% !TEX root = MC23_snippets.tex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%              tW                     %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Single-top \texorpdfstring{\(tW\)}{tW} associated production}
\label{subsec:tW}

This section describes the MC samples used for the modelling of single-top \(tW\) associated production.
\Cref{subsubsec:tW_PP8} describes the \POWPY[8] samples -- both for the diagram removal (DR) set-ups,
which are used for the nominal prediction as well as uncertainties due to additional radiation and PDFs,
and for the diagram subtraction (DS) set-ups, which are used for the uncertainty due to the treatment
of the overlap with \ttbar production.
\Cref{subsubsec:tW_PH7} describes the \POWHER[7] samples used for the uncertainty
due to parton showering and hadronisation modelling, and \cref{subsubsec:tW_aMCP8} describes the
\MGNLOPY[8] samples used for the uncertainty due to the choice of matching scheme.

The reference cross-section values are extracted from Ref.~\cite{LHCTopWGsgtopXsec}.

\subsection[Powheg+Pythia8]{\POWPY[8]}
\label{subsubsec:tW_PP8}

\paragraph{Samples}
%\label{par:tW_PP8_samples}

\Cref{tab:tW_PP8} gives the DSIDs of the \(tW\) \POWPY[8] samples, for both the DR and DS schemes.
Single-top and single-anti-top (\(tW^-\) and \(\bar{t}W^+\)) events were generated in different samples.
The dileptonic samples overlap with the inclusive ones.

\begin{table}[htbp]
  \caption{Single-top \(tW\) associated production samples produced with \POWPY[8].}%
  \label{tab:tW_PP8}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    410646 & \(tW^-\) (DR) inclusive \\
    410647 & \(\bar{t}W^+\) (DR) inclusive \\
    410648 & \(tW^-\) (DR) dileptonic \\
    410649 & \(\bar{t}W^+\) (DR) dileptonic \\
    \midrule
    410654 & \(tW^-\) (DS) inclusive \\
    410655 & \(\bar{t}W^+\) (DS) inclusive \\
    410656 & \(tW^-\) (DS) dileptonic \\
    410657 & \(\bar{t}W^+\) (DS) dileptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

The associated production of top quarks with \(W\) bosons (\(tW\)) was
modelled by the
\POWHEGBOX[v2]~\cite{Re:2010bp,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator at NLO in QCD using the five-flavour scheme and the
\NNPDF[3.0nlo] set of PDFs~\cite{Ball:2014uwa}.
The diagram removal scheme~\cite{Frixione:2008yi} was used to
remove interference and overlap with \ttbar production.
The related uncertainty was estimated by comparison with an alternative sample
generated using the diagram subtraction scheme~\cite{Frixione:2008yi,ATL-PHYS-PUB-2016-020}.\footnote{Analyses which do not use this approach
should obviously not use this sentence in their description.}
The events were interfaced to \PYTHIA[8.230]~\cite{Sjostrand:2014zea} using the A14
tune~\cite{ATL-PHYS-PUB-2014-021} and the \NNPDF[2.3lo] set of
PDFs~\cite{Ball:2012cx}.

\input{top_isrfsr_powpy_short}


\paragraph{Long description:}

Single-top \(tW\) associated production was modelled using the
\POWHEGBOX[v2]~\cite{Re:2010bp,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator, which provided matrix elements at next-to-leading
order~(NLO) in the strong coupling constant \alphas\ in the five-flavour
scheme with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton
distribution function~(PDF) set.  The functional form of the
renormalisation and factorisation scales was set to the default scale,
which is equal to the top-quark mass (\(\mtop = \qty{172.5}{\GeV}\)).
The diagram removal scheme~\cite{Frixione:2008yi} was employed to handle the interference
with \ttbar production~\cite{ATL-PHYS-PUB-2016-020}.  The events were
interfaced with \PYTHIA[8.230]~\cite{Sjostrand:2014zea} using the A14
tune~\cite{ATL-PHYS-PUB-2014-021} and the \NNPDF[2.3lo] PDF set.  The
decays of bottom and charm hadrons were simulated using the
\EVTGEN[1.6.0] program~\cite{Lange:2001uf}.

The inclusive cross-section was corrected to the theory prediction
calculated at NLO in QCD with NNLL soft-gluon
corrections~\cite{Kidonakis:2010ux,Kidonakis:2013zqa}.  For proton--proton
collisions at a centre-of-mass energy of \(\rts = \qty{13}{\TeV}\), this
cross-section corresponds to \(\sigma(tW)_{\text{NLO+NNLL}} = 71.7 \pm 3.8\,\unit{\pb}\),
using a top-quark mass of \(\mtop = \qty{172.5}{\GeV}\).  The uncertainty in
the cross-section due to the PDF was calculated using the \MSTW[nnlo] 90\%
CL~\cite{Martin:2009iq,Martin:2009bu} PDF set, and was added in
quadrature to the effect of the scale uncertainty.

