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\begin{document} \title{CMS: minimum bias studies} 
\author{Ferenc Sikl\'er$^1$\protect\footnote{\ \ speaker},
 Kriszti\'an Krajcz\'ar$^2$ for the CMS Collaboration}
\institute{$^1$KFKI Research Institute for Particle and Nuclear Physics,
Budapest, Hungary,\\ 
$^2$E\"otv\"os University, Budapest, Hungary}
\maketitle

\begin{abstract}
The early data from LHC will allow the first look at minimum bias p-p
collisions initially at the center-of-mass energies of 10 and later 14 TeV.
The plans of the CMS collaboration to measure cross sections and differential
yields of charged particles (unidentified or identified) and neutrals produced
in inelastic p-p collisions at 14 TeV are presented.  The tracking of charged
particles will be possible down to about 100 MeV/c, with good efficiency and
negligible fake rate. The yield of charged kaons and protons can be extracted
for total momenta below 0.8 and 1.5 GeV/c, respectively. Comparisons of the
results to theoretical models are also discussed.
\end{abstract}

%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

The CMS experiment at the LHC is a general purpose detector designed to explore
physics at the TeV energy scale \cite{Ball:2007zza,D'Enterria:2007xr}. It has
a large acceptance and hermetic coverage. The various subdetectors are: a
silicon tracker with pixels and strips ($|\eta|<2.4$); electromagnetic
($|\eta|<3$) and hadronic ($|\eta|<5$) calorimeters; and muon chambers
($|\eta|<2.4$) \cite{Adolphi:2008zzk}. The acceptance is further extended with
forward detectors: CASTOR ($5.2<|\eta|<6.6$) and Zero Degree Calorimeters
($|\eta_{neutrals}|>8.3$). CMS detects leptons and both charged and neutral
hadrons.
%For an extensive review see Ref.~\cite{D'Enterria:2007xr}.
This
example analysis uses 2 million inelastic p-p collisions. They have been
generated by the {\sc pythia} event generator \cite{Sjostrand:2006za}.

\section{Minimum bias triggers}

In case of very low initial intensity the events can be taken by a special high
level trigger, requiring at least one or two reconstructed tracks in the
pixel detector. This trigger has very low bias and an efficiency of about 88\%
for inelastic p-p collisions. Another type of trigger will be based on counting
towers, with energy above the detector noise level, in both forward hadronic
calorimeters (HF, $3<|\eta|<5$).  A minimal number of hits (1, 2 or 3) will be
required on one or on both sides
%, an energy threshold value of 1.4~GeV is used
%in the hit definition
 \cite{minbiastrigger}. The efficiency of this single-sided
trigger for inelastic p-p collisions is about 89\%. The double-sided trigger is
less efficient (about 59\%), but it is also less sensitive to beam-gas
background (Fig.~\ref{fig:triggerPixelcounting}-left). Once the luminosity is
high enough, events can also be taken with the so called zero-bias trigger
based on a random clock each bunch crossing.

%%%%%%%%%%%%%%
\begin{figure}
 \begin{center}
  \includegraphics[width=0.51\textwidth]
                  {figs/BeamGas_dNdeta_Color}
  \includegraphics[width=0.45\textwidth]
                  {figs/RecdNdeta_3layers_10_bw_noband}
 \end{center}

 \vspace{-0.2in}
 \caption{Left: The number of charged particles per unit pseudo-rapidity for
minimum bias collisions compared to beam gas collisions occurring at the center
of the detector. Right: Charged particle $dN_{ch}/d\eta$ distributions from
generated (histogram) and reconstructed (symbols) p-p events at 14 TeV. Error
bars show the statistical errors corresponding to 5000 events.}

 \label{fig:triggerPixelcounting}

\end{figure}
%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%
\section{Charged particle rapidity density}

Charged hadrons with $p_T$ larger than 30~MeV/$c$ can leave hits in the layers
of the pixel detector. Its fine segmentation and small occupancies allow for
the measurement of the $\eta$ distribution of charged hadrons by counting the
number of reconstructed hits \cite{pixelcounting}. With help of the length of
the pixel hit clusters in beam direction, the position of the interaction vertex
can be estimated. It also helps to remove background hits at higher $\eta$ if
their size is incompatible with the found vertex position.  The number of
detected hits has to be corrected for non-primary origin: looping particles,
secondaries, decay products. A systematic error of 7\% is expected
(Fig.~\ref{fig:triggerPixelcounting}-right). The method is attractive since it
does not need particle tracking and it is insensitive to the alignment of the
tracker.

