% !TEX root = MC_snippets.tex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%              ttbar                  %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section[\ttbar production]{\ttbar production}
\label{subsec:ttbar}

This section describes the MC samples used for the modelling of \ttbar production.
\Cref{subsubsec:ttbar_PP8} describes the \POWPY[8] samples,
\cref{subsubsec:ttbar_PH7} and \cref{subsubsec:ttbar_PH713} describes the \POWHER[7] samples,
\cref{subsubsec:ttbar_aMCP8} describes the \MGNLOPY[8] samples,
and finally \cref{subsubsec:ttbar_sherpa} and \cref{subsubsec:ttbar_sherpa2212} describe the \SHERPA samples.

The reference cross-section values are extracted from Ref.~\cite{LHCTopWGttbarXsec}.
Studies of MC simulation performance including comparisons with unfolded data
are collected in the PUB notes~\cite{ATL-PHYS-PUB-2018-009,ATL-PHYS-PUB-2017-007,ATL-PHYS-PUB-2016-020,ATL-PHYS-PUB-2023-029}.

\subsection[Powheg+Pythia8]{\POWPY[8]}
\label{subsubsec:ttbar_PP8}

\paragraph{Samples}
%\label{par:ttbar_PP8_samples}

The descriptions below correspond to the samples in \cref{tab:ttbar_PP8,tab:ttbar_PP8_hdampvar}.

\begin{table}[htbp]
  \caption{Nominal \ttbar samples produced with \POWPY[8]. The \hdamp\ value is set to 1.5\,\mtop.}%
  \label{tab:ttbar_PP8}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID range & Description \\
    \midrule
    410470 & \ttbar non-all-hadronic \\
    410471 & \ttbar dileptonic \\
    410472 & \ttbar all-hadronic \\
    \bottomrule
  \end{tabular}
\end{table}

\begin{table}[htbp]
  \caption{\ttbar samples produced with \POWPY[8] used to estimate \hdamp variation systematic uncertainties.
    The \hdamp value is set to 3.0\,\mtop.}%
  \label{tab:ttbar_PP8_hdampvar}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID range & Description \\
    \midrule
    410480 & \ttbar single lepton \\
    410481 & \ttbar all-hadronic \\
    410482 & \ttbar dileptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

The production of \ttbar events was modelled using the
\POWHEGBOX[v2]~\cite{Frixione:2007nw,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator at NLO with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} PDF set
and the \hdamp parameter\footnote{The
  \hdamp parameter is a resummation damping factor and one of the
  parameters that controls the matching of \POWHEG matrix elements to
  the parton shower and thus effectively regulates the
  high-\pT radiation against which the \ttbar system recoils.} set
to 1.5\,\mtop~\cite{ATL-PHYS-PUB-2016-020}.  The events were interfaced
to \PYTHIA[8.230]~\cite{Sjostrand:2014zea} to model the parton shower,
hadronisation, and underlying event, with parameters set according
to the A14 tune~\cite{ATL-PHYS-PUB-2014-021} and using the \NNPDF[2.3lo]
set of PDFs~\cite{Ball:2012cx}. The decays of bottom and charm hadrons
were performed by \EVTGEN[1.6.0]~\cite{Lange:2001uf}.

\input{top_isrfsr_powpy}


\paragraph{Long description:}

The production of \ttbar events was modelled using the
\POWHEGBOX[v2]~\cite{Frixione:2007nw,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator, which provided matrix elements at next-to-leading
order~(NLO) in the strong coupling constant \alphas, and the
\NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF).
The \hdamp parameter, which controls the matching in \POWHEG and
effectively regulates the high-\pT radiation against which the
\ttbar system recoils, was set to 1.5\,\mtop~\cite{ATL-PHYS-PUB-2016-020}.
The functional form of the renormalisation and factorisation scales was
set to the default scale \(\sqrt{\mtop^{2} + \pTX[2]}\).
The events were interfaced with \PYTHIA[8.230]~\cite{Sjostrand:2014zea} for the parton shower and hadronisation, using the A14 set of tuned parameters~\cite{ATL-PHYS-PUB-2014-021} and the \NNPDF[2.3lo] set of PDFs~\cite{Ball:2012cx}. The \pthard parameter, which regulates how the \PYTHIA[8] radiation phase space is determined to avoid overlaps with the regions of the phase space already covered by \POWHEG \cite{Bierlich:2022pfr}, was set to $\pthard=0$. The modelling of second and subsequent gluon emission in the $t\rightarrow Wb$ process was performed by recoiling the gluon against $b$-quarks, which is the default strategy in \POWHEG \cite{Brooks:2019xso}. The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.

