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\begin{document} \title{TOTEM early measurements } 
\author{F.~Ferro$^{1}$\protect\footnote{\ \ speaker},
 G.~Antchev$^{2}$, 
P.~Aspell$^{2}$, V.~Avati$^{2,9}$, M.G.~Bagliesi$^{5}$,
V.~Berardi$^{4}$, M.~Berretti$^{5}$, U.~Bottigli$^{5}$, 
M.~Bozzo$^{1}$,
E.~Br\"{u}cken$^{6}$, A. Buzzo$^{1}$, F.~Cafagna$^{4}$, M.~Calicchio$^{4}$, 
 M.G.~Catanesi$^{4}$,
P.L.~Catastini$^{5}$, R.~Cecchi$^{5}$, 
M.A.~Ciocci$^{5}$,
M.~Deile$^{2}$, E.~Dimovasili$^{2,9}$,M.~Doubrava$^{12}$,
K.~Eggert$^{9}$, V.~Eremin$^{10}$, 
F.~Garcia$^{6}$, M.~Galu\v{s}ka$^{12}$, S.~Giani$^{2}$, V.~Greco$^{5}$, 
 J.~Heino$^{6}$, T.~Hilden$^{6}$,  
J.~Ka\v{s}par$^{2,7}$,J.~Kopal$^{7}$, V.~Kundr\'{a}t$^{7}$, K.~Kurvinen$^{6}$, 
 S.~Lami$^{5}$, G.~Latino$^{5}$, 
R.~Lauhakangas$^{6}$, E.~Lippmaa$^{8}$, 
M.~Lokaj\'{\i}\v{c}ek$^{7}$, M.~Lo~Vetere$^{1}$, F.~Lucas~Rodriguez$^{2}$, 
 M.~Macr\`{\i}$^{1}$,
G.~Magazz\`{u}$^{5}$, R.~Marek$^{12}$,
M.~Meucci$^{5}$, S.~Minutoli$^{1}$, H.~Niewiadomski$^{2,9}$, 
G.~Notarnicola$^{4}$, 
E.~Oliveri$^{5}$, F.~Oljemark$^{6}$, R.~Orava$^{6}$, M.~Oriunno$^{2}$, 
K.~\"{O}sterberg$^{6}$, E.~Pedreschi$^{5}$,
J.~Pet\"{a}j\"{a}j\"{a}rvi$^{6}$, M.~Quinto$^{4}$,
E.~Radermacher$^{2}$, E.~Radicioni$^{4}$,  
F.~Ravotti$^{2}$, G.~Rella$^{4}$, E.~Robutti$^{1}$,
L.~Ropelewski$^{2}$, G.~Ruggiero$^{2}$, A.~Rummel$^{8}$,
H.~Saarikko$^{6}$, G.~Sanguinetti$^{5}$, A.~Santroni$^{1}$,
A.~Scribano$^{5}$, G.~Sette$^{1}$, W.~Snoeys$^{2}$, F.~Spinella$^{5}$,
P.~Squillacioti$^{5}$, A.~Ster$^{11}$, C.~Taylor$^{3}$, 
 A.~Trummal$^{8}$,
N.~Turini$^{5}$,  V.~Vacek$^{12}$,V.~Vin\v{s}$^{12}$, M.~Vitek$^{12}$,
 J.~Whitmore$^{9}$, J.~Wu$^{2}$}
\institute{$^{1}$Universit\`{a} di Genova and Sezione INFN, Genova, Italy,\\ 
$^{2}$CERN, Gen\`{e}ve, Switzerland,\\ 
$^{3}$Case Western Reserve University, Dept. of Physics, Cleveland, OH, USA,\\
$^{4}$INFN Sezione di Bari and Politecnico di Bari, Bari, Italy,\\  
$^{5}$INFN Sezione di Pisa and Universit\`{a} di Siena, Italy,\\ 
$^{6}$Helsinki Institute of Physics and Department of Physics, 
	University of Helsinki, Finland\\
$^{7}$Institute of Physics of the Academy of Sciences of the Czech Republic, 
Praha, Czech Republic\\ 
$^{8}$National Institute of Chemical Physics and Biophysics NICPB, Tallinn,
Estonia.\\
$^{9}$Penn State University, Dept. of Physics, University Park, PA, USA.\\
$^{10}$On leave from Ioffe Physico-Technical Institute, 
Polytechnicheskaya Str. 26, 194021 St-Petersburg, Russian Federation.\\
$^{11}$Individual participant from MTA KFKI RMKI, Budapest, Hungary.\\
$^{12}$Czech Technical University, Praha, Czech Republic\\ 
 }
\maketitle
\begin{abstract}
The status of the TOTEM experiment is described as well as the prospects for the measurements in the early LHC runs. The primary goal of TOTEM is the measurement of the total p-p cross section, using a method independent of the luminosity. A final accuracy of 1\% is expected with dedicated $\beta^*=1540$ m runs, while at the beginning a 5\% resolution is achievable with a $\beta^*=90$ m optics. Accordingly to the running scenarios TOTEM will be able to measure the elastic scattering in a wide range of $t$ and to study the cross-sections and the topologies of diffractive events. In a later stage, physics studies will be extended to low-x and forward physics collaborating with CMS as a whole experimental apparatus. 

