b(p_6)+q(p_7)+f(p_8)$ [\mbox{t-channel]} & L0 \\
|
|
\hline
|
|
251 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) + W^+(\to \nu(p_{5})+e^+(p_{6}))+f(p_{7})+f(p_{8})$ & LO \\
|
|
252 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) + W^+(\to \nu(p_{5})+e^+(p_{6}))+f(p_{7})+f(p_{8})+f(p_{9})$ & LO \\
|
|
253 & $W^+(\to\nu(p_3)+e^+(p_4)) + Z(\to e^-(p_5)+e^+(p_6))+f(p_7)+f(p_8)$ & LO \\
|
|
254 & $W^-(\to e^-(p_3)+\bar{\nu}(p_4))+ Z(\to e^-(p_5)+e^+(p_6))+f(p_7)+f(p_8)$ & LO \\
|
|
255 & $W^+(\to \nu(p_3)+e^+(p_4)) + Z(\to e^-(p_5)+e^+(p_6))+b(p_7)+f(p_8)$ & LO \\
|
|
256 & $W^-(\to e^-(p_3)+\bar{\nu}(p_4))+ Z(\to e^-(p_5)+e^+(p_6))+b(p_7)+f(p_8)$ & LO \\
|
|
259 & $W^+(\to \nu(p_3)+e^+(p_4)) + Z(\to e^-(p_5)+e^+(p_6))+b(p_7)+b~(p_8)$ & LO \\
|
|
260 & $W^-(\to e^-(p_3)+\bar{\nu}(p_4))+ Z(\to e^-(p_5)+e^+(p_6))+b(p_7)+b~(p_8)$ & LO \\
|
|
\hline
|
|
261 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})$ & NLO \\
|
|
262 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+c(p_{5})$ & NLO \\
|
|
263 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+\bar{b}(p_{5})+b(p_{6}) [\mbox{1 b-tag}]$ & LO \\
|
|
264 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+\bar{c}(p_{5})+c(p_{6}) [\mbox{1 c-tag}]$ & LO \\
|
|
266 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})(+\bar{b}(p_{6}))$ & NLO \\
|
|
267 & $ Z(\to e^-(p_{3})+e^+(p_{4}))+c(p_{5})(+\bar{c}(p_{6}))$ & NLO \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
270 & $ H(\gamma(p_{3})+\gamma(p_{4}))+f(p_{5})+f(p_{6}) [\mbox{in heavy top limit}]$ & NLO \\
|
|
271 & $ H(b(p_{3})+\bar{b}(p_{4}))+f(p_{5})+f(p_{6}) [\mbox{in heavy top limit}]$ & NLO \\
|
|
272 & $ H(\tau^-(p_{3})+\tau^+(p_{4}))+f(p_{5})+f(p_{6}) [\mbox{in heavy top limit}]$ & NLO \\
|
|
273 & $ H(\to W^+(\nu(p_{3}),e^+(p_{4}))W^-(e^-(p_{5}),\bar{\nu}(p_{6})))+f(p_{7})+f(p_{8})$ & NLO \\
|
|
274 & $ H(\to Z(e^-(p_{3}),e^+(p_{4}))Z(\mu^-(p_{5}),\mu^+(p_{6})))+f(p_{7})+f(p_{8})$ & NLO \\
|
|
275 & $ H(b(p_{3})+\bar{b}(p_{4}))+f(p_{5})+f(p_{6})+f(p_{7}) [\mbox{in heavy top limit}]$ & LO \\
|
|
276 & $ H(\tau^-(p_{3})+\tau^+(p_{4}))+f(p_{5})+f(p_{6})+f(p_{7}) [\mbox{in heavy top limit}]$ & LO \\
|
|
278 & $ H(\to W^+(\nu(p_3),e^+(p_4))W^-(e^-(p_5),\bar{\nu}(p_6)))+f(p_7)+f(p_8)+f(p_9)$ & LO \\
|
|
279 & $ H(\to Z(e^-(p_3),e^+(p_4))Z(\mu^-(p_5),\mu^+(p_6)))+f(p_7)+f(p_8)+f(p_9)$ & LO \\
|
|
\hline
|
|
280 & $ \gamma(p_3)+f(p_{4})$ & NLO+F \\
|
|
282 & $ f(p_{1})+f(p_{2})\to \gamma(p_{3})+f(p_{4})+f(p_{5})$ & LO \\
|
|
283 & $ f(p_{1})+f(p_{2})\to \gamma(p_{3})+b(p_{4})$ & LO \\
|
|
284 & $ f(p_{1})+f(p_{2})\to \gamma(p_{3})+c(p_{4})$ & LO \\
|
|
285 & $ f(p_{1})+f(p_{2})\to \gamma(p_{3})+\gamma(p_{4})$ & NLO+F, NNLO \\
|
|
286 & $ f(p_{1})+f(p_{2})\to \gamma(p_{3})+\gamma(p_{4})+f(p_{5})$ & LO \\
|
|
287 & $ f(p_{1})+f(p_{2})\to \gamma(p_{3})+\gamma(p_{4})+\gamma(p_{5})$ & NLO+F \\
|
|
289 & $ f(p_{1})+f(p_{2})\to \gamma(p_{3})+\gamma(p_{4})+\gamma(p_{5})+\gamma(p_{6})$ & NLO+F \\
|
|
\hline
|
|
290 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\gamma(p_{5})$ & NLO+F \\
|
|
292 & $ W^+(\to \nu(p_{3})+e^+(p_{4})) +\gamma(p_{5})+f(p_{6}) $ & LO \\
|
|
295 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+\gamma(p_{5})$ & NLO+F \\
|
|
297 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+\gamma(p_{5})+f(p_{6}) $ & LO \\
|
|
\hline
|
|
300 & $ Z(\to e ^-(p_3)+e^+(p_4))+\gamma(p_5)$ & NNLO \\
|
|
301 & $ Z(\to e ^-(p_3)+e^+(p_4))+\gamma(p_5)+\gamma(p_6) $& NLO +F \\
|
|
302 &$ Z(\to e ^-(p_3)+e^+(p_4))+\gamma(p_5)+f(p_6) $& NLO \\
|
|
303 &$ Z(\to e ^-(p_3)+e^+(p_4))+\gamma(p_5)+\gamma(p_6)+f(p_7) $& LO \\
|
|
304 & $ Z(\to e ^-(p_3)+e^+(p_4))+\gamma(p_5)+f(p_6)+f(p_7) $ & LO \\
|
|
305 & $ Z(\to 3(\nu(p_3)+\bar{\nu}(p_4)))+\gamma(p_5) $& NNLO \\
|
|
306 & $ Z(\to 3(\nu(p_3)+\bar{\nu}(p_4)))+\gamma(p_5)+\gamma(p_6) $& NLO + F \\
|
|
307 &$ Z(\to 3(\nu(p_3)+\bar{\nu}(p_4)))+\gamma(p_5)+f(p_6) $ & NLO \\
|
|
308 &$ Z(\to 3(\nu(p_3)+\bar{\nu}(p_4)))+\gamma(p_5)+\gamma(p_6)+f(p_7) $ & LO \\