\input{top_isrfsr_powpy_long}

The nominal \POWPY[8] sample was compared with an alternative
sample generated using the diagram subtraction
scheme~\cite{Frixione:2008yi,ATL-PHYS-PUB-2016-020} to estimate the
uncertainty arising from the interference with \ttbar production.

To evaluate the PDF uncertainties for the nominal PDF, the 100
variations for \NNPDF[3.0nlo] were taken into account.
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.


\subsection[Powheg+Herwig7]{\POWHER[7]}
\label{subsubsec:tW_PH7}

\paragraph{Samples}
%\label{par:tW_PH7_samples}

\Cref{tab:tW_PH7} gives the DSIDs of the \(tW\) \POWHER[7] DR samples.
Single-top and single-anti-top (\(tW^-\) and \(\bar{t}W^+\)) events were generated in different samples.
The dileptonic samples overlap with the inclusive ones.

\begin{table}[htbp]
  \caption{Single-top \(tW\) associated production samples produced with \POWHER[7].}%
  \label{tab:tW_PH7}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    411036 & \(tW^-\) (DR) inclusive \\
    411037 & \(\bar{t}W^+\) (DR) inclusive \\
    411038 & \(tW^-\) (DR) dileptonic \\
    411039 & \(\bar{t}W^+\) (DR) dileptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

The uncertainty due to the parton shower and hadronisation model was
evaluated by comparing the nominal sample of events with a sample where
events generated with the
\POWHEGBOX[v2]~\cite{Re:2010bp,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator were interfaced to
\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}.


\paragraph{Long description:}

The impact of using a different parton shower and hadronisation model was evaluated
by comparing the nominal \(tW\) sample with another sample produced with the
\POWHEGBOX[v2]~\cite{Re:2010bp,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 in the five-flavour scheme with the
\NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF).
The functional form of the renormalisation and factorisation scales was set to
the default scale, which is equal to the top-quark mass.  The diagram removal
scheme~\cite{Frixione:2008yi} was employed to handle the interference
with \ttbar production~\cite{ATL-PHYS-PUB-2016-020}.  The decays of bottom
and charm hadrons are simulated using the \EVTGEN[1.6.0]
program~\cite{Lange:2001uf}.


\subsection[MadGraph5\_aMC@NLO+Pythia8]{\MGNLOPY[8]}
\label{subsubsec:tW_aMCP8}

\paragraph{Samples}
%\label{par:tW_aMCP8_samples}

\Cref{tab:tW_aMCP8} gives the DSIDs of the \(tW\) \MGNLOPY[8] samples.
The dileptonic sample overlaps with the inclusive one.

\begin{table}[htbp]
  \caption{Single-top \(tW\) associated production samples produced with \MGNLOPY[8].}%
  \label{tab:tW_aMCP8}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    412002 & \(tW\) inclusive \\
    412003 & \(tW\) dileptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

To assess the uncertainty in the matching of NLO matrix elements to the
parton shower, the nominal \(tW\) sample was compared with a sample generated
with the \MGNLO[2.6.2]~\cite{Alwall:2014hca} generator at NLO in QCD using the five-flavour
scheme and the \NNPDF[2.3nlo]~\cite{Ball:2014uwa} PDF set. 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]
PDF.


\paragraph{Long description:}

To assess the uncertainty due to the choice of matching scheme, the nominal \(tW\) sample was compared with a sample generated
with the \MGNLO[2.6.2]~\cite{Alwall:2014hca} generator, which provided matrix elements at next-to-leading order~(NLO) in the strong coupling constant \alphas
in the five-flavour scheme, using the \NNPDF[2.3nlo]~\cite{Ball:2014uwa} PDF set.
The functional form of the renormalisation and factorisation scale was set to the default scale, which is equal to the top-quark mass.
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 diagram removal scheme~\cite{Frixione:2008yi} was employed to handle the interference with \ttbar production~\cite{ATL-PHYS-PUB-2016-020}.
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] PDF.
The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%              t-channel              %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Single-top \texorpdfstring{\(t\)}{t}-channel production}
\label{subsec:tchan}

This section describes the MC samples used for the modelling of single-top \(t\)-channel production.
\Cref{subsubsec:tchan_PP8} describes the \POWPY[8] samples used for the nominal prediction
and for the uncertainty from additional radiation and due to PDFs.
\Cref{subsubsec:tchan_PH7} describes the \POWHER[7] samples used for the uncertainty due to the choice of parton shower and hadronisation model,
and \cref{subsubsec:tchan_aMCP8} describes the \MGNLOPY[8] samples used for the uncertainty due to the choice of matching scheme.

