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+\documentclass[a4paper,11pt,oneside]{article}
+\usepackage[english]{babel}
+\usepackage[ansinew]{inputenc}
+\usepackage[dvips]{graphicx}
+\usepackage{amsmath}
+\usepackage{epic}
+\usepackage{wrapfig}
+\usepackage{eepic}
+\usepackage{color}
+\usepackage{latexsym}
+\usepackage{array}
+
+\usepackage{fancyhdr}
+\usepackage{verbatim}
+\addtolength{\textwidth}{4cm} \addtolength{\hoffset}{-2cm}
+\begin{document}
+
+\section*{Abstract}
+
+\section{Introduction}
+% Motiver l'utilisation d'un simulateur rapide
+% - 1) rapide VS lent
+% - 2) relativement bonne prÃ©diction en premiÃšre approximation
+% - 3) permet de comparer
+Full simulation of the response of large detectors components to high energy particles requires a lot of computing resources. Moreover, a good knowledge of the exact geometry of subdetectors and dead material content is mandatory. 
+
+Fast simulation can be a  powerful predictive tool for typical response of a large detector in high energy collider.
+
+The fast simulation of the detector response takes into account geometrical
+acceptance of sub-detectors and their finite energy resolution, no smearing is
+applied on particle direction. Charged particles, once are in the fiducial
+volume of the detector are assumed to be reconstructed with $100\%$ probability.
+The energy of each particle produced after hadronization, with a lifetime
+$c\tau$ bigger than $10~\textrm{mm}$ is then smeared according to detectors along
+particule's direction. For particles with a short lifetime such as the $K_s$,
+the fraction of electromagnetic or hadronic energy is determined according to
+its decay products. The calorimeter is assumed to cover the pseudorapidity range
+$|\eta|<3$ and consists in an electromagnetic and an hadronic part. The energy
+resolution is given by $\sigma_{E}/E=0.05/\sqrt{E} \oplus 0.25/E \oplus 0.0055$
+for the electromagnetic part and by $\sigma_{E}/E=0.91/\sqrt{E}\oplus 0.038$ for
+the hadronic part, where the energy is given in GeV. A very forward calorimeter
+is assumed to cover $3<|\eta|<5$ with an electromagnetic and hadronic energy
+resolution function given by $\sigma_{E}/E=1.5/\sqrt{E}\oplus 0.06$ and
+$\sigma_{E}/E=2.7/\sqrt{E}\oplus 0.13$ respectively.\\
+
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{detectorAng.eps}
+\caption{\small{detectorAng.eps}}
+\label{h_WW_ss_cut1}
+\end{center}
+\end{figure}
+
+
+The acceptance cuts applied on leptons and jets used in this section are the
+following :\\
+
+\begin{itemize}
+
+\item Electrons and muons are reconstructed if they fall into the acceptance of
+the tracker, assumed to be $|\eta|<2.5$, and have to have a transverse momentum
+above 10~GeV (the energy resolution of muons is taken to be the same as for
+electrons). Lepton isolation demands that there is no other charged particles
+with $p_T>2$~GeV within a cone of $\Delta R<0.5$ around the lepton.\\
+
+\item Jets are reconstructed using a cone algorithm with $R=0.7$ and make only
+use of the smeared particle momenta. The reconstructed jets are required to have
+a transverse momentum above 20~GeV and $|\eta|<3.0$. A jet is tagged as $b$-jets
+if its direction lies in the acceptance of the tracker, $|\eta|<0.5$, and if it
+is associated to a parent $b$-quark. A $b$-tagging efficiency of $40\%$ is
+assumed if the jet has a parent $b$ quark. For $c$-jets and light/gluon jets, a
+fake
+b-tagging efficiency of $10 \%$ and $1 \%$ respectively is assumed.\\
+
+\item A jet is tagged as a $\tau$-jet if more than $90\%$ of its energy is
+localized in a cone of $\Delta R=0.15$ around its axis. Moreover, this jet must
+have its direction in the acceptance of the tracker and have exactly one charged
+particle with $p_{T}>2$~GeV within a cone $\Delta R<0.4$ around the jet axis.
+This procedure selects taus decaying hadronically with a typical efficiency of
+$60\%$. Moreover, the minimal $p_T$ of the $\tau$-jet is required to be
+10~GeV.\\
+
+\end{itemize}
+
+\section{implementation}
+\subsection{Electron smearing}
+The smearing of the electron 4-momentum $p^\mu$ is
+ - if the electron is in the tracker ($\eta < MAX\_TRACKER$)
+	Gaussian smearing with $\sigma = ELG_Ccen*E \oplus ELG_Ncen \oplus
+ELG_Scen*\sqrt{E}$
+ - else Gaussian smearing with $\sigma = ELS_Cfwd*E \oplus ELG_Sfwd*\sqrt{E}$
+function \texttt{SmearElectron}
+Only the energy $E$ is smeared, but neither $\eta$ nor $\phi$.