|
|
309 &$ Z(\to 3(\nu(p_3)+\bar{\nu}(p_4)))+\gamma(p_5)+f(p_6)+f(p_7) $ & LO \\
|
|
\hline
|
|
311 & $ f(p_{1})+b(p_{2}) \to W^+(\to \nu(p_{3})+e^+(p_{4}))+b(p_{5})+f(p_{6})$ & LO \\
|
|
316 & $ f(p_{1})+b(p_{2}) \to W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+b(p_{5})+f(p_{6})$ & LO \\
|
|
\hline
|
|
321 & $ f(p_{1})+c(p_{2}) \to W^+(\to \nu(p_{3})+e^+(p_{4}))+c(p_{5})+f(p_{6})$ & LO \\
|
|
326 & $ f(p_{1})+c(p_{2}) \to W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+c(p_{5})+f(p_{6})$ & LO \\
|
|
\hline
|
|
331 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+c(p_{5})+f(p_{6}) [\mbox{c-s interaction}]$ & LO \\
|
|
336 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+c(p_{5})+f(p_{6}) [\mbox{c-s interaction}]$ & LO \\
|
|
\hline
|
|
341 & $ f(p_{1})+b(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})+f(p_{6}) [+f(p_{7})]$ & NLO \\
|
|
342 & $ f(p_{1})+b(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})+f(p_{6}) [+\bar{b}(p_{7})]$ & (REAL) \\
|
|
346 & $ f(p_{1})+b(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})+f(p_{6})+f(p_{7})$ & LO \\
|
|
347 & $ f(p_{1})+b(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+b(p_{5})+f(p_{6})+\bar{b}(p_{7})$ & LO \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
351 & $ f(p_{1})+c(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+c(p_{5})+f(p_{6}) [+f(p_{7})]$ & NLO \\
|
|
352 & $ f(p_{1})+c(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+c(p_{5})+f(p_{6}) [+\bar{c}(p_{7})]$ & (REAL) \\
|
|
356 & $ f(p_{1})+c(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+c(p_{5})+f(p_{6})+f(p_{7})$ & LO \\
|
|
357 & $ f(p_{1})+c(p_{2}) \to Z(\to e^-(p_{3})+e^+(p_{4}))+c(p_{5})+f(p_{6})+\bar{c}(p_{7})$ & LO \\
|
|
\hline
|
|
361 & $ c(p_{1})+\bar{s}(p_{2}) \to W^+(\to \nu(p_{3})+e^+(p_{4})) [\mbox{mc=0 in NLO}]$ & NLO \\
|
|
362 & $ c(p_{1})+\bar{s}(p_{2}) \to W^+(\to \nu(p_{3})+e^+(p_{4})) [\mbox{massless corrections only}]$ & NLO \\
|
|
363 & $ c(p_{1})+\bar{s}(p_{2}) \to W^+(\to \nu(p_{3})+e^+(p_{4})) [\mbox{massive charm in real}]$ & NLO \\
|
|
\hline
|
|
370 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+\gamma(p_{5})+\gamma(p_{6})$ & LO \\
|
|
371 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+\gamma(p_{5})+\gamma(p_{6})$ & LO \\
|
|
\hline
|
|
401 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+b(p_{5}) ~[\mbox{1,2 or 3 jets, 4FNS}]$ & NLO \\
|
|
402 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+(b+\bar{b})(p_{5}) ~[\mbox{1 or 2 jets, 4FNS}]$ & NLO \\
|
|
403 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+b(p_{5})+\bar b(p_{6}) ~[\mbox{2 or 3 jets, 4FNS}]$ & NLO \\
|
|
406 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+b(p_{5}) ~[\mbox{1,2 or 3 jets, 4FNS}]$ & NLO \\
|
|
407 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+(b+\bar{b})(p_{5}) ~[\mbox{1 or 2 jets, 4FNS}]$ & NLO \\
|
|
408 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+b(p_{5})+\bar b(p_{6}) ~[\mbox{2 or 3 jets, 4FNS}]$ & NLO \\
|
|
\hline
|
|
411 & $ f(p_1)+b(p_2) \to W^+(\to \nu(p_3)+e^+(p_{4}))+b(p_{5})+f(p_{6})$ ~[\mbox{5FNS}] & NLO \\
|
|
416 & $ f(p_1)+b(p_2) \to W^-(\to e^-(p_3)+\bar{\nu}(p_{4}))+b(p_{5})+f(p_{6})$ ~[\mbox{5FNS}] & NLO \\
|
|
\hline
|
|
421 & $ W^+(\to \nu(p_{3})+e^+(p_{4}))+b(p_{5}) ~[\mbox{1,2 or 3 jets, 4FNS+5FNS}]$ & NLO \\
|
|
426 & $ W^-(\to e^-(p_{3})+\bar{\nu}(p_{4}))+b(p_{5}) ~[\mbox{1,2 or 3 jets, 4FNS+5FNS}]$ & NLO \\
|
|
\hline
|
|
431 & $ W^+(\to \nu(p_3)+e^+(p_{4}))+b(p_{5})+\bar b(p_{6})+f(p_{7}) ~[\mbox{massive}]$ & LO \\
|
|
436 & $ W^-(\to e^-(p_3)+\bar{\nu}(p_{4}))+b(p_{5})+\bar b(p_{6})+f(p_{7}) ~[\mbox{massive}]$ & LO \\
|
|
\hline
|
|
500 & $ W^+(\to \nu(p_3)+e^+(p_4)) +t(p_5)+\bar{t}(p_6) \mbox{[massive]}$ & NLO \\
|
|
501 & $ t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to b~(p_6)+e^-(p_7)+\bar{\nu}(p_8))+W^+(\nu(p_9),\mu^+(p_{10}))$ & NLO \\
|
|
502 & $ \mbox{(same as process 501 but with radiation in decay)}$ & NLO \\