The \ttbar sample was normalised to the cross-section prediction at next-to-next-to-leading order (NNLO)
in QCD including the resummation of next-to-next-to-leading logarithmic (NNLL) soft-gluon terms calculated using
\TOPpp[2.0]~\cite{Beneke:2011mq,Cacciari:2011hy,Baernreuther:2012ws,Czakon:2012zr,Czakon:2012pz,Czakon:2013goa,Czakon:2011xx}.
For proton--proton collisions at a centre-of-mass energy of \(\rts = \qty{13}{\TeV}\), this cross-section corresponds to
\(\sigma(\ttbar)_{\text{NNLO+NNLL}} = 832 \pm 51\,\unit{\pb}\) using a top-quark mass of \(\mtop = \qty{172.5}{\GeV}\).
The uncertainties in the cross-section due to the PDF and \alphas were calculated using the \PDFforLHC[15] prescription~\cite{Butterworth:2015oua} with the \MSTW[nnlo]~\cite{Martin:2009iq,Martin:2009bu}, \CT[10nnlo]~\cite{Lai:2010vv,Gao:2013xoa}
and \NNPDF[2.3lo]~\cite{Ball:2012cx} PDF sets in the five-flavour scheme, and were added in quadrature to the effect of the scale uncertainty.

\input{top_isrfsr_powpy}

The \NNPDF[3.0lo] replicas were used to evaluate the PDF uncertainties for the nominal PDF.
In addition, the central value of this PDF was compared with the central values of the
\CT[14nnlo]~\cite{Dulat:2015mca} and \MMHT[nnlo]~\cite{Harland-Lang:2014zoa} PDF sets.

To assess the uncertainty in the matching of NLO matrix elements to the parton shower, a new \ttbar sample was generated using the same settings as the nominal sample but used $\pthard=1$ instead of $\pthard=0$ \cite{Hoche:2021mkv,ATL-PHYS-PUB-2023-029}.



\subsection[Powheg+Herwig7]{\POWHER[7]}
\label{subsubsec:ttbar_PH7}

\paragraph{Samples}
The descriptions below correspond to the samples in \cref{tab:ttbar_PH7}.

\begin{table}[htbp]
  \caption{\ttbar samples produced with \POWHER[7].}%
  \label{tab:ttbar_PH7}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID range & Description \\
    \midrule
    410557 & \ttbar single lepton  \\
    410558 & \ttbar dileptonic  \\
    410559 & \ttbar all-hadronic  \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

The impact of using a different parton shower and hadronisation model was evaluated
by comparing the nominal \ttbar sample with another event sample produced with the
\POWHEGBOX[v2]~\cite{Frixione:2007nw,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator using the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF).
Events in the latter sample were interfaced with \HERWIG[7.04]~\cite{Bahr:2008pv,Bellm:2015jjp},
using the H7UE set of tuned parameters~\cite{Bellm:2015jjp} and the \MMHT[lo] PDF set~\cite{Harland-Lang:2014zoa}.
The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.

\paragraph{Long description:}

The impact of using a different parton shower and hadronisation model was evaluated
by comparing the nominal \ttbar sample with an event sample also produced with the
\POWHEGBOX[v2]~\cite{Frixione:2007nw,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator but interfaced with \HERWIG[7.04]~\cite{Bahr:2008pv,Bellm:2015jjp}, using the H7UE set
of tuned parameters~\cite{Bellm:2015jjp} and the \MMHT[lo] PDF set~\cite{Harland-Lang:2014zoa}.
\POWHEGBOX provided matrix elements at next-to-leading order~(NLO) in the
strong coupling constant \alphas, and used the \NNPDF[3.0nlo]~\cite{Ball:2014uwa}
parton distribution function~(PDF) and an \hdamp parameter value of \(1.5\,\mtop\)~\cite{ATL-PHYS-PUB-2016-020}.
The functional form of the renormalisation and factorisation scales was
set to the default scale \(\sqrt{\mtop^{2} + \pT^2}\).
The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.


\subsection[Powheg+Herwig7.13]{\POWHER[7.13]}
\label{subsubsec:ttbar_PH713}

\paragraph{Samples}
%\label{par:ttbar_PH713_samples}

The descriptions below correspond to the samples in \cref{tab:ttbar_PH713}.

\begin{table}[htbp]
  \caption{\ttbar samples produced with \POWHER[7.13].}%
  \label{tab:ttbar_PH713}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID range & Description \\
    \midrule
    411233 & \ttbar single lepton  \\
    411234 & \ttbar dileptonic  \\
    411316 & \ttbar all-hadronic  \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

The impact of using a different parton shower and hadronisation model was evaluated
by comparing the nominal \ttbar sample with another event sample produced with the
\POWHEGBOX[v2]~\cite{Frixione:2007nw,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator using the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF).
Events in the latter sample were interfaced with \HERWIG[7.13]~\cite{Bahr:2008pv,Bellm:2015jjp,Bellm:2017bvx},
using the \HERWIG[7.1] default set of tuned parameters~\cite{Bellm:2015jjp,Bellm:2017jjp}.
The decays of bottom and charm hadrons
were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.