+No negative values for the energy after smearing. If so, the $4$-momentum is set
+to $(0,0,0,0)$.
+\textbf{For the moment, electrons with $|\eta|> 5$ are also smeared !!!}
+
+\subsection{Muon smearing}
+The smearing ot the muon 4-momentum $p^\mu$ is given
+by a Gaussian smearing of the $p_T$
+function \texttt{SmearMuon}
+Only the $p_T$ is smeared, but neither $\eta$ nor $\phi$.
+No negative values for the energy after smearing. If so, the 4-momentum is set
+to $(0,0,0,0)$.
+
+\subsection{Hadron smearing}
+The energy of the hadron is smeared in the following ways:
+ - if the hadron is in the central calorimeter (eta < MAX\_CALO\_CEN)
+	Gaussian smearing with $\sigma = HAD_Chcal*E_{hcal} \oplus HAD_Nhcal
+\oplus HAD_Shcal*\sqrt{E_{hcal}} 
+			               + HAD_Cecal*E_{ecal} \oplus HAD_Necal
+\oplus HAD_Secal*\sqrt{E_{ecal}}$ 
+	where $E_{hcal} + E_{ecal} = E$. As some long-living particles decay in
+the calorimeters,
+	some of them decay mostly in the ECAL, some mostly in the HCAL.
+$E_{hcal}$ and $E_{ecal}$ are 
+	given by $E_{hcal} = E \times F$ and $E_{ecal} = E times (1-F)$, where
+$F$ is a fraction 
+	$0 \leq F \leq 1$ describing each particles. By default, $F=1.$ but is
+$F=0.7$ for $K^0_S$ and $\Lambda$.
+ - if the hadron is somewhere else (\textbf{even outside the forward
+calorimeters !!!})
+	Gaussian smearing with $\sigma = HAD_Chf*E \oplus HAD_Nhf \oplus
+HAD_Shf*\sqrt{E}$ 
+
+Ainsi, pour les particules considÃ©rÃ©es comme stables par PYTHIA
+mais non stables dans un dÃ©tecteur tel CMS ($c\tau < 4m$), les
+dÃ©pÃŽts laissÃ©s dans les diffÃ©rents dÃ©tecteurs sont directement
+liÃ©s aux modes de dÃ©sintÃ©grations de ces particules. Les
+hypothÃšses des dÃ©pÃŽts d'Ã©nergie sont donnÃ©es dans le tableau
+\ref{depot}.\newline
+
+\begin{table}[!h]
+\begin{center}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+\emph{Particules stables} & \emph{Stable} &\emph{Mode de}
+&$\Gamma_{i}/\Gamma$&\emph{DÃ©pot}&\emph{DÃ©pot}\\
+\emph{dans PYTHIA}&\emph{dans
+CMS}&\emph{desintÃ©gration}&&\emph{ECAL}&\emph{HCAL}\\\hline\hline
+$\pi^{\pm}$ & oui & & & 0 & 1 \\ \hline $K^{\pm}$ & oui & & & 0 &
+1 \\\hline $K^{0}_{S}$ & non & $\gamma\gamma\gamma\gamma$ & 0.31 &
+0.3 & 0.7\\
+& & $\pi^{+}\pi^{-}$& 0.69 &&\\\hline $K^{0}_{L}$ & oui & & & 0 &
+1\\\hline $\Lambda^{0}$ & non & $\pi^{-}p/\pi^{+}\overline{p}$ &
+0.64&
+0.3 & 0.7\\
+& & $n\pi^{0}$ & 0.36 & & \\\hline $\gamma$& oui & & & 1
+&0\\\hline
+\end{tabular}
+\caption{HypothÃšses des dÃ©pÃŽts d'Ã©nergie pour les particules les
+plus abondantes des jets.} \label{depot}
+\end{center}
+\end{table}
+
+
+function \texttt{SmearHadron}
+There is no ecal-hcal separation in the forward calorimeter.
+No negative values for the energy after smearing. If so, the 4-momentum is set
+to $(0,0,0,0)$.
+
+\subsection{Calorimetric towers}
+All final particles, which are neither muons nor neutrinos are produce a
+calorimetric tower.
+The same particles enter in the calculation of the missing transverse energy.
+\textit{what is used is the particle smeared momentum, not the calorimetric
+towers!}
+
+\subsection{Tracks}
+All final charged particles
+
+\subsection{Time of flight}
+Some subdetectors have the ability to measure the time of flight of the particle.
+This correspond to the delay after which the particle is observed in the detector, after the bunch crossing.
+The time of flight measurement of ZDC and FP420 detector is implemented here.
