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169 lines
8.5 KiB
169 lines
8.5 KiB
\topheading{CuTe-MCFM}
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\includegraphics[width=0.4\textwidth]{./sections/cute-mcfmpic.png}
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\midheading{N$^3$LL and N$^4$LL $q_T^2$ resummation for color-singlet processes in MCFM}
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Based on \href{https://arxiv.org/abs/2009.11437}{arXiv:2009.11437} (Becher, Neumann '20).
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The $q_T$ resummation in CuTe-MCFM is available for color-singlet processes and based on a
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factorization theorem in SCET. It is fully differential in the Born kinematics and matches
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to large-$q_T^2$ fixed-order predictions at relative order
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$\alpha_s^2$. It provides an efficient way to estimate uncertainties from
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fixed-order truncation, resummation, and parton distribution
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functions. In addition to $W, Z$ and $H$ production, also the diboson
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processes $\gamma\gamma$, $Z\gamma$, $ZH$, $WH$, $WW$, $WZ$ and $ZZ$ are available, including decays.
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While CuTe-MCFM can calculate $q_T$-resummed results without using
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pregenerated beam functions grids, we recommend that LHAPDF grid files are
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generated for the beam functions beforehand for a choice of a PDF set. This
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\emph{significantly} accelerates the evaluation of the beam functions and the
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integration.
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CuTe-MCFM ships with pregenerated beamfunction grids for the central
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values of \texttt{CT14nnlo} and \texttt{NNPDF31\_nnlo\_as\_0118}, which
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are included in the \texttt{Bin/PDFs} directory. This path is automatically used
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as the preferred path for LHAPDF grid files. With these pregenerated
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grids the example input files work out of the box. For other PDF sets or
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when using PDF errors, the first run of CuTe-MCFM should be with the
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setting \texttt{makegrid=.true.}. Additionally the input and output
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directories for the PDF grids have to be specified. For example the
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input directory is typically \texttt{/usr/local/share/LHAPDF/} (or the
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\texttt{PDFs/} directory relative to the mcfm executable in \texttt{Bin}) and
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the output directory should be a user-writeable directory like
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\texttt{/home/user/gridout/} (or \texttt{PDFs/}). Note the trailing slashes.
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When calling mcfm with \texttt{makegrid=.true.} only the beam function
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grids are written during that run, and mcfm exits afterwards.
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We recommend to use \texttt{PDFs/} as the gridout path, since this
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path is automatically added to the LHAPDF search paths, and you won't have to
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copy the generated grid directories to your LHAPDF grid directory or set the
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\texttt{LHAPDF\_DATA\_PATH} environment variable to the gridout path.
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For example for the set CT14nnlo the grid directories
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\texttt{CT14nnlo\_B00}, \texttt{CT14nnlo\_B10}, \texttt{CT14nnlo\_B11},
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\texttt{CT14nnlo\_B20}, \texttt{CT14nnlo\_B21}, \texttt{CT14nnlo\_B22} and \texttt{CT14nnlo\_G10}
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are written and have to be copied to the
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directory where LHAPDF searches for the grid files. When the gridout path is chosen as
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\texttt{PDFs/} no further action is necessary. The LHAPDF grid file
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search path can be modified by setting the shell
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environment variable \texttt{LHAPDF\_DATA\_PATH} to the desired
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directory, but the \texttt{PDFs} directory is always used as the preferred directory.
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The next run of mcfm should be done with \texttt{makegrid=.false.} and \texttt{usegrid=.true.}.
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Other important parameters for the resummation are \texttt{res\_range},
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determining the integration range of the purely resummed part,
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\texttt{resexp\_range}, determining the integration range of the
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fixed-order expanded resummed part, and \texttt{fo\_cutoff} which sets
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the lower $q_T$ cutoff for the fixed-order part. Typically this cutoff
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should agree with the lower range of \texttt{resexp\_range}. For example
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for $Z$ production one can integrate up to $m_Z$ with a cutoff of 1 GeV: \texttt{res\_range =
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0.0 90.0},
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\texttt{resexp\_range = 1.0 90.0}, \texttt{qt\_cutoff = 1.0}.
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For details regarding these parameters see the next section. The
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transition function is also discussed below.