\paragraph{Long description:}

The impact of using a different parton shower and hadronisation model was evaluated
by comparing the nominal \ttbar sample with an event sample also produced with the
\POWHEGBOX[v2]~\cite{Frixione:2007nw,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator but interfaced with \HERWIG[7.13]~\cite{Bahr:2008pv,Bellm:2015jjp,Bellm:2017bvx}, using the
\HERWIG[7.1] default set of tuned parameters~\cite{Bellm:2015jjp,Bellm:2017jjp}.
\POWHEGBOX provided matrix elements at next-to-leading
order~(NLO) in the strong coupling constant \alphas, and used the
\NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF) and
an \hdamp parameter value of 1.5\,\mtop~\cite{ATL-PHYS-PUB-2016-020}.
The functional form of the renormalisation and factorisation scales was
set to the default scale \(\sqrt{\mtop^{2} + \pTX[2]}\).
The decays of bottom and charm hadrons
were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.


\subsection[MadGraph5\_aMC@NLO+Pythia8]{\MGNLOPY[8]}
\label{subsubsec:ttbar_aMCP8}

\paragraph{Samples}
%\label{par:ttbar_aMCP8_samples}

The descriptions below correspond to the samples in \cref{tab:ttbar_aMCP8}.
\begin{table}[htbp]
  \caption{\ttbar samples produced with \MGNLOPY[8].}%
  \label{tab:ttbar_aMCP8}
  \centering
  \begin{tabular}{l l}
  \toprule
  DSID range & Description \\
  \midrule
  410464 & \ttbar single lepton \\
  410465 & \ttbar dileptonic \\
  410466 & \ttbar all-hadronic \\
  \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

An alternative \ttbar sample was generated using \MGNLO[2.6.0]~\cite{Alwall:2014hca} interfaced with \PYTHIA[8.230]~\cite{Sjostrand:2014zea}. The \MGNLO calculation used the \NNPDF[3.0nlo] set of PDFs~\cite{Ball:2014uwa} and \PYTHIA[8] used the A14 set of tuned parameters~\cite{ATL-PHYS-PUB-2014-021} and the \NNPDF[2.3lo] set of PDFs~\cite{Ball:2012cx}. The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.

\paragraph{Long description:}

An alternative \ttbar sample was generated by \MGNLOPY[8]. For the calculation of the hard-scattering, \MGNLO[2.6.0]~\cite{Alwall:2014hca} with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} PDF set was used. The events were interfaced with \PYTHIA[8.230]~\cite{Sjostrand:2014zea}, using the A14 set of tuned parameters~\cite{ATL-PHYS-PUB-2014-021} and the \NNPDF[2.3lo] set of PDFs~\cite{Ball:2012cx}.
Top quarks were decayed at LO using \MADSPIN~\cite{Frixione:2007zp,Artoisenet:2012st} to preserve spin
correlations. The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.  The parton-shower starting scale had the functional form \(\muQ = \HT/2\)~\cite{ATL-PHYS-PUB-2017-007}, where \HT is defined as the scalar sum of the \pT of all outgoing partons. The renormalisation and factorisation scale choice was the same as for the
\POWHEGBOX set-up.

\subsection[MadGraph5\_aMC@NLO+Herwig7.13]{\MGNLOHER[7.13]}
%\label{subsubsec:ttbar_aMCH713}

\paragraph{Samples}
%\label{par:ttbar_aMCH713_samples}

The descriptions below correspond to the samples in \cref{tab:ttbar_aMCH713}.
\begin{table}[htbp]
  \caption{\ttbar samples produced with \MGNLOHER[7.13].}%
  \label{tab:ttbar_aMCH713}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID range & Description \\
    \midrule
    412116 & \ttbar single lepton \\
    412117 & \ttbar dileptonic \\
    412175 & \ttbar all-hadronic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

An alternative \ttbar sample was generated with \MGNLO[2.6.0]~\cite{Alwall:2014hca}, both using the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF) and interfaced with \HERWIG[7.13]~\cite{Bahr:2008pv,Bellm:2015jjp}, using the \HERWIG[7.1] default set of tuned parameters~\cite{Bellm:2015jjp} and the \MMHT[lo] PDF set~\cite{Harland-Lang:2014zoa}. The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.


