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.
96 lines
5.2 KiB
96 lines
5.2 KiB
|
|
\section{Benchmark results at NNLO }
|
|
\label{sec:NNLO}
|
|
\label{sec:benchmark}
|
|
We perform 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
|
|
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 \Delta R(\text{photon}, \text{lepton}) > 0.3 \quad
|
|
\end{eqnarray}
|
|
For $Z$ production we also impose a minimum $Z^*$ virtuality ({\tt m34min})
|
|
of $40$~GeV.
|
|
|
|
Our benchmark results are shown in Table~\ref{NNLObenchmarks} and were performed on an Intel Xeon X5650 @ 2.67GHz
|
|
system with 16 nodes of 12 cores each. MCFM was compiled with the Intel compiler and default optimizations as well
|
|
as the default MCFM setup including all pre-defined histograms. The NNLO \CPU{} time includes the time necessary
|
|
for the NLO calculation. The numbers for the NLO and NNLO results were obtained independently. By tweaking the
|
|
initial number of calls or the number of iterations per batch it is
|
|
certainly possible to optimize the runtimes. While the numerical precision is not yet good sufficient for most of the
|
|
fitted corrections to significantly improve the results, the fits are highly reliable and correctly estimate the
|
|
residual $\taucut$ dependence.
|
|
|
|
\begin{table}[]
|
|
\caption{Benchmark cross-sections at NLO and NNLO, using the parameters
|
|
and settings described in the text. All numbers are obtained for a numerical 0.2\% precision goal.
|
|
All NLO numbers are obtained within minutes on a desktop system, except for $Z\gamma$, which requires at the
|
|
order of 20-30 minutes. The NNLO \CPU{} time includes the time for the NLO calculation.}
|
|
\label{NNLObenchmarks}
|
|
\vspace{0.5em}
|
|
\begin{tabular}{@{}lcccccc@{}}
|
|
\hline
|
|
Process & \texttt{nproc} & $\taucut$ [GeV] & $\sigma^\text{NLO}$ &
|
|
$\sigma^\text{NNLO}$ & fitted corr. & CPU time [h] \\ \hline
|
|
$W^+$ & 1 & $6\cdot10^{-3}\, m_W$ & \SI{4.221}{nb} & \SI{4.209\pm0.005}{nb} & \SI{-27\pm15}{pb} & 7.6
|
|
\\
|
|
$W^-$ & 6 & $6\cdot10^{-3}\, m_W$ & \SI{3.315}{nb} & \SI{3.275\pm0.004}{nb} & \SI{-25\pm10}{pb} & 7.8 \\
|
|
$Z$ & 31 & $6\cdot10^{-3}\, m_Z$ & \SI{885.3}{pb} & \SI{875.8\pm0.9}{nb} & \SI{-3.5\pm 2}{fb} & 13.0 \\
|
|
$H$ & 112 & $4\cdot10^{-3}\, m_H$ & \SI{1.396}{pb} & \SI{1.872\pm0.002}{pb} & \SI{7\pm6}{fb} & 9.7 \\
|
|
$\gamma\gamma$ & 285 & $1\cdot10^{-4}\, m_{\gamma\gamma}$ & \SI{27.91}{pb} & \SI{43.54\pm0.08}{pb} &
|
|
\SI{0.36\pm0.10}{pb} & 83.2 \\
|
|
$W^+ H$ & 91 & $3\cdot10^{-3}\, m_{W^+ H}$ & \SI{2.204}{fb} & \SI{2.262\pm0.004}{fb} &
|
|
\SI{0.002\pm0.008}{fb} & 16.0 \\
|
|
$W^- H$ & 96 & $3\cdot10^{-3}\, m_{W^- H}$ & \SI{1.491}{fb} & \SI{1.526\pm0.003}{fb} &
|
|
\SI{-0.005\pm0.007}{fb} & 13.0 \\
|
|
$Z H$ & 110 & $3\cdot10^{-3}\, m_{Z H}$ & \SI{0.753}{fb} & \SI{0.842\pm0.001}{fb} &
|
|
\SI{-0.005\pm0.003}{fb} & 12.5 \\
|
|
$Z \gamma$ & 300 & $3\cdot10^{-4}\, m_{Z \gamma}$ & \SI{434}{fb} & \SI{525.5\pm1.0}{fb} &
|
|
\SI{4.5\pm1.7}{fb} & 202.5 \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{table}
|
|
|
|
%%%\begin{table}
|
|
%%%\begin{center}
|
|
%%% \caption{Benchmark cross-sections at NLO and NNLO, using the parameters
|
|
%%% and settings described in the text. $\delta\sigma^{MC}$ represents the uncertainty
|
|
%%% from the integration, while $\delta\sigma^{pc}$ is an estimate of the
|
|
%%% uncertainty due to neglected power corrections at NNLO.}
|
|
%%% \label{NNLObenchmarks}
|
|
%%% \vspace{0.5em}
|
|
%%%\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}
|
|
%%%\end{center}
|
|
%%%\end{table}
|