The reference cross-section values are extracted from Ref.~\cite{LHCTopWGsgtopXsec}.


\subsection[Powheg+Pythia8]{\POWPY[8]}
\label{subsubsec:tchan_PP8}

\paragraph{Samples}
%\label{par:tchan_PP8_samples}

\Cref{tab:tchan_PP8} gives the DSIDs of the \(t\)-channel \POWPY[8] samples.
Single-top and single-anti-top events were generated in distinct samples.

\begin{table}[!htbp]
  \caption{Single-top \(t\)-channel event samples produced with \POWPY[8].}%
  \label{tab:tchan_PP8}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    410658 & \(t\)-channel \(t\) leptonic \\
    410659 & \(t\)-channel \(\bar{t}\) leptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

Single-top \(t\)-channel production was modelled using the
\POWHEGBOX[v2]~\cite{Frederix:2012dh,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator at NLO in QCD using the four-flavour scheme and the
corresponding \NNPDF[3.0nlo] set of PDFs~\cite{Ball:2014uwa}.  The events were
interfaced with \PYTHIA[8.230]~\cite{Sjostrand:2014zea} using the A14
tune~\cite{ATL-PHYS-PUB-2014-021} and the \NNPDF[2.3lo] set of
PDFs~\cite{Ball:2012cx}.

\input{top_isrfsr_powpy_short}


\paragraph{Long description:}

Single-top \(t\)-channel production was modelled using the
\POWHEGBOX[v2]~\cite{Frederix:2012dh,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator, which provided matrix elements at next-to-leading-order~(NLO)
accuracy in the strong coupling constant \alphas\ in the four-flavour
scheme with the corresponding \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton
distribution function~(PDF) set.  The functional form of the
renormalisation and factorisation scales was set to
\(\sqrt{m_b^2 + \pTX[2][b]}\) following the
recommendation of Ref.~\cite{Frederix:2012dh}. Top quarks were decayed at
LO using \MADSPIN~\cite{Frixione:2007zp,Artoisenet:2012st} to preserve
all spin correlations.  The events were interfaced with
\PYTHIA[8.230]~\cite{Sjostrand:2014zea} using the A14
tune~\cite{ATL-PHYS-PUB-2014-021} and the \NNPDF[2.3lo] PDF set.
The decays of bottom and charm hadrons were simulated using the
\EVTGEN[1.6.0] program~\cite{Lange:2001uf}.

The inclusive cross-section was corrected to the theory prediction calculated at NLO in QCD with
\HATHOR[2.1]~\cite{Aliev:2010zk,Kant:2014oha}.
For proton--proton collisions at a centre-of-mass energy of \(\rts = \qty{13}{\TeV}\), this cross-section corresponds to
\(\sigma(t,t\text{-chan})_\text{NLO}= 136.02^{+5.40}_{-4.57}\)\,pb (\(\sigma(\bar{t},t\text{-chan})_\text{NLO}=80.95^{+4.06}_{-3.61}\)\,pb)
for single-top (single-anti-top) production, 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 prescription~\cite{Butterworth:2015oua}
with the \MSTW[nlo] 68\% CL~\cite{Martin:2009iq,Martin:2009bu}, \CT[10nlo]~\cite{Lai:2010vv}
and \NNPDF[2.3nlo]~\cite{Ball:2012cx} PDF sets,
and were added in quadrature to the effect of the scale uncertainty.

\input{top_isrfsr_powpy_long}

To evaluate the PDF uncertainties for the nominal PDF, the 100 variations for \NNPDF[3.0nlo] were taken into account.
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.


\subsection[Powheg+Herwig7]{\POWHER[7]}
\label{subsubsec:tchan_PH7}

\paragraph{Samples}
%\label{par:tchan_PH7_samples}

\Cref{tab:tchan_PH7} gives the DSIDs of the \(t\)-channel \POWHER[7] samples.
Single-top and single-anti-top events were generated in distinct samples.

\begin{table}[htbp]
  \caption{Single-top \(t\)-channel event samples produced with \POWHER[7].}%
  \label{tab:tchan_PH7}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    411032 & \(t\)-channel \(\bar t\) leptonic \\
    411033 & \(t\)-channel \(t\) leptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

The uncertainty due to the parton shower and hadronisation model was
evaluated by comparing the nominal sample of events with a sample where
the events generated with the
\POWHEGBOX[v2]~\cite{Frederix:2012dh,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator were interfaced to
\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}.