+For the ZDC, the formula is simply
+\begin{equation}
+ t_2 = t_1 + \frac{1}{v} \times \big( \frac{s-z}{\cos \theta}\big),
+\end{equation}
+where $t_2$ is the time of flight, $t_1$ is the true time coordinate of the vertex from which the particle originates, $v$ the particle velocity, $s$ is the ZDC distance to the interaction point, $z$ is the longitudinal coordinate of the vertex from which the particle comes from, $theta$ is the particle emission angle. This assumes that the neutral particle observed in the ZDC is highly relativistic, i.e. travelling at the speed of light $c$. We also assume that $\cos \theta = 1$, i.e. $\theta \approx 0$ or equivalently $\eta$ is large. As an example, $\eta = 5$ leads to $\theta = 0.013$ and $1 - \cos \theta < 10^{-4}$.
+The formula then reduces to
+\begin{equation}
+ t_2 = \frac{1}{c} \times (s-z)
+\end{equation}
+NB : for the moment, only neutrons and photons are assumed to be able to reach the ZDC. All other particles are neglected
+
+To fix the ideas, if the ZDC is located at $s=140~\textrm{m}$, neglecting $z$ and $\theta$, and assuming that $v=c$, one gets $t=0.47~\mu\textrm{s}$.
+
+\subsection{Tau identification}
+
+Two ways to identify a tau : using the energy inside a cone or the number of
+tracks in the cone.
+\begin{itemize}
+\item From the energy in the cone of radius TAU\_CONE\_ENERGY. To be taken into
+account, a calo tower should (1) have a transverse energy $E_T = \sqrt{E_X^2 +
+E_Y^2}$ above a given threshold M\_SEEDTHRESHOLD, (2) be inside a cone with a
+radius R and the axis defined by (eta,phi).
+\item From the number of tracks in the cone of radius TAU\_CONE\_TRACKS. To be
+taken into account, a track should (1) have a transverse momentum $ p_T =
+\sqrt{p_X^2 + p_Y^2} $ above a given threshold, (2) be inside a cone with a
+radius R and the axis defined by (eta,phi).
+\end{itemize}
+
+\begin{wrapfigure}{l}{0.3\textwidth}
+\includegraphics[width=0.3\textwidth]{Tau.eps}
+\caption{\small{detectorAng.eps}}
+\label{h_WW_ss_cut1}
+\end{wrapfigure}
+
+
+To identify a tau, one requires the \textit{electromagnetic collimation} and the
+\textit{tracking isolation}.
+The electromagnetic collimation is a kind of calorimetric isolation required
+around the jet axis.
+One requires that most of the energy of the cone is located in a small cone in
+the middle of the jet cone:
+ \begin{equation}
+   %C_{\tau}^{e.m.} = \frac{ \Sum E_T^{cell}(\Delta R= TAU\_CONE\_ENERGY)}{ 
+\sum E_T^{cell} (\Delta R= CONE\_RADIUS) > TAU\_EM\_COLLIMATION
+ \end{equation}
+ Typical values are TAU\_CONE\_ENERGY=0.15 ,  CONE\_RADIUS=0.7 and
+TAU\_EM\_COLLIMATION = 0.95.
+No further calorimetric isolation is required.
+
+The tracking isolation for the tau identification requires that the number of
+tracks associated to a particle with $p_T > PT\_TRACK\_TAU$ is one and only one
+in a cone with $\Delta R = TAU\_CONE\_TRACKS$. This cone should be entirely
+included in the tracker to be taken into account. Typical calues are
+$TAU\_CONE\_TRACKS = 0.4$ and $PT\_TRACK\_TAU = 2 GeV$.
+
+
+
+\subsection{B-tagging}
+The simulation of the b-tagging is based on the detector efficiencies assumed
+(1) for the tagging of a b-jet and (2) for the mis-identification of other jets
+as b-jets. This relies on the TAGGING\_B, MISTAGGING\_C and MISTAGGING\_L
+constants, for (respectively) the efficiency of tagging of a b-jet, the
+efficiency of mistagging a c-jet as a b-jet, and the efficiency of mistatting a
+light jet (u,d,s,g) as a b-jet. The (mis)tagging relies on the particle ID of
+the most energetic particle within a cone around the observed (eta,phi) region,
+with a radius CONERADIUS.
+
+\section{Validation}	
+\section{conclusion}
+
+\appendix
+Attention : in SmearUtil::NumTracks, the function arguments 'Eta' and 'Phi' have
+been switched. Previously, 'Phi' was before 'Eta', now 'Eta' comes in front.
+This is for consistency with the other functions in SmearUtil. Check your
+routines, when using NumTracks !
+
+In the list of input files, all files should have the same type 
+
+Attention : in SmearUtil::RESOLution::BJets, the maximal energy was looked in
+CONERADIUS/2 instead of CONERADIUS. This bug has been removed.
+
+Attention : for the tau-jet identification : CONERADIUS /2 was used instead of
+CONERADIUS !
+
+\end{document}
