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\begin{document} \title{Measurement of the Underlying Event at LHC with the CMS detector} 
\author{Ambroglini Filippo$^1$\protect\footnote{\ \ speaker}, Bartalini Paolo$^2$, Fan\`o Livio$^3$}
\institute{$^1$Universit\`a degli Studi di Trieste \& INFN,\\
$^2$ National Taiwan University \\
$^3$ Universit\`a degli Studi di Perugia \& INFN}

\maketitle
\begin{abstract}
A study of \textit{Underlying Events} (UE) at \textit{Large Hadron Collider} (LHC) with CMS detector under nominal conditions is discussed. Using charged particle and charged particle jets, it will be possible to discriminate between various QCD models with different multiple parton interaction schemes, which correctly reproduce Tevatron data but give different predictions when extrapolated to the LHC energy. This will permit improving and tuning Monte Carlo models at LHC start-up, and opens prospects for exploring QCD dynamics in proton-proton collisions at 14TeV.
\end{abstract}

\section{Introduction}
\label{sec:intro}
From a theoretical point of view, the underlying event (UE) in a hadron-hadron interaction is 
defined as all particle production accompanying the hard scattering component of the collision. 
From an experimental point of view, it is impossible to separate these two components. 
However, the topological structure of hadron-hadron collisions can be used to define physics 
observables which are sensitive to the UE. 
The ability to properly identify and calculate the UE activity, and in particular the contribution 
from Multiple Parton Interactions � MPI \cite{art1}, has direct implications for other measurements at 
the LHC. 
This work is devoted to the analysis of the sensitivity of UE observables, as measured by CMS\cite{art0}, 
to different QCD models which describe well the Tevatron UE data but largely differ when 
extrapolated to the LHC energy. MPI are implemented in the PYTHIA simulations \cite{art2}, for 
which the following tunes are considered: tune DW (reproducing the CDF Run-1 Z boson 
transverse momentum distribution \cite{art3}), tune DWT (with a different MPI energy dependence 
parametrization \cite{art4}) and tune S0 (which uses the new multiple interaction model implemented 
in PYTHIA \cite{art5}). In addition, an Herwig \cite{art6} simulation has also been performed, providing a 
useful reference to a model without multiple interactions. 

\section{Analysis strategy}
\label{sec:analysis_strategy}
Significant progress in the phenomenological study of the UE in jet events has been achieved by 
the CDF experiment at the Tevatron \cite{art7,art8}. In the present work, plans are discussed to 
study the topological structure of hadron-hadron collisions and the UE at the LHC, using only 
charged particle multiplicity and momentum densities in charged particle jets. A charged particle jet 
(referred to as a charged jet from now on) is defined using charged particles only, with no recourse 
to calorimeter information. 
The direction of the leading charged jet, which in most cases results from the hard scattering, is 
used to isolate different hadronic activity regions in the $\eta$-$\phi$ space and to study correlations 
in the azimuthal angle $\phi$. The plane transverse to the jet direction is where the 2-to-2 hard 
scattering has the smallest influence and, therefore, where the UE contributions are easier to 
observe. 
In order to combine measurements with different leading charged jet energies, events are selected 
with a Minimum Bias (MB) trigger \cite{art9} and with three triggers based on the transverse 
momentum of the leading calorimetric jet ( $P^{calo}_{T} >$ 20, 60 and 120 GeV/c). 
Charged jets are reconstructed with an iterative cone algorithm with radius R = 0.5, using 
charged particles emitted in the central detector region $|\eta| <$ 2. Two variables allow evaluating 
charged jet performances: the distance $\Delta R =\sqrt{ \Delta\phi^{2} + \Delta\eta^{2}}$ between the 
leading charged jet and  the leading calorimetric jet, and the ratio of their transverse momenta 
$P_{T}$ (transverse momenta are defined with respect to the beam axis). The transverse momentum 
of the leading charged jet is used to define the hard scale of the event. 

