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361 lines
14 KiB
361 lines
14 KiB
\section{Configuration}
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\label{Input_parameters}
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\subsection{Compile-time settings}
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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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\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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\vspace{0.5em}
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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 \\
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$\sin^2 \theta_w$& {\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.ini}
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& calculated & input & input & input \\
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\hline
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\end{tabular}
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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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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
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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}.
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{\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.ini}).
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\begin{table}
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\begin{center}
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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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\vspace{0.5em}
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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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\end{center}
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\end{table}
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% I consider this setting dangerous, where is it used?
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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 \\
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%\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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\subsection{Parton distributions}
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\label{subsec:pdfsets}
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The value of $\alpha_s(M_Z)$ is not adjustable; it is hardwired with the
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parton distribution. In addition, the parton distribution also specifies
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the number of loops that should be used in the running of $\alpha_s$.
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As default the code uses the LHAPDF library for PDF evaluation; a native
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implementation of some (mostly older) PDF sets is also retained, see
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Appendix~\ref{olderPDFs}.
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\subsection{Electroweak corrections}
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\label{subsec:EW}
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As of version 8.1, {\tt MCFM} allows the calculation of weak corrections to a
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selection of processes: {\tt 31} (neutral-current DY),
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{\tt 157} (top-pair production) and {\tt 190} (di-jet production).
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This is controlled by the flag {\tt ewcorr} in the input file. A complete description
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of the calculations is provided in Ref.~\cite{Campbell:2016dks}.
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By setting {\tt ewcorr} to {\tt sudakov}, the program performs a calculation of
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the leading weak corrections to these processes using a Sudakov approximation that
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is appropriate at high energies. The calculation of the weak corrections using the
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exact form of the one-loop amplitudes is obtained by using the flag {\tt exact}.
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A comparison between the two approaches, together with discussions of the validity of
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the Sudakov approximation, may be found in Ref.~\cite{Campbell:2016dks}.
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For the case of top-pair and di-jet production, the weak one-loop corrections contain
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infrared divergences that must be cancelled against corresponding real radiation
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contributions (in much the same manner as a regular NLO QCD calculation). For this
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reason the screen output will contain two sets of iterations corresponding to the
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virtual and real contributions.
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For all processes, performing the calculation of weak
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corrections enables a special mode of phase-space integration that is designed to
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better-sample events produced at high-energies. For this reason the VEGAS output that
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appears on the screen does not correspond to a physical cross-section -- and a corresponding
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warning message to this effect will be displayed. In many cases the quantity of most interest
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is the relative correction to the leading order result ($\delta_\mathrm{wk}$) given by,
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\begin{equation}
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\delta_\mathrm{wk} = \frac{d\sigma_\mathrm{wk}^{NLO} - d\sigma^{LO}}{d\sigma^{LO}} \;.
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\end{equation}
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It is straightforward to compute this quantity for a distribution by editing the appropriate
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{\tt nplotter} routine. This is achieved by filling a histogram with the weight corresponding
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to the LO result, another with the weight for the NLO weak result and then an additional placeholder
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histogram that contains the special string {\tt '+RELEW+'}. Examples of the syntax and correct calling
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sequence can be seen in the code.
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% \subsection{Nuclear collisions}
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% \label{sec:nucleus}
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%
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% It is possible to specify nuclear collisions by choosing values
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% of {\tt ih1} and/or {\tt ih2} above {\tt 1000d0}. In that case,
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% the identity of the nucleus is specified by the atomic number
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% and mass ($Z$ and $A$ respectively) as follows:
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% \begin{equation}
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% {\tt ih} = 1000Z+A.
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% \end{equation}
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% For example, to choose an incoming lead beam one would set
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% {\tt ih1=+82207d0}, corresponding to $Z=82$ and $A=207$.
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% When running the program, the value of {\tt sqrts} should also be
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% changed. This must be done by hand and is not automatically taken
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% care of by the
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% program. The centre-of-mass energy is decreased by a factor of
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% $\sqrt{Z/A}$ for each nuclear beam.
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%
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% The nucleon \PDF{}s are calculated by applying the correction
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% factors of EKS98~\cite{Eskola:1998df} on top of the \PDF{} set that is selected.
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% This construction simply corrects each parton distribution by
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% a factor that depends on the value of $(x,\mu)$ in the event.
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% This parametrization is limited to the region $\mu < 100$~GeV and
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% any value above that threshold will instead default to $100$~GeV.
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%
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% Note that the cross-section reported by the program at the end
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% of the run is given per nucleon per beam. Therefore the
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% appropriate factors of $A$ should be applied in order to obtain
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% the total cross section.