\paragraph{Long description:}

An alternative \ttbar sample was generated with \MGNLO~\cite{Alwall:2014hca}. The first sample was produced with the same hard-scatter set-up as the nominal sample using the \POWHEGBOX[v2]~\cite{Frixione:2007nw,Nason:2004rx,Frixione:2007vw,Alioli:2010xd} generator, which provided matrix elements at next-to-leading order~(NLO) in the strong coupling constant \alphas, with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF) and the \hdamp parameter set to 1.5\,\mtop~\cite{ATL-PHYS-PUB-2016-020}. The functional form of the renormalisation and factorisation scales was set to the default scale \(\sqrt{\mtop^{2} + \pTX[2]}\). The second sample used \MGNLO[2.6.0] with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} PDF set for the calculation of the hard-scattering. Top quarks were decayed at LO using \MADSPIN~\cite{Frixione:2007zp,Artoisenet:2012st} to preserve spin correlations. The parton-shower starting scale had the functional form \(\muQ = \HT/2\)~\cite{ATL-PHYS-PUB-2017-007}, where \HT is defined as the scalar sum of the \pT of all outgoing partons. The events from both generators were interfaced with \HERWIG[7.13]~\cite{Bahr:2008pv,Bellm:2015jjp}, using the \HERWIG[7.1] default set of tuned parameters~\cite{Bellm:2015jjp} and the \MMHT[lo] PDF set \cite{Harland-Lang:2014zoa}. The renormalisation and factorisation scale choice in the \MGNLO set-up was the same as for the \POWHEGBOX set-up. The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf} in both set-ups.


\subsection[Sherpa 2.2.1]{\SHERPA[2.2.1]}
\label{subsubsec:ttbar_sherpa}

\paragraph{Samples}
%\label{par:ttbar_sherpa_samples}

The descriptions below correspond to the samples in \cref{tab:ttbar_sherpa}.
\begin{table}[htbp]
  \caption{\ttbar samples produced with \SHERPA[2.2.1].}%
  \label{tab:ttbar_sherpa}
  \centering
  \begin{tabular}{l l}
  \toprule
  DSID range & Description \\
  \midrule
  410249 & \ttbar all-hadronic  \\
  410250 & \ttbar single lepton  \\
  410251 & \ttbar single lepton  \\
  410252 & \ttbar dileptonic  \\
  \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

Additional samples of \ttbar events were produced with the
\SHERPA[2.2.1]~\cite{Bothmann:2019yzt} generator using NLO-accurate
matrix elements for up to one additional parton, and LO-accurate
matrix elements for up to four additional partons calculated with the
Comix~\cite{Gleisberg:2008fv} and
\OPENLOOPS~\cite{Buccioni:2019sur,Cascioli:2011va,Denner:2016kdg} libraries. They were
matched with the \SHERPA parton shower~\cite{Schumann:2007mg} using
the \MEPSatNLO
prescription~\cite{Hoeche:2011fd,Hoeche:2012yf,Catani:2001cc,Hoeche:2009rj}
and
%the set of tuned parameters developed by the \SHERPA authors to match
the \NNPDF[3.0nnlo] set of PDFs~\cite{Ball:2014uwa}.

\textbf{Additional information}: The central scale had the functional
form \(\mu^{2} = \mtop^{2} + 0.5\times(\pTX[2][t]p + \pTX[2][\bar{t}])\).
The CKKW matching scale of the
additional emissions was set to \qty{30}{\GeV}.



\subsection[Sherpa 2.2.12]{\SHERPA[2.2.12]}
\label{subsubsec:ttbar_sherpa2212}

\paragraph{Samples}
%\label{par:ttbar_sherpa_samples}

The descriptions below correspond to the samples in \cref{tab:ttbar_sherpa}.
\begin{table}[htbp]
  \caption{\ttbar samples produced with \SHERPA[2.2.12].}%
  \label{tab:ttbar_sherpa}
  \centering
  \begin{tabular}{l l}
  \toprule
  DSID range & Description \\
  \midrule
  700659 & \ttbar all-hadronic  \\
  700660 & \ttbar single lepton  \\
  700661 & \ttbar single lepton  \\
  700662 & \ttbar dileptonic  \\
  \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

Additional samples of \ttbar events were produced with the \SHERPA[2.2.12]~\cite{Bothmann:2019yzt} generator using matrix elements at NLO in QCD for up to one additional parton, and at LO in QCD for up to four partons calculated with the Comix~\cite{Gleisberg:2008fv} and \OPENLOOPS~\cite{Buccioni:2019sur,Cascioli:2011va,Denner:2016kdg} libraries. They were matched with the \SHERPA parton shower~\cite{Schumann:2007mg} using the \MEPSatNLO prescription~\cite{Hoeche:2011fd,Hoeche:2012yf,Catani:2001cc,Hoeche:2009rj}.
%and a dedicated set of tuned parton-shower parameters developed by the \SHERPA authors authors.
The NNPDF3.0nnlo~\cite{Ball:2014uwa} set of PDFs was used.

\textbf{Additional information}: The central scale had the functional form \(\mu^{2} = \mtop^{2} + 0.5\times(\pTX[2][t]p + \pTX[2][\bar{t}])\). The CKKW matching scale of the additional emissions was set to \qty{30}{\GeV}.