|
|
503 & $ t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to b~(p_6)+q(p_7)+q~(p_8))+W^+(\nu(p_9),\mu^+(p_{10}))$ & NLO \\
|
|
506 & $ t(\to q(p_3)+q~(p_4)+b(p_5))+\bar{t}(\to b~(p_6)+e^-(p_7)+\bar{\nu}(p_8))+W^+(\nu(p_9),\mu^+(p_{10}))$ & NLO \\
|
|
\hline
|
|
510 & $ W^-(\to e^-(p_3)+\bar{\nu}(p_4))+t(p_5)+\bar{t}(p_6) \mbox{[massive]} $ & NLO \\
|
|
511 & $ t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to b~(p_6)+e^-(p_7)+\bar{\nu}(p_8))+W^-(\mu^-(p_9),\bar{\nu}(p_{10}))$ & NLO \\
|
|
512 & $ \mbox{(same as process 511 but with radiation in decay)}$ & NLO \\
|
|
513 & $ t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to b~(p_6)+q(p_7)+q~(p_8))+W^-(\mu^-(p_9),\bar{\nu}(p_{10}))$ & NLO \\
|
|
516 & $ t(\to q(p_3)+q~(p_4)+b(p_5))+\bar{t}(\to b~(p_6)+e^-(p_7)+\bar{\nu}(p_8))+W^-(\mu^-(p_9),\bar{\nu}(p_{10}))$ & NLO \\
|
|
529 & $ Z(\to e^-(p_3)+e^+(p_4))+t(p5)+\bar{t}(p_6) $ & LO \\
|
|
530 & $ t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to e^-(p_7)+\bar{\nu}(p_8)+b~(p_6))+Z(e^-(p_9),e^+(p_{10}))$ & LO \\
|
|
531 & $ t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to e^-(p_7)+\bar{\nu}(p_8)+b~(p_6))+Z(b(p_9),b~(p_{10}))$ & LO \\
|
|
532 & $ t(\to \nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to q(p_7)+\bar{q}(p_8)+b~(p_6))+Z(e^-(p_9),e^+(p_{10}))$ & LO \\
|
|
533 & $ t(\to q(p_3)+\bar{q}(p_4)+b(p_5))+\bar{t}(\to e^-(p_7)+\bar{\nu}(p_8)+b~(p_6))+Z(e^-(p_9),e^+(p_{10}))$ & LO \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
540 & $H(b(p_3)+\bar{b}(p_4))+t(p_5)+q(p_6)$ & NLO \\
|
|
541 & $H(b(p_3)+\bar{b}(p_4))+\bar{t}(p_5)+q(p_6)$ & NLO \\
|
|
544 & $H(b(p_3)+\bar{b}(p_4))+t(\nu(p_5)+e^+(p_6)+b(p_7))+q(p_9)$ & NLO \\
|
|
547 & $H(b(p_3)+\bar{b}(p_4))+\bar{t}(e^-(p_5)+\bar{\nu}(p_6)+b(p_7))+q(p_9)$ & NLO \\
|
|
\hline
|
|
550 & $H(\gamma(p_3)+\gamma(p_4))+t(p_5)+q(p_6)$ & NLO \\
|
|
551 & $H(\gamma(p_3)+\gamma(p_4))+\bar{t}(p_5)+q(p_6)$ & NLO \\
|
|
554 & $H(\gamma(p_3)+\gamma(p_4))+t(\nu(p_5)+e^+(p_6)+b(p_7))+q(p_9)$ & NLO \\
|
|
557 & $H(\gamma(p_3)+\gamma(p_4))+\bar{t}(e^-(p_5)+\bar{\nu}(p_6)+b(p_7))+q(p_9)$ & NLO \\
|
|
\hline
|
|
560 & $Z(e^-(p_3)+e^+(p_4))+t(p_5)+q(p_6)$ & NLO \\
|
|
561 & $Z(e^-(p_3)+e^+(p_4))+\bar{t}(p_5)+q(p_6)$ & NLO \\
|
|
562 & $Z(e^-(p_3)+e^+(p_4))+t(p_5)+q(p_6)+f(p_7)$ & LO \\
|
|
563 & $Z(e^-(p_3)+e^+(p_4))+\bar{t}(p_5)+q(p_6)+f(p_7)$ & LO \\
|
|
564 & $Z(e^-(p_3)+e^+(p_4))+t(\to\nu(p_5)+e^+(p_6)+b(p_7))+q(p_8)$ & NLO \\
|
|
566 & $Z(e^-(p_3)+e^+(p_4))+t(\to\nu(p_5)+e^+(p_6)+b(p_7))+q(p_8)+f(p_9)$ & LO \\
|
|
567 & $Z(e^-(p_3)+e^+(p_4))+\bar{t}(\to e^-(p_5)+\bar{\nu}(p_6)+\bar{b}(p_7))+q(p_8)$ & NLO \\
|
|
569 & $Z(e^-(p_3)+e^+(p_4))+\bar{t}(\to e^-(p_5)+\bar{\nu}(p_6)+\bar{b}(p_7))+q(p_8)+f(p_9)$ & LO \\
|
|
\hline
|
|
601 & $H(b(p_3)+\bar{b}(p_4))+H(\tau^-(p_5)+\tau^+(p_6)) $ & LO \\
|
|
602 & $H(b(p_3)+\bar{b}(p_4))+H(\gamma(p_5)+\gamma(p_6)) $ & LO \\
|
|
640 & $t(p_3)+\bar{t}(p_4)+H(p_5)$ & LO \\
|
|
641 & $t(\to\nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to\bar{\nu}(p_7)+e^-(p_8)+\bar{b}(p_6))+H(b(p_9)+\bar{b}(p_{10}))$ & LO \\
|
|
644 & $t(\to\nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to\bar{q}(p_7)+q(p_8)+\bar{b}(p_6))+H(b(p_9)+\bar{b}(p_{10}))$ & LO \\
|
|
647 & $t(\to q(p_3)+\bar{q}(p_4)+b(p_5))+\bar{t}(\to\bar{\nu}(p_7)+e^-(p_8)+\bar{b}(p_6))+H(b(p_9)+\bar{b}(p_{10}))$ & LO \\
|
|
651 & $t(\to\nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to\bar{\nu}(p_7)+e^-(p_8)+\bar{b}(p_6))+H(\gamma(p_9)+\gamma(p_{10}))$ & LO \\
|
|
654 & $t(\to\nu(p_3)+e^+(p_4)+b(p_5))+\bar{t}(\to\bar{q}(p_7)+q(p_8)+\bar{b}(p_6))+H(\gamma(p_9)+\gamma(p_{10}))$ & LO \\
|
|
657 & $t(\to q(p_3)+\bar{q}(p_4)+b(p_5))+\bar{t}(\to\bar{\nu}(p_7)+e^-(p_8)+\bar{b}(p_6))+H(\gamma(p_9)+\gamma(p_{10}))$ & LO \\
|
|
661 & $t(\to\nu(p_3) e^+(p_4) b(p_5)) +\bar{t}(\to\bar{\nu}(p_7)e^-(p_8)\bar{b}(p_6))+H(W^+(p_{9},p_{10})W^-(p_{11},p_{12}))$ & LO \\
|
|
664 & $t(\to\nu(p_3) e^+(p_4) b(p_5)) +\bar{t}(\to\bar{q}(p_7)q(p_8)\bar{b}(p_6))+H(W^+(p_{9},p_{10})W^-(p_{11},p_{12}))$ & LO \\
