\chapter{\Pileup overlay}

\paragraph{Description for MC20/MC23 and later:}

The effect of multiple interactions in the same and neighbouring bunch crossings (\pileup) 
was modelled by overlaying~\cite{SIMU-2020-01} the simulated hard-scattering event 
with inelastic proton--proton (\(pp\)) events generated from a mix of 
\EPOS[2.0.1.4]~\cite{Werner:2005jf} and \PYTHIA[8.308]~\cite{Bierlich:2022pfr}.
The \EPOS events were generated with the \EPOS LHC tune~\cite{Pierog:2013ria} 
and the \PYTHIA events with the A3 tune~\cite{ATL-PHYS-PUB-2016-017} 
and the \NNPDF[2.3lo]~\cite{Ball:2012cx} set of parton distribution functions (PDF).
\PYTHIA pileup events include either a high transverse momentum (\pt) jet, 
a prompt photon, or a lepton from a $b$-hadron decay, 
while \EPOS was filtered to simulate all remaining pileup events in the overlay sample.
The individual simulations were first reweighted to ensure a smooth connection across jet \pt then
the combination reweighted to match the distribution of the actual number of interactions per bunch crossing (\(\mu\)) measured in data.

\paragraph{Description for MC16 and earlier:}

The effect of multiple interactions in the same and neighbouring bunch
crossings (\pileup) was modelled by overlaying the simulated hard-scattering event with
inelastic proton--proton (\(pp\)) events generated with \PYTHIA[8.186]~\cite{Sjostrand:2007gs}
using the \NNPDF[2.3lo] set of parton distribution functions (PDF)~\cite{Ball:2012cx} and the
A3 set of tuned parameters~\cite{ATL-PHYS-PUB-2016-017}.

\paragraph{Optional description:}

The Monte Carlo (MC) events were weighted to reproduce the
distribution of the average number of interactions per bunch crossing
(\(\left<\mu \right>\)) observed in the data. The \(\left<\mu \right>\)
value in data was rescaled by a factor of \(1.03\pm 0.04\) to improve
agreement between data and simulation in both charged-particle track distributions and 
the visible inelastic proton--proton (\(pp\)) cross-section~\cite{STDM-2015-05}.