%%%%%%%%%%%%%%%%%%%%%%
\section{Charged particle spectra, particle identification}

Both pixel and strip silicon tracker detectors are used for the
reconstruction of charged particles.  With a modified hit triplet finding
algorithm the pixel detector can be employed for the reconstruction of low
$p_T$ charged particles \cite{D'Enterria:2007xr, Sikler:2007uh, spectra}. The
acceptance of the method extends down to 0.1, 0.2 and 0.3~GeV/$c$ in $p_T$ for
pions, kaons and protons, respectively. The obtained pixel tracks are used for
finding and fitting the primary vertex or vertices \cite{Cucciarelli:2006,
Adam:2006, Ball:2007zza}. The
found vertices are reused, ensuring that the track comes from an interaction
point. This brings the fake track rate down to per mille levels. The measured
shape of tracker hits is compared to the dimensions predicted from the local
direction of the trajectory. This filter helps to eliminate incompatible
trajectory candidates at an early stage.  At the end, the trajectory is
refitted with the primary vertex constraint.

%%%%%%%%%%%%%%
\begin{figure}
 \begin{center}
  \includegraphics[width=0.32\textwidth]{figs/allpRec}
  \includegraphics[width=0.32\textwidth]{figs/pionLowRec}
  \includegraphics[width=0.32\textwidth]{figs/protLowRec}
 \end{center}

 \vspace{-0.2in}
 \caption{Selection of particle spectra. Left: Measured invariant yields of
charged hadrons in the range $0 < |\eta| < 2.4$.  Right: Measured differential
yields of identified charged pions and protons in the range $0 < |y| < 1.2$.
Measured values and empirical fit functions are plotted, with a series of $0.2$
unit wide bins. Values are successively multiplied by 10 or shifted for
clarity.}

 \label{fig:allPlusPion}

\end{figure}
%%%%%%%%%%%%%%

The hadron spectra are corrected for particles of non-primary origin. Their
main source is the feed-down from weakly decaying resonances.  While the
correction is around 2\% for pions, it can go up to 15\% for protons with $p_T
\approx 0.3~\mathrm{GeV}/c$. The resonances $\mathrm{K^0_S}$, $\Lambda$ and
$\overline{\Lambda}$ can be extracted from the measured data.
%with help of V0
%finding methods \cite{D'Enterria:2007xr, Sikler:2007uh,
%spectra}.

Charged particles can be singly identified or their yields can be extracted
(identification in the statistical sense) using deposited energy in the pixel
and strip silicon tracker, with help of the truncated mean estimator
\cite{spectra}. The distribution of $\log\mathrm{d}E/\mathrm{d}x$ can be
successfully fitted in slices of momentum. The fit function is a sum of
properly scaled Gaussians for each particle species: here pions, kaons and
protons are assumed. The relative resolution of $\mathrm{d}E/\mathrm{d}x$ for
tracks with average number of hits ($\sim$15) is around 5-7\%. The yield of
kaons can be extracted if $p < 0.8~\mathrm{GeV}/c$ and that of protons if $p <
1.5~\mathrm{GeV}/c$. Both limits correspond to approximately $3\sigma$
separation. 

The measured invariant yields of charged hadrons are shown in
Fig.~\ref{fig:allPlusPion}-left, as a function of $p_T$, in narrow $\eta$
bins. (Results refer to the sum of positively and negatively charged particles.
Symmetric positive and negative $\eta$ bins are also added.) Measured
differential yields of identified charged pions and protons are shown in
Fig.~\ref{fig:allPlusPion}-right. The obtained invariant yields were fitted by
the Tsallis function \cite{Tsallis:1987eu}, a function that successfully
combines and describes both the low $p_T$ exponential and the high $p_T$
power-law behaviors. The pseudorapidity distribution of charged hadrons is
shown in Fig.~\ref{fig:densityEnergy}-left. The energy dependence of some
measured quantities can also be studied (Fig.~\ref{fig:densityEnergy}-right).
The curve shows a quadratic fit on data
points of other experiments
\cite{Ullrich:2002tq}.


%%%%%%%%%%%%%%
\begin{figure} 
 \begin{center}
  \vspace{-0.1in}
  \includegraphics[width=0.50\textwidth]
                  {figs/fitResult_dNdeta_comparison}
  \includegraphics[width=0.48\textwidth]
                  {figs/measured_apt_qm08}
 \end{center}

 \vspace{-0.2in}
 \caption{Left: Pseudorapidity density distribution of charged hadrons. The
distribution from simulated tracks is given by the purple curve for comparison.
Right:  Energy dependence of average transverse momentum of unidentified
charged hadrons at $\eta \approx 0$.
The result of this analysis is shown with red pentagons.}

 \label{fig:densityEnergy}

\end{figure}
%%%%%%%%%%%%%%  

%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusions}

In summary, spectra and yields of charged and neutral particles (unidentified
and identified) produced in inelastic proton-proton collisions can be measured
with good precision with the CMS tracker. They will help to improve the QCD
understanding of p-p collisions.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgment}

The authors wish to thank the Hungarian Scientific Research Fund and the
National Office for Research and Technology (K 48898, H07-B 74296, H07-C
74248).


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