|
|
667 & $t(\to q(p_3) \bar{q}(p_4) b(p_5)) +\bar{t}\to(\bar{\nu}(p_7)e^-(p_8)\bar{b}(p_6))+H(W^+(p_{9},p_{10})W^-(p_{11},p_{12}))$ & LO \\
|
|
\hline
|
|
\hline
|
|
\end{tabular}
|
|
\caption{Processes indicated by choice of the variable {\tt nproc}.}
|
|
\end{center}
|
|
\end{table}
|
|
\newpage
|
|
\begin{table}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline
|
|
800 & $ V\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5) $ [Vector Mediator] & NLO \\
|
|
801 & $ A\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)$ [Axial Vector Mediator] & NLO \\
|
|
802 & $ S\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)$ [Scalar Mediator] & NLO \\
|
|
803 & $ PS\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)$ [Pseudo Scalar Mediator] & NLO \\
|
|
804 & $ GG\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)$ [Gluonic DM operator] & NLO \\
|
|
805 & $ S--({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)$ [Scalar Mediator, mt loops] & NLO \\
|
|
\hline
|
|
820 & $V\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5)$ [Vector Mediator] & NLO + F \\
|
|
821 & $A\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5) $[Axial Vector Mediator] & NLO + F \\
|
|
822 & $ S\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5) $[Scalar Mediator] & NLO + F \\
|
|
823 &$ PS\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5) $[Pseudo Scalar Mediator] & NLO + F \\
|
|
\hline
|
|
840 &$ V\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)+f(p_6)$ [Vector Mediator] & LO\\
|
|
841 &$A\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)+f(p_6)$ [Axial Vector Mediator] & LO\\
|
|
842 &$ S\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)+f(p_6)$ [Scalar Mediator] & LO\\
|
|
843 &$ PS\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)+f(p_6)$ [Pseudo Scalar Mediator] & LO\\
|
|
844 &$ GG\to({\chi}(p_3)+\bar{\chi}(p_4)) +f(p_5)+f(p_6)$ [Gluonic DM operator] & LO\\
|
|
\hline
|
|
845 & $V\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5)+f(p_6)$ [Vector Mediator] & LO\\
|
|
846 & $A\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5)+f(p_6)$ [Axial Vector Mediator] & LO\\
|
|
847 & $S\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5)+f(p_6)$ [Scalar Mediator] & LO\\
|
|
848 & $PS\to({\chi}(p_3)+\bar{\chi}(p_4)) +\gamma(p_5)+f(p_6)$ [Pseudo Scalar Mediator] & LO\\
|
|
\hline
|
|
902 & Check of Volume of 2 particle phase space & \\
|
|
903 & Check of Volume of 3 particle phase space & \\
|
|
904 & Check of Volume of 4 particle phase space & \\
|
|
905 & Check of Volume of 5 particle phase space & \\
|
|
906 & Check of Volume of 6 particle phase space & \\
|
|
908 & Check of Volume of 8 particle phase space & \\
|
|
909 & Check of Volume of 4 particle massive phase space & \\
|
|
910 & Check of Volume of 3 particle (2 massive) phase space & \\
|
|
911 & Check of Volume of 5 particle W+t (with decay) massive phase space & \\
|
|
912 & Check of Volume of 5 particle W+t (no decay) massive phase space & \\
|
|
913 & Check of Volume of 5 particle W+t+g (in decay) massive phase space & \\
|
|
914 & Check of Volume of 5 particle W+t+g (in production) massive phase space & \\
|
|
\hline
|
|
\hline
|
|
\end{tabular}
|
|
\caption{Processes indicated by choice of the variable {\tt nproc}.\label{nproctable}}
|
|
\end{center}
|
|
\end{table}
|
|
\clearpage
|
|
|
|
|
|
\section{Historical PDF sets}
|
|
\label{olderPDFs}
|
|
The availability of a number of historical PDF sets is retained in the code. These should
|
|
typically not be used in modern analyses, but they may be helpful for comparison with
|
|
older codes or in specialized cases.
|
|
|
|
These distributions, together with their associated $\alpha_S(M_Z)$
|
|
values, are given in Tables~\ref{pdlabelmrs} and~\ref{pdlabelcteq}.
|
|
For the older distributions, where the
|
|
coupling was specified by $\Lambda$ this requires
|
|
some calculation and/or guesswork.