\paragraph{Long description:}

The impact of using a different parton shower and hadronisation model was evaluated by comparing the nominal sample
with another sample produced with the \POWHEGBOX[v2]~\cite{Frederix:2012dh,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
in the four-flavour scheme with the corresponding \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF).
The functional form of the renormalisation and factorisation scales was set to \(\sqrt{m_b^2 + \pTX[2][b]}\)
following the recommendation of Ref.~\cite{Frederix:2012dh}.
Top quarks were decayed at LO using \MADSPIN~\cite{Frixione:2007zp,Artoisenet:2012st} to preserve all spin correlations.
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:tchan_aMCP8}

\paragraph{Samples}
%\label{par:tchan_aMCP8_samples}

\Cref{tab:tchan_aMCP8} gives the DSIDs of the \(t\)-channel \MGNLOPY[8] samples.

\begin{table}[htbp]
  \caption{Single-top \(t\)-channel event samples produced with \MGNLOPY[8].}%
  \label{tab:tchan_aMCP8}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    412004 & \(t\)-channel leptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

To assess the uncertainty in the matching of NLO matrix elements to the
parton shower, the nominal sample was compared with a sample generated
with the \MGNLO[2.6.2]~\cite{Alwall:2014hca} generator at NLO in QCD using the five-flavour
scheme and the \NNPDF[2.3nlo]~\cite{Ball:2014uwa} PDF set. 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] PDF set.


\paragraph{Long description:}

To assess the uncertainty due to the choice of matching scheme, the nominal sample was compared with a sample generated
with the \MGNLO[2.6.2]~\cite{Alwall:2014hca} generator, which provided matrix elements at next-to-leading order~(NLO) in the strong coupling constant \alphas
in the four-flavour scheme, using the corresponding \NNPDF[3.0nlo]~\cite{Ball:2014uwa} PDF set.
The functional form of the renormalisation and factorisation scales was set to \(\sqrt{m_b^2 + \pTX[2][b]}\)
following the recommendation of Ref.~\cite{Frederix:2012dh}.
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.
Top quarks were decayed at LO using \MADSPIN~\cite{Frixione:2007zp,Artoisenet:2012st} to preserve all spin correlations.
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] PDF set.
The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%              s-channel              %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Single-top \texorpdfstring{\(s\)}{s}-channel production}
\label{subsec:schan}

This section describes the MC samples used for the modelling of single-top \(s\)-channel production.
\Cref{subsubsec:schan_PP8} describes the \POWPY[8] samples used for the nominal prediction
and for the uncertainty from additional radiation and due to PDFs.
\Cref{subsubsec:schan_PH7} describes the \POWHER[7] samples used for the uncertainty due to the parton shower and hadronisation model,
and \cref{subsubsec:schan_aMCP8} describes the \MGNLOPY[8] samples used for the uncertainty due to the choice of matching scheme.

The reference cross-section values are extracted from Ref.~\cite{LHCTopWGsgtopXsec}.

\subsection[Powheg+Pythia8]{\POWPY[8]}
\label{subsubsec:schan_PP8}

\paragraph{Samples}
%\label{par:schan_PP8_samples}

\Cref{tab:schan_PP8} gives the DSIDs of the \(s\)-channel \POWPY[8] samples.
Single-top and single-anti-top events were generated in distinct samples.

\begin{table}[htbp]
  \caption{Single-top \(s\)-channel event samples produced with \POWPY[8].}%
  \label{tab:schan_PP8}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    410644 & \(s\)-channel \(t\) leptonic \\
    410645 & \(s\)-channel \(\bar{t}\) leptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

Single-top \(s\)-channel production was modelled using the \POWHEGBOX[v2]~\cite{Alioli:2009je,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator at NLO in QCD in the five-flavour scheme with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF) set.
The events were interfaced with \PYTHIA[8.230]~\cite{Sjostrand:2014zea} using the A14 tune~\cite{ATL-PHYS-PUB-2014-021} and the
\NNPDF[2.3lo] PDF set.