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\subsection{Run-time input file configuration}
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\MCFM{} execution is performed in the {\tt Bin/} directory,
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with syntax:
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\begin{center}
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{\tt mcfm\_omp }{\it input.ini}
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\end{center}
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If no command line options are given, then \MCFM{} will default
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to using the file {\tt input.ini} in the current directory for
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choosing options. The \texttt{input.ini} file can be in any directory and
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then the first argument to \texttt{mcfm\_omp} should be the location
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of the file. Furthermore, one can overwrite or append single
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configuration options with additional parameters like
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\texttt{./mcfm\_omp benchmark/input.ini -general\%part=nlo -lhapdf\%dopdferrors=.true.}.
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Here specifying a parameter uses a single dash, then the section name as in the configuration file, followed
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by a percent sign, followed by the option name, followed by an equal sign and the actual value of the setting.
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All default settings in the input file are explained below, as well as further optional parameters.
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The top level setting \texttt{mcfm\_version} specifies the input file version number and it must match the version of
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the code being used.
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\clearpage
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\input{tex/table_general.tex}
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\input{tex/table_resummation.tex}
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\input{tex/table_nnlo.tex}
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\input{tex/table_pdf.tex}
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\input{tex/table_lhapdf.tex}
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\input{tex/table_scales.tex}
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\begin{table}
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\begin{center}
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\begin{longtable}{|l|l|l|}
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\hline
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{\tt dynamic scale} & $\mu_0^2$ & comments\\
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\hline
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{\tt m(34)} & $(p_3+p_4)^2$ & \\
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{\tt m(345)} & $(p_3+p_4+p_5)^2$ & \\
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{\tt m(3456)} & $(p_3+p_4+p_5+p_6)^2$ & \\
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{\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 \\
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{\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
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particle 3+4+5 \\
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{\tt sqrt(M\pow 2+pt5\pow 2)} & $M^2 + \vec{p_T}_5^2$ & $M=$~mass of particle 3+4 \\
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{\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 \\
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{\tt pt(photon)} & $\vec{p_T}_\gamma^2$ & \\
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{\tt pt(j1)} & $\vec{p_T}_{j_1}^2$ & \\
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{\tt HT} & $\sum_{i=1}^n {p_T}_i$ & $n$ particles (partons, not jets) \\
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\hline
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\hline\end{longtable}
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\end{center}
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\caption{Choices of the input parameter {\tt dynamicscale} that result in an event-by-event
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calculation of all relevant scales using the given reference scale-squared $\mu_0^2$.
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\label{tab:dynamicscales}}
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\end{table}
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\input{tex/table_masses.tex}
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\clearpage
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\input{tex/table_basicjets.tex}
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\input{tex/table_masscuts.tex}
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\input{tex/table_cuts1.tex}
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\input{tex/table_cuts2.tex}
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\clearpage
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\input{tex/table_photon.tex}
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\input{tex/table_histogram.tex}
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\input{tex/table_integration.tex}
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\clearpage
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\subsection{Process specific options}
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\input{tex/table_singletop.tex}
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\clearpage
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\input{tex/table_anom_wz.tex}
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\input{tex/table_wz2jet.tex}
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\input{tex/table_hjetmass.tex}
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\input{tex/table_anom_higgs.tex}
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\input{tex/table_extra.tex}
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\input{tex/table_dipoles.tex}
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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\clearpage
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%\begin{table}[]
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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%\begin{table}[]
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%\end{table}
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\subsection{User modifications to the code}
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Modifying the plotting routines in the files \texttt{src/User/nplotter*.f} allows for modification of the pre-defined
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histograms and addition of any number of arbitrary observables. The routine \texttt{gencuts\_user} can be adjusted in
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the file
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\texttt{src/User/gencuts\_user.f90} for additional cuts after the jet algorithm has performed the
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clustering. In the same file the routine \texttt{reweight\_user} can be modified to include a manual re-weighting
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for all integral contributions. This can be used to obtain improved uncertainties in, for example, tails of
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distributions.
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One example is included in the subdirectory \texttt{examples}, where the \texttt{reweight\_user} function approximately
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flattens the Higgs transverse momentum distribution, leading to equal relative uncertainties even in the tail at
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\SI{1}{TeV}.
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\label{user}
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\begin{itemize}
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\item {\tt subroutine nplotter\_user(pjet, wt,wt2, nd)}
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This subroutine is called to allow the user to bin their own
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histograms. Variables passed to this routine:
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\begin{itemize}
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\item p: 4-momenta of incoming partons(i=1,2), outgoing leptons
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and
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jets in the format p(i,4) with the particles
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numbered
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according to the input file and components labelled
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by
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(px,py,pz,E).
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\item wt: weight of this
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event
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\item wt2: weight$^2$ of this
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event
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\item nd: an integer specifying the dipole number of this
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contribution
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(if applicable), otherwise equal to zero.
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\end{itemize}
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\end{itemize}
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