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c||c|c|c|}
|
|
\hline
|
|
{\tt mrstqed} & 0.1205 & hep-ph/0411040 &
|
|
{\tt mrs02nl} & 0.1197 & \mrstohtwo \\
|
|
{\tt mrs02nn} & 0.1154 & \mrstohtwo &
|
|
{\tt mrs4nf3} & 0.1083 & \mrstff \\
|
|
{\tt mrs4lf3} & 0.1186 & \mrstff &
|
|
{\tt mrs4nf4} & 0.1153 & \mrstff \\
|
|
{\tt mrs4lf4} & 0.1251 & \mrstff &
|
|
{\tt mrs0119} & 0.119 & \mrstohone \\
|
|
{\tt mrs0117} & 0.117 & \mrstohone &
|
|
{\tt mrs0121} & 0.121 & \mrstohone \\
|
|
{\tt mrs01\_j} & 0.121 & \mrstohone &
|
|
{\tt mrs01lo} & 0.130 & \mrstohtwofirst \\
|
|
{\tt mrs99\_1} & 0.1175 & \mrsninenine &
|
|
{\tt mrs99\_2} & 0.1175 & \mrsninenine \\
|
|
{\tt mrs99\_3} & 0.1175 & \mrsninenine &
|
|
{\tt mrs99\_4} & 0.1125 & \mrsninenine \\
|
|
{\tt mrs99\_5} & 0.1225 & \mrsninenine &
|
|
{\tt mrs99\_6} & 0.1178 & \mrsninenine \\
|
|
{\tt mrs99\_7} & 0.1171 & \mrsninenine &
|
|
{\tt mrs99\_8} & 0.1175 & \mrsninenine \\
|
|
{\tt mrs99\_9} & 0.1175 & \mrsninenine &
|
|
{\tt mrs9910} & 0.1175 & \mrsninenine \\
|
|
{\tt mrs9911} & 0.1175 & \mrsninenine &
|
|
{\tt mrs9912} & 0.1175 & \mrsninenine \\
|
|
{\tt mrs98z1} & 0.1175 & \mrsnineeight &
|
|
{\tt mrs98z2} & 0.1175 & \mrsnineeight \\
|
|
{\tt mrs98z3} & 0.1175 & \mrsnineeight &
|
|
{\tt mrs98z4} & 0.1125 & \mrsnineeight \\
|
|
{\tt mtungb1} & 0.109 & \mrsnineeight &
|
|
{\tt mrs98z5} & 0.1225 & \mrsnineeight \\
|
|
{\tt mrs96r1} & 0.113 & \mrsninesix &
|
|
{\tt mrs96r2} & 0.120 & \mrsninesix \\
|
|
{\tt mrs96r3} & 0.113 & \mrsninesix &
|
|
{\tt mrs96r4} & 0.120 & \mrsninesix \\
|
|
{\tt mrs95ap} & 0.1127 & \mrsninefive &
|
|
{\tt mrs95\_g} & 0.1148 & \mrsninefive \\
|
|
{\tt hmrs90e} & 0.09838 & \hmrs &
|
|
{\tt hmrs90b} & 0.10796 & \hmrs \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{Historical MRS-type pdf sets, their corresponding values of
|
|
$\alpha_S(M_Z)$ and a reference to the paper or preprint that
|
|
describes their origin.
|
|
\label{pdlabelmrs}}
|
|
\end{table}
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c||c|c|c|}
|
|
\hline
|
|
& & &
|
|
{\tt cteq66m} & 0.118 & \cteqsixsixm \\
|
|
{\tt cteq61m} & 0.118 & \cteqsixonem &
|
|
{\tt cteq6\_m} & 0.118 & \cteqsix \\
|
|
{\tt cteq6\_d} & 0.118 & \cteqsix &
|
|
{\tt cteq6\_l} & 0.118 & \cteqsix \\
|
|
{\tt cteq6l1} & 0.130 & \cteqsix &
|
|
{\tt cteq5hq} & 0.118 & \cteqfive \\
|
|
{\tt cteq5f3} & 0.106 & \cteqfive &
|
|
{\tt cteq5f4} & 0.112 & \cteqfive \\
|
|
{\tt cteq5\_m} & 0.118 & \cteqfive &
|
|
{\tt cteq5\_d} & 0.118 & \cteqfive \\
|
|
{\tt cteq5\_l} & 0.127 & \cteqfive &
|
|
{\tt cteq5l1} & 0.127 & \cteqfive \\
|
|
{\tt cteq5hj} & 0.118 & \cteqfive &
|
|
{\tt cteq5m1} & 0.118 & \cteqfive \\
|
|
{\tt ctq5hq1} & 0.118 & \cteqfive &
|
|
{\tt cteq4a5} & 0.122 & \cteqfour \\
|
|
{\tt cteq4hj} & 0.116 & \cteqfour &
|
|
{\tt cteq4lq} & 0.114 & \cteqfour \\
|
|
{\tt cteq4\_m} & 0.116 & \cteqfour &
|
|
{\tt cteq4\_d} & 0.116 & \cteqfour \\
|
|
{\tt cteq4\_l} & 0.132 & \cteqfour &
|
|
{\tt cteq4a1} & 0.110 & \cteqfour \\
|
|
{\tt cteq4a2} & 0.113 & \cteqfour &
|
|
{\tt cteq4a3} & 0.116 & \cteqfour \\
|
|
{\tt cteq4a4} & 0.119 & \cteqfour &
|
|
{\tt cteq3\_m} & 0.112 & \cteqthree \\
|
|
{\tt cteq3\_l} & 0.112 & \cteqthree &
|
|
{\tt cteq3\_d} & 0.112 & \cteqthree \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{Historical CTEQ-type pdf sets, their corresponding values of
|
|
$\alpha_S(M_Z)$ and a reference to the paper or preprint that
|
|
describes their origin.
|
|
\label{pdlabelcteq}}
|
|
\end{table}
|
|
|
|
|
|
\clearpage
|
|
|
|
\section{Version 8.3 changelog}
|
|
\label{changelog8.3}
|
|
\begin{itemize}
|
|
\item New processes 164,169 for off-shell SM and SMEFT single-top-quark and
|
|
anti-quark production, respectively. With this a new input.DAT block
|
|
'Single top SMEFT' is introduced which sets the SMEFT parameters, see
|
|
description for process 164.
|
|
\item Improve QCDLoop 2 interface performance with OpenMP. We no longer initialize
|
|
the library with each call and keep a global cache per thread.
|
|
\item New dynamic scale 'fixed', which keeps the settings for the fixed scales but
|
|
runs all dynamicscale code. This is mostly useful for debugging.