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\hypertarget{input-file-parameters}{%
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\midheading{Input file parameters}\label{input-file-parameters}}
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The \texttt{[resummation]} section has been added to the input file to
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control the resummation. The following keys are available:
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\begin{longtable}[]{@{}ll@{}}
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% \toprule
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\begin{minipage}[b]{0.24\columnwidth}\raggedright
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Key\strut
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\end{minipage} & \begin{minipage}[b]{0.71\columnwidth}\raggedright
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Description\strut
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\end{minipage}\tabularnewline
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% \midrule
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\endhead
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{usegrid}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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\texttt{.true.} or \texttt{.false.} determines whether pregenerated
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LHAPDF interpolation grids should be used for the resummation beam
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functions.\strut
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\end{minipage}\tabularnewline
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{makegrid}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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If \texttt{.true.}, then MCFM runs in grid generation mode. This
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generates LHAPDF grid files in the directory \texttt{gridoutpath} from
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LHAPDF grids in the directory \texttt{gridinpath}. After the grid
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generation MCFM stops and should be run subsequently with
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\texttt{makegrid = .false.} and \texttt{usegrid = .true.}. When
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\texttt{lhapdf\%dopdferrors=.true.} then also grids for the error sets
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are generated.\strut
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\end{minipage}\tabularnewline
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{gridoutpath}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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Output directory for LHAPDF grid files, for example
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\texttt{/home/tobias/local/share/LHAPDF/}\strut
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\end{minipage}\tabularnewline
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{gridinpath}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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Input directory for LHAPDF grid files, for example
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\texttt{/home/tobias/local/share/LHAPDF/}\strut
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\end{minipage}\tabularnewline
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{res\_range}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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Integration range of purely resummed part, for example \texttt{0.0 80.0}
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for $q_T$ integration between 0 and 80 GeV.\strut
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\end{minipage}\tabularnewline
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{resexp\_range}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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Integration range of fixed-order expanded resummed part, for example
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\texttt{1.0 80.0} for $q_T$ integration between 1 and 80 GeV.\strut
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\end{minipage}\tabularnewline
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{fo\_cutoff}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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Lower $q_T$ cutoff $q_0$ for the fixed-order part, see eq.~\eqref{eq:matchingmod} below.
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Typically the value should agree with the lower range of \texttt{resexp\_range}.\strut
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\end{minipage}\tabularnewline
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\begin{minipage}[t]{0.24\columnwidth}\raggedright
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\texttt{transitionswitch}\strut
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\end{minipage} & \begin{minipage}[t]{0.71\columnwidth}\raggedright
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Parameter passed to the plotting routine to modify the transition
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function, see text.\strut
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\end{minipage}\tabularnewline
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% \bottomrule
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\end{longtable}
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We strongly recommend to calculate resummed results with pregenerated
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grids, see the previous section.
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The integration range for the purely resummed part can be controlled with the key
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\texttt{res\_range} and should typically be between $0$ and some upper
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value. For example for $W^\pm, Z$ or $H$ production this can just be
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the boson mass. For other processes there can be thresholds and this
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number must be selected more carefully to not run into numerical issues,
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see arXiv:2009.11437.
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The setting \texttt{resexp\_range} and \texttt{fo\_cutoff} are relevant
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for the matching corrections. The values of the \texttt{resexp\_range}
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determine the integration range for the fixed-order expansion of the
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resummed part. The minimum should typically be at least one GeV for
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numerical stability. For smaller values significantly more time goes
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into the integration, and the minimum number of Vegas calls might need
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to increased. For single boson processes the maximum value can again be
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the boson mass, although it can be set to a value where the implemented
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transition function fully switches to zero. The fixed-order cutoff
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\texttt{fo\_cutoff} determines the minimum $q_T$ for the fixed-order
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calculation. This should typically agree with the lower range of the
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\texttt{resexp\_range}.
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Lastly, the parameter \texttt{transitionswitch} is passed for
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convenience to the plotting routines where the transition function is
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implemented. It can be used for for an easy control of the transition
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region as described in the following.
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\input{sections/CMplottingandtransition.tex}
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\input{sections/CMmodifyingplotting.tex}
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