\input{top_isrfsr_powpy_short}


\paragraph{Long description:}

Single-top \(s\)-channel production was modelled using the \POWHEGBOX[v2]~\cite{Alioli:2009je,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator, which provided matrix elements at next-to-leading order~(NLO) in the strong coupling constant \alphas in the
five-flavour scheme with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF) set.
The functional form of the renormalisation and factorisation scales was set to the default scale, which was equal to the top-quark mass.
The events were interfaced with \PYTHIA[8.230]~\cite{Sjostrand:2014zea} using the A14 tune~\cite{ATL-PHYS-PUB-2014-021} and the
\NNPDF[2.3lo] PDF set.
The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.

The inclusive cross-section was corrected to the theory prediction calculated at NLO in QCD with
\HATHOR[2.1]~\cite{Aliev:2010zk,Kant:2014oha}.
For proton--proton collisions at a centre-of-mass energy of \(\rts = \qty{13}{\TeV}\), this cross-section corresponds to
\(\sigma(t,s\text{-chan})_{\text{NLO}} = 6.35^{+0.23}_{-0.20}\,\unit{\pb}\)
(\(\sigma(\bar{t},s\text{-chan})_{\text{NLO}} = 3.97^{+0.19}_{-0.17}\,\unit{\pb}\))
for single-top (single-anti-top) production, 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 prescription~\cite{Butterworth:2015oua}
with the \MSTW[nlo] 68\% CL~\cite{Martin:2009iq,Martin:2009bu}, \CT[10nlo]~\cite{Lai:2010vv} and \NNPDF[2.3nlo]~\cite{Ball:2012cx} PDF sets,
and were added in quadrature to the effect of the scale uncertainty.

\input{top_isrfsr_powpy_long}

To evaluate the PDF uncertainties for the nominal PDF, the 100 variations for \NNPDF[3.0nlo] were taken into account.
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.


\subsection[Powheg+Herwig7]{\POWHER[7]}
\label{subsubsec:schan_PH7}

\paragraph{Samples}
%\label{par:schan_PH7_samples}

\Cref{tab:schan_PH7} gives the DSIDs of the \(s\)-channel \POWHER[7] samples.
Single-top and single-anti-top events were generated in distinct samples.

\begin{table}[htbp]
  \caption{Single-top \(s\)-channel event samples produced with \POWHER[7].}%
  \label{tab:schan_PH7}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    411034 & \(s\)-channel \(t\) leptonic \\
    411035 & \(s\)-channel \(\bar{t}\) leptonic \\
    \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 sample
with another sample produced with the \POWHEGBOX[v2]~\cite{Alioli:2009je,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}
generator at NLO in the strong coupling constant \alphas in the five-flavour scheme 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}.


\paragraph{Long description:}

The impact of using a different parton shower and hadronisation model was evaluated by comparing the nominal sample
with another sample produced with the \POWHEGBOX[v2]~\cite{Alioli:2009je,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
in the five-flavour scheme with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF).
The functional form of the renormalisation and factorisation scales was set to the default scale, which is equal to the top-quark mass.
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:schan_aMCP8}

\paragraph{Samples}
%\label{par:schan_aMCP8_samples}

\Cref{tab:schan_aMCP8} gives the DSIDs of the \(s\)-channel \MGNLOPY[8] samples.

\begin{table}[htbp]
  \caption{Single-top \(s\)-channel event samples produced with \MGNLOPY[8].}%
  \label{tab:schan_aMCP8}
  \centering
  \begin{tabular}{l l}
    \toprule
    DSID & Description \\
    \midrule
    412005 & \(s\)-channel leptonic \\
    \bottomrule
  \end{tabular}
\end{table}

\paragraph{Short description:}

%% the MG5_aMC@NLO version was double checked in the tag collector
To assess the uncertainty due to the choice of matching scheme, the nominal sample was compared with a sample generated
with the \MGNLO[2.6.2]~\cite{Alwall:2014hca} generator at NLO in the strong coupling constant \alphas in the five-flavour scheme,
using the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} PDF set.
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] PDF set.


\paragraph{Long description:}

To assess the uncertainty due to the choice of matching scheme, the nominal sample was compared with a sample generated
with the \MGNLO[2.6.2]~\cite{Alwall:2014hca} generator, which provided matrix elements at next-to-leading order~(NLO) in the strong coupling constant \alphas
in the five-flavour scheme with the \NNPDF[3.0nlo]~\cite{Ball:2014uwa} parton distribution function~(PDF).
The functional form of the renormalisation and factorisation scales was set to the default scale, which is equal to the top-quark mass.
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.
Top quarks were decayed at LO using \MADSPIN~\cite{Frixione:2007zp,Artoisenet:2012st} to preserve all spin correlations.
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] PDF set.
The decays of bottom and charm hadrons were simulated using the \EVTGEN[1.6.0] program~\cite{Lange:2001uf}.