|
|
\item Toggle for rapidity/pseudorapidity in definition of R and jet cuts, in mdata.f.
|
|
\item 'writetxt' option in input.DAT, which writes each histogram as a plain
|
|
text file with space-separated columns.
|
|
\item Add COPYING.txt GPL license file.
|
|
\item Fixed \texttt{jets\_opphem}, which likely had no effect, depending on compiler.
|
|
|
|
\end{itemize}
|
|
|
|
\section{Version 8.2 changelog}
|
|
\label{changelog8.2}
|
|
\begin{itemize}
|
|
\item Implemented H+jet high energy amplitudes \cite{Neumann:2018bsx}. See description for process 200.
|
|
\end{itemize}
|
|
|
|
\section{Version 8.1 changelog}
|
|
\label{changelog8.1}
|
|
\begin{itemize}
|
|
\item Implemented one-loop electroweak corrections for $Z$, $t\bar t$ and di-jet production.
|
|
\item Implemented $Z\gamma$ process at NNLO including anomalous couplings \cite{Campbell:2017aul}.
|
|
\item Implemented $Z\gamma$ decay for $H+jet$ production.
|
|
\item Implemented $H$+2jet process with a finite top-quark mass and $H$+jet with finite
|
|
top-quark mass effects \cite{Neumann:2016dny}. This adds a new parameter [mtex] to the
|
|
the input file, which specifies to which order in 1/$m_t^k$ (k=0,2,4) the finite
|
|
part of the virtual corrections are computed.
|
|
\item Support for random seeds by setting the seed value (previously [ij]) to 0.
|
|
\item Support for boosted (as opposed to hadronic) definition of jettiness, which
|
|
is also now as default.
|
|
\item Support for $p_T$ and rapidity ranges for most cuts in the input file.
|
|
\item Added native implementation of two PDF sets containing photons ({\tt mrstqed}, {\tt CT14qed}).
|
|
\item Modified format of input file slightly to allow for $p_T$ and rapidity ranges for most cuts.
|
|
\item EXPERIMENTAL: Integration routine that adaptively selects the cross section
|
|
contribution with the largest integration uncertainty. It also adapts
|
|
integration calls in the warmup phase and then continuously increases them to
|
|
not run into grid bias problems. This ingration can be enabled by setting
|
|
{\tt newIntegration} to {\tt .true.} in {\tt Need/mcfmmain.f}. After each iteration a snapshot is
|
|
saved for resumption. When {\tt readin} is set to {\tt .true.} in the {\tt gridinfo\_logic}
|
|
common block, the integration will be resumed from any stage. Currently this
|
|
integration mode does not stop the integration, but the user can at any point
|
|
abort manually when the desired precision has been reached. It has only been
|
|
thoroughly tested with $Z\gamma$ and $H+$jet. Other processes might need
|
|
tweaks or specific initializations.
|
|
|
|
\item Fixed FROOT implementation.
|
|
\item Upgraded QCDLoop to QCDLoop 2.
|
|
\item Using new random number generator (Mersenne Twister) from libstdc++ (C++11).
|
|
\item Fixed bug concerning integration uncertainty of histogram bins.
|
|
\item Fixed bug in implementation of $H+$jet processes with finite top-quark mass effects
|
|
({\tt 201}, {\tt 202}, {\tt 206}, {\tt 207}) when using {\tt zerowidth = F}.
|
|
|
|
\item Removed flags virtonly,realonly,vanillafiles,creategrid in input.DAT, as well as broken
|
|
parameters for resuming integrations.
|
|
\item Removed support for PDFLIB.
|
|
\item Removed noomp version. If just a single thread is wanted, please set {\tt OMP\_NUM\_THREADS} to 1.
|
|
|
|
\end{itemize}
|
|
|
|
\section{Version 8.0 changelog}
|
|
\label{changelog8.0}
|
|
\begin{itemize}
|
|
\item Introduced NNLO capability for color-singlet processes.
|
|
\item Overall improvement in speed.
|
|
\item Added native support for additional pdf sets, NNPDF, CT14, MMHT.
|
|
\item Fixed small asymmetry in calculation of $W+1$~jet process at NLO.
|
|
\item Fixed per-mille level bug in NLO calculations of $W,Z,H+2$~jet processes.
|
|
\item Replace QCDLoop by QCDLoop 2.
|
|
\end{itemize}
|
|
|
|
\section{Version 7.0 changelog}
|
|
\label{changelog7.0}
|
|
\begin{itemize}
|
|
\item Implementation of OpenMP (Open Multi-processing)
|
|
\item Inclusion of four-photon process at NLO, {\tt nproc=289}.
|
|
\item Inclusion of vector boson fusion/vector boson scattering processes at LO,
|
|
{\tt nproc=220,2201,222,2221,224,2241,226,228,2281,229,2291,223,2231,225,2251}.
|
|
\item After Higgs discovery, added s-channel Higgs diagrams to the $gg \to VV$ process,
|
|
in $VV$ production processes, {\tt nproc=61,62,64,81-84,86-90}
|
|
\end{itemize}
|
|
|
|
\section{Version 6.7 changelog}
|
|
\label{changelog6.7}
|
|
\begin{itemize}
|
|
\item Fixed errors reported in histograms
|
|
\item Changed implementation of PDF uncertainty output for cross sections and histograms; code now differentiates
|
|
between appropriate calculations for CTEQ and MSTW, NNPDF, Alekhin et al
|
|
\item Added possibility of (unweighted) LHE output for select LO processes
|
|
\item Added a check to VEGAS to enable graceful exit if integral is zero
|
|
\item Included changes to allow production of grids for use with APPLGRID
|
|
\item Moved $H+b$ processes from {\tt nproc=131,132,133} to {\tt nproc=136,137,138}
|
|
\item Added effect of massive loops in $gg\to ZZ$ box process and interference with Higgs diagrams,
|
|
{\tt nproc=128,129,130,131,132,133}
|
|
\item Changed implementation of $gg \to WW$ interference-related processeses {\tt nproc=126,127} to
|
|
the same style as $gg\to ZZ$, {\tt nproc=123,124,125,126}
|
|
\item Added 1-loop $HH$ processes, {\tt nproc=601,602}
|
|
\item Added triphoton process at NLO, {\tt nproc=287}
|
|
\item Added $W\gamma\gamma$ process at LO, {\tt nproc=370,371}
|
|
\item New, faster implementation of H+5 parton amplitudes
|
|
\item Added two new cuts to the input file, {\tt ptmin\_photon(3rd)} and {\tt R(photon,jet)\_min}
|
|
\item Added a flag to the input file to control creation of APPLGRID output, {\tt creategrid}
|
|
\item Changed previous {\tt evtgen} logical flag in input file to an integer, {\tt nevtrequested}
|
|
\item Added a line in the input file to allow for an anomalous Higgs width for {\tt nproc=128,129,130,131,133}
|
|
\end{itemize}
|
|
|
|
\section{Versions 6.6 and 6.5 changelog}
|
|
\label{changelog6.5}
|
|
\begin{itemize}
|
|
\item Moved the ttH processes to the 640's
|
|
\item Added $tH$ and $\bar{t}H$ processes.