\end{abstract}

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

The TOTEM experiment at the LHC will measure\cite{tdr,tdr-add}
the total cross section with $\sim$1\% uncertainty, by using the luminosity independent method,
      which requires simultaneous measurements of elastic p-p scattering down to the  four-momentum transfer
      squared $-t~\sim 10^{-3}\,{\rm GeV}^2$ and of the inelastic p-p interaction rate with an extended acceptance
      in the forward region. The extrapolation of the present data to the LHC energy together with the existing
      cosmic ray data give a typical uncertainty of $\pm 15\% $ on the total cross-section.
TOTEM will also measure the elastic p-p scattering up to $-t ~ \sim \, 10\,{\rm GeV}^2$ and study soft diffraction.

Moreover, in collaboration with CMS will
study jets, W's and heavy flavour production in single diffractive (SD) and double Pomeron exchange (DPE) events,
measure particle and energy flow in the forward direction
and study central exclusive particle production and
low-x physics.
 \vspace{4mm}

\begin{figure}[!ht] 

%\vspace{1mm}
%\begin{center}
\begin{center}

\includegraphics[width=0.45\textwidth, angle=270]{images/cs-el.eps}

\end{center}
\caption{Left: COMPETE predictions for total p-p cross section 
with PS,
ISR, SPS, Tevatron and cosmic ray data. Right: elastic p-p cross section as predicted by the BSW model; the two columns on the right side show the number of events expected after 1 day running at 10$^{28}$ and 10$^{32}$cm$^{-2}$s$^{-1}$ luminosity. 
}
\label{cross}
%\end{center}
\end{figure}

The TOTEM experiment is designed to measure  $\sigma_{tot}$ with an accuracy which is sufficient to 
 discriminate between the current model predictions for the LHC energy ranging between 90 and 130\,mb (see Fig.~\ref{cross} for COMPETE \cite{xsection} fits).
 %;
%recent fits performed by the COMPETE 
%collaboration\cite{cross-section} using all the available data, have estimated 
%$\sigma_{tot} = 111.5\pm 1.2^{+4.1}_{-2.1}\, {\rm mb}$ and $\rho = \frac{Re(F)}{Im(F)}=0.1361\pm 0.0015 ^ {\pm 0.0058}_{\pm 0.0025}$.
Using the optical theorem the total cross section can be written as:
$$\sigma_{tot}=\frac{16 \pi}{(1+\rho^2)} \frac{({dN_{el}/dt})_{t=0}}{(N_{el}+N_{inel})}$$
where $N_{el}$ and $N_{inel}$ are respectively the elastic and inelastic rate.
\begin{figure}[!ht] 