Figure \ref{fig0} presents, for the different trigger streams used , the density $dN/d\eta d\phi$ of the charged particle
multiplicity and the density $dp^{sum}_{T} /d\eta d\phi$ of the total charged particle transverse momentum
$p^{sum}_{T}$ , as a function of the azimuthal distance to the leading charged jet. Enhanced activity is
observed around the jet direction, in the "toward" region ($\simeq$ 0 degrees from the jet direction),
together with a corresponding rise in the "away" region ($\simeq$ 180 degrees), due to the recoiling
jet. The "transverse" region ($\simeq \pm $ 90 degrees) is characterized by a lower activity and almost
flat density distributions, as expected.

\section{UE observable measurement}
\label{sec:ue_obs}
\subsection{Tracking}
\label{sec:tracking}
Tracks of charged particles with $p_{T} >$ 0.9 GeV/c are reconstructed in CMS following the procedure described in
 \cite{art10}. The possibility to build the UE observables using tracks with $p_{T} >$ 0.5 GeV/c enhances sensitivity to 
 the differences between the models. The standard CMS tracking algorithm was, thus, adapted to a 0.5 GeV/c threshold, 
 by decreasing the $p_{T}$ cut of the seeds and of the trajectory builder, and adapting other parameters of the trajectory 
 reconstruction to optimize performance.
\subsection{Results on density measurements}
\label{sec:res1}
The densities $dN/d\eta d\phi$ of charged particle multiplicity and $dp^{sum}_{T}/d\eta d\phi$ of charged $p^{sum}_{T}$ 
are presented in Figure\ref{fig1} for the toward region and in Figure\ref{fig2} for the transverse region. 
The data, corresponding to an integrated luminosity of 10 $pb^{-1}$ , are presented at the reconstruction level, using the DWT tune. 
In the toward region, the expected strong correlation between the transverse momentum of 
the charged jet and the charged $p^{sum}_{T}$ density is clearly visible. In the transverse region, 
two contributions to the hadronic activity can be identified: a fast saturation of the UE densities for 
charged jets with $P_{T} <$ 20 GeV/c, and a smooth rise for $P_{T} >$ 40 GeV/c. The latter is due to 
initial and final state radiation, which increases with the hard scale of the event. 
In Figure \ref{fig3}, the ratio between generated and reconstructed UE observables is presented as a 
function of the charged jet $P_{T}$ , for simulations performed with the PYTHIA DWT tune and the 
$p_{T} >$ 0.9 GeV/c tracking reconstruction parameter set. The average corrections for both the $P_{T}$ 
scale and the UE observables are found to be independent of the particular model used for the 
simulations. 
Figure \ref{fig4} presents the predictions for the transverse activity, as obtained using the PYTHIA 
DWT tune and corrected following the results of Figure \ref{fig3}. The statistical precision and the 
alignment conditions correspond to those achieved with an integrated luminosity of 100 $pb^{-1}$ . 
The curves represent the predictions of the different PYTHIA (DW, DWT and S0 tunes) and 
HERWIG simulations. 
Lowering the pT threshold for track reconstruction to 0.5 GeV/c leads to an increase of about 
50\% of the charged particle multiplicity and of about 30\% of the charged transverse momentum 
density. As shown in Figure \ref{fig5}, this enhances the discrimination power between the different 
models in the charged jet $P_{T}$ region below 40 GeV/c, where the differences between models are 
expected to be the largest. This is particularly clear when comparing the DWT and S0 tunes. 

\subsection{Results using observable ratios}
\label{sec:res2} 
The ratios between (uncorrected) UE density observables in the transverse region, for charged 
particles with $p_{T} >$ 0.9 GeV/c and with $p_{T} >$ 1.5 GeV/c, are presented in Figure \ref{fig6}, for an 
integrated luminosity of 100 $pb^{-1}$ . Ratios are shown here as obtained after track reconstruction, 
without applying additional reconstruction corrections; given the uniform performance of 
track reconstruction, the ratios presented here at detector level are similar to those at generator 
level. These ratios show a significant sensitivity to differences between different MPI models, 
thus providing a feasible (and original) investigation method. 