|
|
\item Added $tZ$ and $\bar{t}Z$ processes.
|
|
\item Added $\gamma+b$ and $\gamma+c$ process at leading order.
|
|
\item Added $W Z $ + 2 parton processes.
|
|
\item Shuffled 144 and 145.
|
|
\item Added new Dark Matter mono-jet and mono-photon processes (with process numbers in the 800's)
|
|
\end{itemize}
|
|
|
|
\section{Version 6.4 changelog}
|
|
\label{changelog6.4}
|
|
|
|
\subsection{Code changes}
|
|
\begin{itemize}
|
|
\item Corrected bug in implementation of $H\bar q q gg$ virtual amplitudes.
|
|
\item Enabled effect of {\tt removebr} for process 307.
|
|
\item Fixed the implementation of a dynamic scale for single top + b processes.
|
|
\item Added a new scale choice for top production ($m(345)^2+p_T(345)^2$).
|
|
\item Improved numerical stability in calculation of virtual contribution to process
|
|
201 and in calculation of real corrections to processes 180--187.
|
|
\end{itemize}
|
|
|
|
\section{Version 6.3 changelog}
|
|
\label{changelog6.3}
|
|
|
|
\begin{itemize}
|
|
\item Implementation of new processes:
|
|
\begin{itemize}
|
|
\item
|
|
Added processes {\tt 63,65} giving the radiation in the hadronic decay of the $W^+W^-$ process.
|
|
\item
|
|
Added processes {\tt 114} and {\tt 115} giving the $gg\to H\to WW$ process with radiation in the hadronic decay of the $W$.
|
|
\item
|
|
Added processes {\tt 501-516} giving the production and decay of
|
|
$t \bar{t} W^\pm$ including radiation in the semi-leptonic decay of the top and the anti-top.
|
|
\item
|
|
Added processes {\tt 120} and {\tt 121} giving the $H\to Z/\gamma^*(\to l \bar{l})+\gamma$
|
|
in the gluon fusion production process
|
|
\item
|
|
Added processes in the range {\tt 300-309} describing production of $Z+\gamma+\gamma$
|
|
and $Z+\gamma$+jet at NLO.
|
|
\item
|
|
Process numbers from version 6.2 were moved to make space
|
|
(e.g. old $64 \to 69$ and old $63\to 64$, old $192-198 \to 500-531$.).
|
|
\end{itemize}
|
|
\subsection{Code changes}
|
|
\item Lengthened the number of characters allowed for the input parameter LHAPDF {\tt group},
|
|
that is read from the input file.
|
|
\item Removed the tacit assumption of unitarity in processes, {\tt 13} and {\tt 18},
|
|
subprocess $gg \to \bar{q}$,
|
|
allowing arbitrary values of $V_{cs}$ and $V_{cd}$.
|
|
\item
|
|
Corrected closed fermion loop virtual corrections to the $gg \to Z+2$-jet subprocess which were assigned to the wrong
|
|
helicities in error. This bug was of minor numerical importance.
|
|
\item
|
|
Fixed number of jets expected in nplotter\_generic.f for ZH and WH processes with removebr=T.
|
|
\item
|
|
Added additional parameters to the input files,
|
|
especially for powheg style output and photon cuts, as specified in section \ref{Input_parameters}.
|
|
\item
|
|
changed mbook so that zero bins still appear in the Topdrawer output,
|
|
(for consistency, especially for combining runs).
|
|
\item
|
|
Removed a correction used to debug hadronic $W$ decays, that was erroneously left in the code.
|
|
The hadronic branching ratio of the $W$ now changes at NLO as it should.
|
|
|
|
\item Corrected bug that led to the $W^-t$ process (187) being calculated incorrectly.
|
|
|
|
\item Removed a bug that caused the real part Higgs+1 jet process (203)
|
|
to crash (in version 6.2 only).
|
|
|
|
\item
|
|
Coupling of Higgs boson to top and bottom quarks expressed in terms of the running mass.
|
|
|
|
\item
|
|
Corrected normalization of pseudoscalar Higgs cross section (processes 206 and 207)
|
|
and set active quark in the loop to be the top rather than the bottom.
|
|
|
|
\end{itemize}
|
|
|
|
\section{Version 6.2 changelog}
|
|
\label{changelog6.2}
|
|
|
|
A number of changes to the code and input files have been implemented
|
|
between v6.1 and v6.2. These are listed below.
|
|
|
|
\subsection{Input file changes}
|
|
\begin{itemize}
|
|
\item Implementation of new processes:
|
|
\begin{itemize}
|
|
\item
|
|
Added process {\tt 233-235} and {\tt 238-240} that give results in the four-flavour scheme
|
|
with top decay.
|
|
\item
|
|
Added process {\tt 270} (Higgs + 2 jets, with Higgs decaying to $\gamma \gamma$).
|
|
\item
|
|
Added LO processes {\tt 278} and {\tt 279} (Higgs + 3 jets with Higgs decaying to $WW$ or $ZZ$).
|
|
\item
|
|
Adding process {\tt 90} for identical fermions in $ZZ$ decay.