%\vspace{1mm}
\begin{center}
\includegraphics[angle=90,width=0.8\textwidth]{images/rplace1.eps}

\caption{The LHC beam line with the Roman Pots at 147 and 220 m.}
\label{rplace}
\end{center}
\end{figure}

\vspace{3cm}
\begin{figure}[!ht] 


\vspace{3mm}
\begin{center}
\includegraphics[angle=270,width=0.8\textwidth]{images/cms-totem.eps}
\caption{The TOTEM detectors T1 and T2 installed in the CMS forward region.}

\label{totem}
\end{center}
\end{figure}



The precise measurement of $\sigma_{tot}$ provides also an absolute 
 calibration of the machine luminosity: 
 $$\mathcal{L} = \frac{(N_{el}+N_{inel})^2}{16 \pi({dN_{el}/dt})_{t=0}}\cdot (1+\rho^2)$$
TOTEM needs to run with special running conditions ($\beta^{*} = 1540$ m and
luminosity $\mathcal{L} \approx 10^{28}\ {\rm cm}^{-2}{\rm s}^{-1}$).
The $\beta$ value at the interaction point requires zero crossing-angle,
due to the increased beam size (proportional to $\beta$),
and then a reduced number of bunches which is compatible with the LHC 
injection scheme.
%The most likely configuration is 36 proton bunches with 2.5 $\mu$s spacing. 
Almost half of the total cross--section at the LHC is predicted to come from elastic scattering, single, double 
 and central diffractive processes. 
With the TOTEM acceptance extending up to the pseudorapidities of 6.5, and with the efficient proton detection 
capabilities close to the LHC beams, the diffractively excited states with masses higher than $10\,{\rm GeV}/c^2$ are seen by the experiment.
The precise luminosity independent measurement of the total cross section requires the measurement of 
 $d\sigma_{el}/dt$ down to $-t \sim 10^{-3}\,{\rm GeV}^2$, which corresponds to a proton scattering angle
 of  $5\,\mu{\rm rad}$, and the extrapolation of $d\sigma_{el} /dt$ to the optical point  ($t = 0$).
The leading proton will be detected
by silicon detectors placed inside movable sections of the vacuum pipe (Roman Pots), located symmetrically with respect to the interaction point (IP) (Fig.~\ref{rplace}). 
In order to measure the inelastic rate,
two separate forward telescopes will be installed on both sides, with a rapidity coverage 
 of $3.1 < | \eta | < 6.5$ (Fig.~\ref{totem}). 
With these additional detectors, a fully inclusive trigger, also for single diffraction, can be provided with 
 an expected uncertainty on the inelastic rate of the order of 1\%, after corrections. 

