You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
185 lines
8.6 KiB
185 lines
8.6 KiB
\topheading{Configuration}
|
|
\label{Input_parameters}
|
|
|
|
\midheading{Compile-time settings}
|
|
MCFM allows the user to choose between a number of schemes
|
|
for defining the electroweak couplings. These choices are summarized
|
|
in Table~\ref{ewscheme}. The scheme is selected by modifying the
|
|
value of {\tt ewscheme} in {\tt src/User/mdata.f} prior to compilation,
|
|
which also contains
|
|
the values of all input parameters (see also Table~\ref{default}).
|
|
|
|
\begin{table}
|
|
\begin{center}
|
|
\caption{Different options for the scheme used to fix the electroweak
|
|
parameters of the Standard Model and the corresponding default input
|
|
values. $M_W$ and $M_Z$ are taken from ref.~\cite{Amsler:2008zzb}.}
|
|
\label{ewscheme}
|
|
\vspace{0.5em}
|
|
\begin{tabular}{|c|c|c|c|c|c|c|} \hline
|
|
Parameter & Name & Input Value
|
|
& \multicolumn{4}{c|}{Output Value determined by \tt ewscheme} \\
|
|
\cline{4-7}
|
|
& ({\tt \_inp}) & & {\tt -1} & {\tt 0} & {\tt 1} & {\tt 2} \\ \hline
|
|
$G_F$ & {\tt Gf} & 1.16639$\times$10$^{-5}$
|
|
& input & calculated & input & input \\
|
|
$\alpha(M_Z)$ & {\tt aemmz} & 1/128.89
|
|
& input & input & calculated & input \\
|
|
$\sin^2 \theta_w$& {\tt xw} & 0.2223
|
|
& calculated & input & calculated & input \\
|
|
$M_W$ & {\tt wmass} & 80.385 GeV
|
|
& input & calculated & input & calculated \\
|
|
$M_Z$ & {\tt zmass} & 91.1876 GeV
|
|
& input & input & input & calculated \\
|
|
$m_t$ & {\tt mt} & {\tt input.ini}
|
|
& calculated & input & input & input \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{table}
|
|
|
|
The default scheme corresponds to {\tt ewscheme=+1}. As described below, this corresponds to a scheme
|
|
in which the top quark mass is an input parameter so that it is
|
|
more suitable for many processes now included in the program.
|
|
|
|
The choice of ({\tt ewscheme=-1}) enforces the use of an effective field
|
|
theory approach, which is valid for scales below the top mass. In this
|
|
approach there are 4 independent parameters (which we choose to be
|
|
$G_F$, $\alpha(M_Z)$, $M_W$ and $M_Z$). For further details,
|
|
see Georgi~\cite{Georgi:1991ci}.
|
|
|
|
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
|
|
parameters from the remaining 5. The variable {\tt ewscheme} then performs
|
|
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
|
|
new MadEvent default, which is also the same as that used in
|
|
Alpgen~\cite{Alpgen} and LUSIFER~\cite{Lusifer}.
|
|
For processes in which the top quark is directly produced it is
|
|
preferable to use the schemes ({\tt ewscheme=0,1,2}), since in these schemes
|
|
one can adjust the top mass to its physical value (in the input file
|
|
{\tt input.ini}). Schemes where the $W$ and $Z$ masses are fixed to their measured
|
|
values are the most appropriate for $W$ and $Z$ production processes.
|
|
|
|
\begin{table}
|
|
\begin{center}
|
|
\caption{Default values for the remaining parameters in MCFM.
|
|
$\Gamma_W$ and $\Gamma_Z$ from ref.~\cite{Amsler:2008zzb}.}
|
|
\label{default}
|
|
\vspace{0.5em}
|
|
\begin{tabular}{|c|c|c|} \hline
|
|
Parameter & Fortran name & Default value \\
|
|
\hline
|
|
$m_\tau$ & {\tt mtau} & 1.777 GeV \\
|
|
$m^2_\tau$& {\tt mtausq} & 3.1577 GeV$^2$ \\
|
|
$\Gamma_\tau$ & {\tt tauwidth}& 2.269$\times$10$^{-12}$~GeV \\
|
|
$\Gamma_W$ & {\tt wwidth} & 2.093 GeV \\
|
|
$\Gamma_Z$ & {\tt zwidth} & 2.4952 GeV \\
|
|
$V_{ud}$ & {\tt Vud} & 0.975 \\
|
|
$V_{us}$ & {\tt Vus} & 0.222 \\
|
|
$V_{ub}$ & {\tt Vub} & 0. \\
|
|
$V_{cd}$ & {\tt Vcd} & 0.222 \\
|
|
$V_{cs}$ & {\tt Vcs} & 0.975 \\
|
|
$V_{cb}$ & {\tt Vcb} & 0. \\
|
|
\hline
|
|
\end{tabular}
|
|
|
|
\end{center}
|
|
\end{table}
|
|
|
|
% I consider this setting dangerous, where is it used?
|
|
|
|
%In the same file ({\tt mdata.f}) one can also choose the definition
|
|
%that the program uses for computing transverse quantities, namely
|
|
%transverse momentum or transverse energy. These are defined by,
|
|
%\begin{eqnarray}
|
|
%\mbox{transverse momentum:} & \sqrt{p_x^2+p_y^2} \; ,\nonumber \\
|
|
%\mbox{transverse energy:} &
|
|
% \frac{E \sqrt{p_x^2+p_y^2}}{\sqrt{p_x^2+p_y^2+p_z^2}} \; .
|
|
%\end{eqnarray}
|
|
%The two definitions of course coincide for massless particles.
|
|
%The chosen definition is used for all cuts that are applied to the
|
|
%process and it is the one that is used in the default set of histograms.
|
|
|
|
\midheading{Parton distributions}
|
|
\label{subsec:pdfsets}
|
|
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 $\alpha_s$.
|
|
As default the code uses the LHAPDF library for PDF evaluation; a native
|
|
implementation of some (mostly older) PDF sets is also retained.
|
|
|
|
\midheading{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 ($\delta_{\mathrm{wk}}$) given by,
|
|
|
|
\begin{equation}
|
|
\delta_{\mathrm{wk}} = \frac{d\sigma_{\mathrm{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. (The appropriate nplotter routine is displayed on the process web-page, reachable from
|
|
the tables in Section~\ref{MCFMprocs}.)
|
|
|
|
|
|
|
|
% \midheading{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 PDFs 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.
|
|
|
|
|