|
|
\item
|
|
Added processes {\tt 12} and {\tt 17}, $Wb$ production from charm quarks
|
|
\end{itemize}
|
|
\end{itemize}
|
|
|
|
|
|
\subsection{Code changes}
|
|
\begin{itemize}
|
|
\item
|
|
Included new plotting routines for s-channel single top, 4F t-channel single top and
|
|
top pair production,
|
|
\begin{verbatim} nplotter_tbbar.f, nplotter_4ftwdk.f, nplotter_ttbar.f
|
|
\end{verbatim}
|
|
\item
|
|
Corrected all nplotter files to ensure ntuple output.
|
|
\item
|
|
Added CT10 parton distributions.
|
|
\item
|
|
Upgraded treatment of $t \bar{t}$ one-loop matrix elements for processes {\tt 141-150} to use results of
|
|
ref.~\cite{Badger:2011yu} rather than ref.~\cite{Korner:2002hy} with consequent improvement in speed.
|
|
\item
|
|
Updated check on whether non-zero $m_{56}$ cut is applied to exclude $Z \to$~neutrino processes (for which is is not needed).
|
|
\item
|
|
Removed overcounting of neutrinos for non-resonant diagrams in the $ZZ$ process.
|
|
\item
|
|
Removed effect of $m_{34}$ for dirgam process {\tt 280}.
|
|
Therefore for this process $m_{34}$ cut is not operative.
|
|
\item
|
|
Corrected $ZZ$ processes {\tt 80-90} where the Z's decayed differently
|
|
to different final states.
|
|
There was a bug in the gluon-gluon contribution since \begin{verbatim} gg_ZZ.f \end{verbatim} did not handle the
|
|
different couplings for Z(3+4) and Z(5+6) correctly.
|
|
\item
|
|
Removed dependence on path in \begin{verbatim} ffinit_mine.f \end{verbatim} and modified Install script
|
|
to create symbolic links.
|
|
\item
|
|
Updated handling of anomalous couplings to allow for no form-factors if tevscale $< 0$, see section \ref{sec:anomalous}.
|
|
\item
|
|
Moved processes ({\tt 151-156} to {\tt 141-151}), ({\tt 131,132} to {\tt 251,252}) and ({\tt 141-143} to {\tt 131-133}).
|
|
\item
|
|
Improved implementation of $p_T$ cut in
|
|
\begin{verbatim} gg_WW.f, gg_ZZ.f \end{verbatim}
|
|
\item
|
|
Added improvements to mbook.f for Root histogram errors
|
|
\item
|
|
Corrected masscuts.f to avoid problems with $m_{56}$ cut.
|
|
\end{itemize}
|
|
|
|
|
|
\section{Version 6.1 changelog}
|
|
\label{changelog}
|
|
|
|
A number of changes to the code and input files have been implemented
|
|
between v6.0 and v6.1. These are listed below.
|
|
|
|
\subsection{Input file changes}
|
|
\begin{itemize}
|
|
\item Implementation of new processes:
|
|
\begin{itemize}
|
|
\item Higgs decay modes for various
|
|
production channels ({\tt 93, 94, 98, 99, 104, 105, 109, 210, 214, 215}).
|
|
\item Calculation of $gg \to H \to WW$ including exact top and bottom loops ({\tt 121})
|
|
and interference with S.M. box diagrams ({\tt 122}).
|
|
\item Production of top pairs in association with a $W$ ({\tt 198, 199}).
|
|
\item Direct photon production including fragmentation ({\tt 280}).
|
|
\item Reorganization of $Wb$ calculations in
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4FNS ({\tt 401}-{\tt 408}), 5FNS ({\tt 411, 416}) and when combined
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({\tt 421, 426}).
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\end{itemize}
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\item Addition of flags {\tt writetop}, {\tt writedat}, {\tt writegnu}
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and {\tt writeroot} to input file, to control writing of output into Topdrawer,
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plain ascii, gnuplot and root script files.
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\item New flag to trigger exclusion of gluon-gluon initiated sub-processes
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|
({\tt omitgg}).
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|
\item New lines in input file to specify anomalous $ZZ\gamma$
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|
and $Z\gamma\gamma$ couplings.
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|
\item Changed implementation of transverse mass cut ({\tt m34transcut})
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|
to be process-specific (see manual).
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|
\item Added fragmentation functions of Gehrmann-de Ridder and Glover
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|
(see description of {\tt fragset} in manual).
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|
\item Added ability to over-ride switching from a scaling to a fixed isolation
|
|
cut according to value of {\tt epsilon\_h} (see manual).
|
|
\item Changed the role of {\tt dynamicscale} from a boolean flag to a string
|
|
variable specifying the type of dynamic scale to be applied. See manual
|
|
for description of new scale choices available.
|
|
\end{itemize}
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\subsection{Code changes}
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|
\begin{itemize}
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|
\item Re-enabled n-tuple output for processes with specific {\tt nplotter} routines.
|
|
\item Corrected phase-space generation for diphoton and direct photon production
|
|
when cut on $p_T({\rm photon})$ is less than cut on $p_T({\rm jet})$.
|
|
\item Corrected implementation of errors in histogram output.
|
|
\item Added code to allow histogram output in {\tt gnuplot} and {\tt root} format.
|
|
\item Corrected virtual amplitudes for $WZ$ production with $Z \to $~neutrinos
|
|
({\tt 72, 77}).
|
|
\item Corrected implementation of processes {\tt 52, 53, 54}.
|
|
\item Implemented anomalous couplings for $W\gamma$ and $Z\gamma$ processes.
|
|
\item Corrected calculation of $W+2$~jet and $Z+2$~jet processes with
|
|
{\tt Gflag = Qflag = .true.} and a dynamic scale.
|
|
\item Added non-perturbative contributions to fragmentation functions.
|
|
\item Fixed implementation of finite $m_t$ correction factor that is applied to
|
|
$gg \to H$ cross-sections. Differences with v6.0 for $m_H > 2 m_t$ only.
|
|
\item Added ability to calculate direct photon production including fragmentation
|
|
contributions.
|
|
\item Corrected definition of array containing particle momenta in $H+1$~jet virtual
|
|
routines (v6.0 results for these processes may be compiler-dependent).
|
|
\item Corrected implementation of invariant mass cuts for cases when invariant
|
|
masses do not correspond to electroweak bosons.
|
|
\item Allowed off-shell $W$ bosons in top decays for processes {\tt 36},
|
|
{\tt 151}, {\tt 152} and {\tt 153}.
|
|
\end{itemize}
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|
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|
\printbibliography
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\end{document}
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