\section{LHC optics}
The detection of forward protons 
from elastic or diffractive scattering at LHC energies requires the 
measurement of very small scattering angles (5--10 $\mu$rad).
These particles remain close to the beam and can be detected
on either side of the IP 
if the displacement at the detector location is large enough.  
The beam divergence at the IP must be small compared to the scattering angle.
To obtain these conditions, a special high-$\beta^*$ insertion optics
is required. A large value (O(km)) of the
$\beta$-function at the IP ($\beta^*$) and a smaller beam emittance reduce the
beam divergence.  A large effective length ${L}^{eff}$ at the
detector location ensures a sizeable displacement.
In fact the displacement ($x(s),y(s)$) of a scattered proton at distance $s$ from the IP  can be described by the following formula, where $\theta^*_{x,y}$ is the scattering angle at the interaction point, ${L}^{eff}$ the effective length, $v$ the magnification and $D$ the dispertion of the machine:
%\begin{center}
%\begin{equation}
$$x(s) = v_x(s)\cdot x^* + L_x^{eff}\cdot \theta_x^* + \frac{\Delta p}{p}\cdot D(s)
%\label{ottica_y}
%\end{equation}
%\begin{equation}
\hspace{4mm}
{\rm and}
\hspace{4mm}
y(s) = v_y(s)\cdot y^* + L_y^{eff}\cdot \theta_y^* 
$$
%\label{ottica_x}
%\end{equation}
%\end{center}
The LHC optics with $\beta^*=1540$ m, limited by the strength of the insertion
quadrupoles, provides large $L_{eff}$ values and parallel-to-point focusing conditions
in both projections at 220 m from the IP. This is the ideal scenario for TOTEM to measure the total cross section and to study minimum bias events and soft diffraction. \\
This large-$\beta^*$ optics requires an injection optics different from the one which will be used at the starting runs of LHC. For this reason, an intermediate-$\beta^*$ optics ($\beta^*$=90 m), which can use the standard LHC injection optics and can thus be operated in the first period of physics runs, has been proposed\cite{ottica90m}. This optics provides parallel-to-point focusing only in the vertical plane and a measurement of $t$ down to $-t \sim 3\cdot 10^{-2}$ GeV$^2$, about one order of magnitude higher than with the nominal TOTEM optics, but nevertheless very useful.




\section{The experimental apparatus}

The TOTEM experiment uses precision silicon microstrip detectors inserted in Roman Pots, movable sections of 
vacuum chamber (Fig.~\ref{dets}), installed in the 
 machine tunnel, at 147 and 220 m from the IP, to measure the elastically and diffractively scattered protons close to the beam direction.
 Each Roman Pot station consists of
	2 units with a distance of 4 (for 220 m station) and 1.5 m (for 147 m station).
	Each unit consists of 3 roman pots, 1 horizontal
	and 2 vertical (top and bottom).
 %Each Roman Pot station counts for three Roman Pot units, equipped with ten planes of detectors (Fig.~\ref{dets}).
 %Two units approach the beam vertically and one horizontally, providing also an overlap among the detectors. 
 The lever arm among different units allows local track reconstruction and a fast trigger selection based on track angle.
In order to measure the elastic scattering to the smallest $|t|$ values,
the detectors should be active as close to their physical edge as possible.
In particular
the detectors will have to be efficient up to a few tens of microns to their edge. These are planar silicon detectors with a current terminating structure,
which consists in replacing the commonly used voltage terminating guard rings (usually 0.5-1 mm wide) with a 50$\mu$m wide structure of rings which strongly reduces the influence
of the current generated at the detector edge on the active
detector volume\cite{ruggiero}. The detectors inside the 220 m stations will be installed during year 2009.

