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\begin{document}
\title{Modeling the underlying event: generating predictions for the LHC }
\author{Arthur Moraes\protect\footnote{\ \ Speaker}~ on behalf of the ATLAS Collaboration}
\institute{University of Glasgow}
\maketitle

\begin{abstract}
This report presents tunings for PYTHIA version 6.416 and JIMMY
version 4.3 to the underlying event. 
The MC generators are tuned to describe underlying event 
measurements made by CDF for p$\overline{\text{p}}$ collisions at 
$\sqrt{\text{s}}$ = 1.8 TeV. 
LHC predictions for the underlying event
generated by the tuned models are also compared in this report. 
\end{abstract}

\section{INTRODUCTION}
\label{sec:1}

Over the last few years, the Tevatron experiments CDF and D0 have managed to reduce 
uncertainties in various measurements to a level in which the corrections due to the 
underlying event (UE) have become yet more relevant than they were in Run I analyses. 
Studies in preparation for LHC collisions have also shown that an accurate 
description of the underlying event will be of great importance for reducing 
the uncertainties in virtually 
all measurements dependent on strong interaction processes. 
It is therefore very important to produce models for the 
underlying event in hadron collisions which can accurately describe Tevatron data and are also 
reliable to generate predictions for the LHC.

The Monte Carlo (MC) event generators PYTHIA \cite{PYTHIA64} and HERWIG \cite{HERWIG} 
are widely used for the simulation of hadron interactions by both Tevatron and LHC 
experiments. Both generators are designed to simulate the event activity produced as part
of the underlying event in proton-antiproton (p$\overline{\text{p}}$) and 
proton-proton (pp) events. 
In this report we focus on the fortran version of HERWIG. This needs
to be linked to dedicated package, named ``JIMMY" 
\cite{Butterworth:96, JIMMY}, to produce the underlying event activity.

PYTHIA version 6.2 has been shown to describe both minimum bias and
underlying event data reasonably well when appropriately tuned
\cite{Sjostrand:87,Moraes:2007,CDF-tuneA}.
Major changes related to the description
of minimum bias interactions and the underlying event have been
introduced in PYTHIA version 6.4 
\cite{PYTHIA64}. 
There is a new, more sophisticated scenario for multiple interactions, 
new $p_{\text{T}}$-ordered initial- and final-state showers (ISR and FSR) and a 
new treatment of beam remnants \cite{PYTHIA64}.

JIMMY \cite{JIMMY} is a library of routines which should be
linked to the HERWIG MC event generator \cite{HERWIG}
and is designed to generate multiple parton scattering events in
hadron-hadron events.
JIMMY implements ideas of the eikonal model which are discussed in
more detail in Ref. \cite{Butterworth:96,JIMMY}. 

In this report we present a tuning for PYTHIA version 6.416 which has been obtained by comparing
PYTHIA version 6.416 to the underlying event measurements done by CDF for p$\overline{\text{p}}$ collisions 
at 1.8 TeV \cite{Acosta:04,Affolder:02}. 
We also compare the ATLAS tune for HERWIG version 6.510 with JIMMY
version 4.3 to these data distributions 
\cite{ATLAS-JIMMY}.

\section{MC predictions vs. UE data}

Based on the CDF analysis in Ref. \cite{Affolder:02}, the underlying event is defined 
as the angular region in $\phi$ which is transverse to the leading charged
particle jet.  
\begin{figure}[h!]
\begin{center}
\begin{tabular}{cc}
\resizebox{0.5\textwidth}{!}{\includegraphics{figures/mult-trans.eps}} 
&
\resizebox{0.5\textwidth}{!}{\includegraphics{figures/ptsum-trans.eps}} 
\\
(a) & (b)
\end{tabular}

\caption{PYTHIA version 6.416 predictions for the underlying event
  compared to the $<N_{\text{chg}}>$ (a) and $<p_{\text{T}}^{\text{sum}}>$ (b).}
\label{fig:cdf-pythia}
\end{center}
\end{figure}