\section{Conclusions}
\label{sec:conc}

The predictions on the amount of hadronic activity in the region transverse to the jets produced 
in proton-proton interactions at the LHC energies are based on extrapolations from lower energy 
data (mostly from the Tevatron). These extrapolations are uncertain and predictions differ 
significantly among model parameterisations. It is thus important to measure the UE activity 
at the LHC as soon as possible, and to compare those measurements with Tevatron data. 
This will lead to a better understanding of the QCD dynamics and to improvements of QCD 
based Monte Carlo models aimed at describing �ordinary� events at the LHC, an extremely 
important ingredient for �new� physics searches. 
Variables well suited for studying the UE structure and to discriminate between models are the 
densities $dN/d\eta d\phi$ of charged particle multiplicity and $dp^{sum}_{T}/d\eta d\phi$ of total charged particle 
transverse momentum $p^{sum}_{T}$ , in charged particle jets. An original approach is proposed, by 
taking the ratio of these variables for different charged particle $p_{T}$ thresholds. 
With 10 $pb^{-1}$ and a partially calibrated detector, it will be possible to control systematic uncertainties 
on the UE observables, to keep them at the level of the statistical errors and to perform a first discrimination 
between UE models. Extending the statistics to 100 $pb^{-1}$ and exploiting the uniform performance of track 
reconstruction for $p_{T} >$ 1.5 GeV/c and $p_{T} >$ 0.9 GeV/c, the ratio of observables will probe more 
subtle differences between models.

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\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=1.]{fig0.pdf} 
\caption{Densities $dN/d\eta d\phi$ of charged particle multiplicity (left) and $dp^{sum}_{T}/d\eta d\phi$ of total
charged transverse momentum (right), as a function of the azimuthal distance to the leading charged jet direction..}
\label{fig0}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=1.]{fig1.pdf} 
\caption{Densities $dN/d\eta d\phi$ of charged particle multiplicity (left) and $dp^{sum}_{T}/d\eta d\phi$ of total
charged transverse momentum (right), as a function of the leading charged jet $P_{T}$, in the toward
region, for an integrated luminosity of 10 $pb^{-1}$ (uncorrected distributions).}
\label{fig1}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=1.]{fig2.pdf} 
\caption{Same as in Figure \ref{fig1} but in the transverse region.}
\label{fig2}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=1.]{fig3.pdf} 
\caption{Ratio between generator (MC) and reconstructed (RECO) level predictions from the PYTHIA DWT tune, for the $dN/d\eta d\phi$ (left) and 
$dp^{sum}_{T}/d\eta d\phi$ (right) densities, as a function of the leading charged jet $P_{T}$, for an integrated luminosity of 10 $pb^{-1}$.}
\label{fig3}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=1.]{fig4.pdf} 
\caption{Densities $dN/d\eta d\phi$ (left) and $dp^{sum}_{T}/d\eta d\phi$ (right) for tracks with $p_{T} >$ 0.9 GeV/c, as
a function of the leading charged jet $P_{T}$, in the transverse region, for an integrated luminosity of 100 $pb^{-1}$ (corrected distributions).}
\label{fig4}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=1.]{fig5.pdf} 
\caption{Same as in Figure \ref{fig4} but using tracks with $p_{T} >$ 0.5 GeV/c.}
\label{fig5}
\end{center}
\end{figure}

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=1.]{fig6.pdf} 
\caption{Ratio of the UE event observables, computed with track transverse momenta $p_{T}>$1.5 GeV/c and $p_{T} >$0.9 GeV/c: densities 
$dN/d\eta d\phi$ (left) and $dp^{sum}_{T}/d\eta d\phi$ (right), as a function of the leading charged jet $P_{T}$, in the transverse region, 
for an integrated luminosity of 100 $pb^{-1}$(uncorrected distributions).}
\label{fig6}
\end{center}
\end{figure}

\end{document}