\vspace{1cm}
\begin{figure}[!ht] 
\begin{center}
\includegraphics[width=0.45\textwidth]{images/rp.eps}
\hspace{2mm}
\includegraphics[width=0.474\textwidth]{images/sil.eps}
\caption{Left: horizontal and vertical roman pots. Right: mounted silicon detectors.}
\label{dets}
\end{center}
\end{figure}
%Test-beam's performed at the CERN SPS have shown that the transition region at the edge of the
%2003 prototype detectors has a width of $\sim6 \mu$m for the 3D and $\sim 50 \mu$m for the cold planar. 
\par The telescopes for the detection of the inelastic events have a good trigger capability, 
provide tracking with a good angular resolution and allow the measurement of the trigger efficiency. 
 To discriminate beam-beam from beam-gas events, the telescopes will identify the primary interaction vertex with
 an accuracy  at the level of a cm in the transverse plane by reconstructing a few tracks from each side of the interaction point; the
 knowledge of the full event is not needed. \\
 The T1 telescope (Fig.~\ref{telescopi})
is made of 5 planes of 6 trapezoidal Cathode Strip Chambers 
 (CSC)~\cite{cmsmutdr} and 
will be placed in the CMS end-caps in the rapidity range $3.1\, <\, |\eta | \,<\, 4.7$
with a $2\pi$ azimuthal coverage. It will provide a spatial resolution of $\sim$1 mm.
T2 (Fig.~\ref{telescopi}) is made of 20 half circular sectors of triple-GEM\cite{sauli} (Gas Electron Multiplier) detectors mounted back-to-back and which will provide a spatial resolution of $\sim$ 100 $\mu$m in the radial direction; it
will be placed in the shielding behind the CMS Hadronic 
Forward (HF) calorimeter to extend the coverage at larger $\eta$. 
With the present dimension of the vacuum pipe, the T2 telescope will cover with good efficiency the 
 range $5.3\, <\, |\eta |\,<\, 6.5$.\\
 Both telescopes will be ready for the installation during year 2009. 
\begin{figure}[!ht] 
\begin{center}
\includegraphics[width=0.45\textwidth]{images/t1.eps}
\includegraphics[width=0.45\textwidth]{images/t2.eps}
\caption{Left: T1 quarter ready for the installation. Right: T2 quarter ready for the installation. }
\label{telescopi}
\end{center}
\end{figure}
%In order to discriminate beam-beam events with respect to beam-gas ones, it is necessary to achieve a
%good resolution in the primary vertex reconstruction. Results from the simulation of
%minimum bias events show that the primary vertex position in the (R,z) plane can be reconstructed 
%with the following resolutions: $\sigma_R = 2.9$ mm and $\sigma_z = 4.5$ cm.  

\section{TOTEM programme and early physics}
\subsection{Elastic scattering}


\begin{figure}[!ht] 
\begin{center}
\includegraphics[width=0.46\textwidth]{images/elastic.eps}
\hspace{2mm}
\includegraphics[width=0.43\textwidth]{images/exponential.eps}
\caption{Left: elastic cross section for different theoretical models and $t$ acceptance for $\beta^*=90$ and 2 m optics. Right: elastic cross section zoomed in the exponential region (the pure exponential behavior is plotted as reference) and t acceptance for $\beta^*=1540$ m and 90 m optics. }
\label{elastic}
\end{center}
\end{figure}
The measurement of the elastic cross-section is one of the main goals of TOTEM. Different theoretical models \mcite{teo1,teo2,teo3,teo4} predict different behaviors of the differential cross-section $d\sigma /dt$, as shown in Fig.~\ref{elastic}.
All these $t$ ranges can be accessed by TOTEM using different running scenarios. In particular, for what concerns the nuclear region ($10^{-3}<t<0.5\ {\rm GeV}^2$), it can be accessed with high and intermediate $\beta^*$ optics (Fig.~\ref{elastic}). Due to the high cross-sections involved even at very low luminosities ($10^{28}<{\cal L}<10^{31}{\rm cm}^{-2}{\rm s}^{-1}$) enough statistics can be accumulated in a few runs (at least for low-$t$ values).
The measurement in the nuclear region, which is theoretically described by the exchange of a single Pomeron, is crucial for the extrapolation of $d\sigma_{el} /dt$ to the optical point ($t=0$), needed for the measurement of the total p-p cross-section. This can be done fitting and extrapolating the measured rate with a generalized exponential function $e^{B(t)}$.  The early LHC runs will be characterized by low $\beta^*$ optics with a reduced number of bunches and a lower number of protons per bunch, with respect to the nominal ones. Under these conditions only elastic events with $|t|$ values between 2 GeV$^2$ and 10 GeV$^2$ will be at reach, allowing TOTEM to study high-$t$ elastic scattering. The exponential region will be accessible only if a high/intermediate $\beta^*$ optics will be included in the early physics LHC programme.