Figures \ref{fig:cdf-pythia}(a) and \ref{fig:cdf-pythia}(b) show
PYTHIA version 6.416 predictions for the underlying event 
compared to the CDF data for the average charged particle multiplicity, 
$<N_{\text{chg}}>$ (charged particles with $p_{\text{T}} >0.5~$GeV and 
$\left| \eta \right| <1$) 
and average sum of charged particle's transverse momenta, $<p_{\text{T}}^{\text{sum}}>$ 
in the underlying event \cite{Affolder:02}, respectively.
Two MC generated distributions are compared to the data in these
plots: one generated with all default settings in PYTHIA version 6.416
except for the explicit selection of the new multiple 
parton interaction and new parton shower model, which is switched on by setting MSTP(81)=21 
\cite{PYTHIA64}, and a second distribution with a tuned set of parameters. This particular 
PYTHIA version 6.416 - tune was prepared for use in the 2008 production of simulated events 
for the ATLAS Collaboration.
The list of tuned parameters is shown in Table \ref{tab:PYTHIA-tuning}.
\begin{table}[h!]
\begin{center}
\caption{PYTHIA version 6.416 - tuned parameter list for the underlying event.}  
\begin{tabular}{|c|c|c|}
\hline
\multicolumn{1}{|c}{\textbf{Default} \cite{PYTHIA64}} &
\multicolumn{1}{|c|}{\textbf{PYTHIA6.416 - tuned}} &
\multicolumn{1}{|c|}{\textbf{Comments}}\\ 

\hline

 & MSTP(51)=10042 & \\
MSTP(51)=7 &  MSTP(52)=2 & PDF set \\
CTEQ5L & CTEQ6L (from LHAPDF) &  \\[0.2cm]

MSTP(81)=1 & MSTP(81)=21 & multiple interaction model \\
(old MPI model) & (new MPI model) & \\[0.2cm]

MSTP(95)=1 & MSTP(95)=2 & method for colour \\[-0.05cm]
 & & reconnection \\[0.2cm]

PARP(78)=0.025 & PARP(78)=0.3 & regulates the number of \\[-0.05cm]
 & & attempted colour reconnections \\[0.2cm]

PARP(82)=2.0 & PARP(82)=2.1 & $p_{\text{T}_{\text{min}}}$
parameter \\[0.2cm] 

PARP(83)=0.5 & PARP(83)=0.8 & fraction of matter in \\[-0.05cm]
 & & hadronic core\\[0.2cm]

PARP(84)=0.4 & PARP(84)=0.7 & hadronic core radius \\[0.2cm]

\hline
\end{tabular}
\label{tab:PYTHIA-tuning}
\end{center}
\end{table}         

The guiding principles to obtain the parameters listed in Table \ref{tab:PYTHIA-tuning} were 
two: firstly the new multiple parton interaction model with interleaved showering and colour 
reconnection scheme was to be used and, secondly, changes to ISR and FSR parameters should be 
avoided if at all possible.

In order to obtain a tuning which could successfully reproduce the underlying event data, 
we have selected a combination of parameters that induce PYTHIA to preferably choose shorter 
strings to be drawn between the hard and the soft systems in the hadronic interaction. We have
also increased the hadronic core radius compared to the tunings used in previous PYTHIA versions, such
as the ones mentioned in Ref. \cite{Moraes:2007,CDF-tuneA}.   
As can be seen in Fig. \ref{fig:cdf-pythia} PYTHIA version 6.416 - tuned describes the data.
\begin{figure}[h!]
\begin{center}
\begin{tabular}{cc}
\resizebox{0.5\textwidth}{!}{\includegraphics{figures/mult-trans-jmy.eps}} 
&
\resizebox{0.5\textwidth}{!}{\includegraphics{figures/ptsum-trans-jmy.eps}} 
\\
(a) & (b)
\end{tabular}

\caption{PYTHIA version 6.416 - tuned and JIMMY version 4.3 - UE
  predictions for the underlying event compared to the
  $<N_{\text{chg}}>$ (a) and $<p_{\text{T}}^{\text{sum}}>$ (b).}
\label{fig:cdf-jimmy}
\end{center}
\end{figure}