\subsection{Inelastic rate and total cross-section}
The measurement of the inelastic rate will be done using all TOTEM detectors and using various trigger and offline analysis strategies, depending on the actual running scenario. At low luminosities a single arm trigger which requires activity in one side of T1 or T2 can be utilized to have very high efficiency; it misses only low mass single diffractive events but it would suffer from beam-gas interactions, which strongly depend on the beam current.
With a double arm T1/T2 trigger the beam-gas background can be suppressed but, on the other hand, the efficiency in detecting single diffractive events is quite reduced. Offline, the sample purity can be enhanced reconstructing the primary interaction vertex. Moreover, the rate of low mass diffractive events which escape detection can be partly recovered extrapolating the measured cross-section with theoretical assumptions on $d\sigma / dM^2$.
\par Combining the uncertainties that come from the measurement of the inelastic and elastic rate and from the extrapolation of the diffractive cross-section to the optical point, it results that a 1\% error on the total cross-section is achievable with the dedicated $\beta^*=1540$ m optics and a 
5\% can be reachable in an earlier stage with the intermediate 90 m optics (see Table 1).
\par With T1 and T2 detectors minimum bias events can be studied, mainly focusing on the charged multiplicity in the covered $\eta$ range.
\begin{table}[hbt]
\centering
\begin{tabular}{|ccc|}
\hline
Uncertainty & $\beta^* = 90$ m & $\beta^* = 1540$ m \\
$dN_{el}/dt\rightarrow0$ & 4\% & 0.2\% \\
$N_{el}$ & 2\% & 0.1\% \\
$N_{inel}$ & 1\% & 0.8\% \\
$\rho$ & 1.2\% & 1.2\% \\
\hline
$\sigma_{tot}$ & 5\% & 1-2\% \\
\hline
\end{tabular}
\caption{Contributions to the total cross-section for two different LHC optics.}
\end{table}


\subsection{Diffraction}
During the early runs with low $\beta^*$ beams, diffractive protons with $\xi=\frac{\Delta p}{p}$ in the range 0.02-0.2 will be detectable by the Roman Pots at 220 m (Fig.~\ref{acc}). This will allow TOTEM to measure the differential cross-section for single diffractive events ($d\sigma^{SD}/dM$) for masses from 2 to 6 TeV/c$^2$ ($M=\sqrt{\xi s}$) with a mass resolution of 10\% or better. Also double Pomeron exchange events (DPE) can be detected with sufficient statistics and the differential cross section can be measured in the range $0.25 < M < 2.8$ TeV/c$^2$ with a mass resolution of 10\% or better.
\begin{figure}[!ht] 
\begin{center}
\includegraphics[width=0.45\textwidth]{images/acc.eps}
\hspace{2mm}
\includegraphics[width=0.45\textwidth]{images/acc2.eps}
\caption{Left: acceptance in $log_{10}t$ and $log_{10}\xi$ for diffractive protons at RP220 for different optics. Right: acceptance for DPE protons for different optics (both protons detected). }
\label{acc}
\end{center}
\end{figure}
Using a higher $\beta^*$ optics a much larger fraction of diffractive protons can be observed ($\sim65\%$ for $\beta^*=90$ m and $\sim95\%$ for $\beta^*=1540$ m). Since with these optics protons with $\xi$ values down to $10^{-8}$ can be detected, all the mass spectrum for SD and DPE events can be investigated.
\section{Conclusion}
The TOTEM detectors will be operational for the first physics runs of the LHC.
The accessible physics is strongly dependent on the running condition of the accelerator. At the beginning, with a low-$\beta^*$ optics, diffraction at large masses and elastic scattering at large $t$ can be studied. The use of an intermediate $\beta^*=90$ m optics will allow even at an early stage to measure, even if with a $\sim$5\% precision the total $p-p$ cross-section, which the main goal of the experiment. A better precision will be achieved only when the TOTEM nominal optics ($\beta^*=1540$ m) is available. Moreover, at a later stage, a common physics progamme about low-x and forward physics will be brought on with CMS \cite{totem-cms}.  


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