Figures \ref{fig:cdf-jimmy}(a) and \ref{fig:cdf-jimmy}(b) show
PYTHIA version 6.416 - tuned and JIMMY version 4.3 - UE \cite{ATLAS-JIMMY} 
predictions for the underlying event compared to the CDF data for $<N_{\text{chg}}>$ 
and $<p_{\text{T}}^{\text{sum}}>$, respectively. Both models describe the data reasonably well. 
However, as shown in Fig. \ref{fig:cdf-pt-nchg}, the ratio 
$<p_{\text{T}}^{\text{sum}}>$/$<N_{\text{chg}}>$
is better described by PYTHIA version 6.416 - tuned. This indicates
that charged particles generated by JIMMY version 4.3 - UE are
generally softer than the data and also softer than those generated by
PYTHIA version 6.416 - tuned.
\begin{figure}[h!]
\begin{center}
\scalebox{0.4}[0.375]{\includegraphics{figures/pt-nchg-jmy.eps}} 
\caption{PYTHIA version 6.416 - tuned and JIMMY version 4.3 - UE predictions for the
  underlying event in p$\overline{\text{p}}$ collisions at 1.8 TeV
  compared to the ratio $<p_{\text{T}}^{\text{sum}}>$/$<N_{\text{chg}}>$.}    
\label{fig:cdf-pt-nchg}
\end{center}
\end{figure}

Another CDF measurement of the underlying event was made by defining two cones in
$\eta - \phi$ space, at the same pseudorapidity $\eta$ as the leading
$E_{\text{T}}$ jet (calorimeter jet) and $\pm \pi/2$ in the azimuthal
direction, $\phi$ \cite{Acosta:04}. The total charged track transverse momentum
inside each of the two cones was then measured and the higher of the
two values used to define the ``MAX'' cone, with the remaining cone
being labelled ``MIN'' cone. 
\begin{figure}[h!]
\begin{tabular}{cc}
\resizebox{0.45\textwidth}{!}{\includegraphics{figures/cdf-et-mult.eps}}
&
\resizebox{0.5\textwidth}{!}{\includegraphics{figures/cdf-et-pt.eps}}
\\
(a) & (b)

\end{tabular}
\caption{(a) Average charged particle multiplicity, $<N_{\text{chg}}>$, 
in MAX (top distributions) and MIN (bottom distributions) cones; 
(b) average total $P_{\text{T}}$ of charged particles in MAX and MIN
cones.}
\label{fig:maxmin-pythia}
\end{figure}

Figure \ref{fig:maxmin-pythia} shows PYTHIA version 6.416 - tuned
predictions for the underlying event in p$\overline{\text{p}}$ collisions at 
$\sqrt{\text{s}}$ = 1.8 TeV compared to CDF data \cite{Acosta:04} for
$<N_{\text{chg}}>$ and $<P_{\text{T}}>$ of charged particles in the MAX 
and MIN cones. PYTHIA version 6.416 - tuned describes the data reasonably well. 
However, we notice that the $<P_{\text{T}}>$ in the MAX cone is slightly 
harder than the data.

\section{LHC predictions for the UE}

Predictions for the underlying event in LHC collisions (pp collisions at $\sqrt{\text{s}}$ = 14 TeV)
have been generated with PYTHIA version 6.416 - tuned and JIMMY
version 4.3 - UE.
Figures \ref{fig:ue-lhc}(a) and \ref{fig:ue-lhc}(b) show $<N_{\text{chg}}>$ and
$<p_{\text{T}}^{\text{sum}}>$ distributions for the region transverse
to the leading jet (charged particles with $p_{\text{T}} >0.5~$GeV 
and $\left| \eta \right| <1$), as generated by PYTHIA version 6.416 - tuned
(Table \ref{tab:PYTHIA-tuning}) and JIMMY version 4.3 - UE \cite{ATLAS-JIMMY}, respectively.
The CDF data (p$\overline{\text{p}}$ collisions at $\sqrt{\text{s}}$ = 1.8 TeV)
for the underlying event is also included in Fig. \ref{fig:ue-lhc} for comparison. 
\begin{figure}[h!]
\begin{center}
\begin{tabular}{cc}
\resizebox{0.5\textwidth}{!}{\includegraphics{figures/mult-trans-lhc.eps}} 
&
\resizebox{0.5\textwidth}{!}{\includegraphics{figures/ptsum-trans-lhc.eps}} 
\\
(a) & (b)
\end{tabular}

\caption{PYTHIA version 6.416 - tuned and JIMMY version 4.3 - UE predictions for the underlying event
  in pp collisions at $\sqrt{\text{s}}$ = 14TeV for $<N_{\text{chg}}>$ (a) 
  and $<p_{\text{T}}^{\text{sum}}>$ (b).}
\label{fig:ue-lhc}
\end{center}
\end{figure}

A close inspection of predictions for the $<N_{\text{chg}}>$ in the 
underlying event given in Fig.\ref{fig:ue-lhc}(a), shows that the average charged particle
multiplicity for events with leading jets with $P_{\text{T}_{\text{ljet}}} >
15$ GeV reaches a plateau at $\sim 5.5$ charged particles according to
both PYTHIA version 6.416 - tuned and JIMMY version 4.3-UE. This corresponds to a rise of a factor of 
$\sim 2$ in the plateau of $<N_{\text{chg}}>$ as the colliding energy is increased from 
$\sqrt{\text{s}}$ = 1.8 TeV to $\sqrt{\text{s}}$ = 14 TeV.

The $<p_{\text{T}}^{\text{sum}}>$ distributions in Fig. \ref{fig:ue-lhc}(b) 
show that PYTHIA version 6.416 - tuned generates harder particles in the underlying event 
compared to JIMMY version 4.3-UE.
This is in agreement with the results shown in Fig. \ref{fig:cdf-pt-nchg}, 
although for the LHC prediction the discrepancy between the two models is
considerably larger than the observed at the Tevatron energy.

The difference between the predictions for the charged particle's $p_{\text{T}}$ 
in the underlying event is a direct result of the tuning of the colour reconnection parameters
in the new PYTHIA version 6.4 model. This component of the PYTHIA model has been specifically
tuned to produce harder particles, whereas in JIMMY version 4.3 - UE
this mechanism (or an alternative option) is not yet available.


\section{CONCLUSIONS}

In this report we have compared tunings for PYTHIA version 6.416
(Table \ref{tab:PYTHIA-tuning}) and JIMMY version 4.3
\cite{ATLAS-JIMMY} to the underlying event. Both models have shown
that, when appropriately tuned, they can describe the data.

In order to obtain the parameters for PYTHIA version 6.416 - tuned,
we have deliberately selected a combination of parameters that generate shorter 
strings between the hard and the soft systems in the hadronic interaction. We have
also increased the hadronic core radius compared to the tunings used in previous 
PYTHIA versions (see Refs. \cite{Moraes:2007,CDF-tuneA} for example). 

We have noticed that PYTHIA version 6.416 - tuned and JIMMY version
4.3 - UE generate approximately the same densities of charged
particles in the underlying event. This is observed for the underlying
event predictions at the Tevatron and LHC energies alike.

However, there is a considerable disagreement between these tuned models in their 
predictions for the $p_{\text{T}}$ spectrum in the underlying event, as can be seen in Figs. 
\ref{fig:cdf-pt-nchg} and \ref{fig:ue-lhc}(b). PYTHIA version 6.416 - tuned has been calibrated 
to describe the ratio $<p_{\text{T}}^{\text{sum}}>$/$<N_{\text{chg}}>$, 
which has been possible through the tuning of the colour reconnection parameters in PYTHIA.
JIMMY version 4.3 - UE has not been tuned to this ratio. 

As a final point, we would like to mention that this is an
``\textit{ongoing}'' study. At the moment these are the best
parameters we have found to describe the data, but as the models are
better understood, the tunings could be improved in the near future. 


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