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Changeset 121 in svn


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Timestamp:
Jan 3, 2009, 7:09:11 PM (16 years ago)
Author:
Xavier Rouby
Message:

two column; chap1,2 ok. chap3 ok sauf Etmis. validation presque ok

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  • trunk/paper/notes.tex

    r120 r121  
    1 \documentclass[a4paper,11pt,oneside,onecolumn]{article}
     1\documentclass[a4paper,11pt,oneside,twocolumn]{article}
    22%\usepackage[english]{babel}
    33\usepackage[ansinew]{inputenc}
    4 %\usepackage{abstract}
     4\usepackage{abstract}
    55
    66\usepackage{amsmath}
    … …  
    1515\usepackage{fancyhdr}
    1616\usepackage{verbatim}
    17 \addtolength{\textwidth}{2cm} \addtolength{\hoffset}{-1cm}
     17\addtolength{\textwidth}{1cm} \addtolength{\hoffset}{-0.5cm}
    1818\usepackage[colorlinks=true, pdfstartview=FitV, linkcolor=black, citecolor=black, urlcolor=black, unicode]{hyperref}
    1919\usepackage{ifpdf}
    … …  
    4646\begin{document}
    4747
    48 
     48\twocolumn[
    4949\maketitle
    50 
     50\begin{abstract}
    5151Knowing whether theoretical predictions are visible and measurable in a high energy experiment is always delicate, due to the
    5252complexity of the related detectors, data acquisition chain and software. We introduce here a new framework, \textsc{Delphes}, for fast simulation of
    … …  
    6161\textit{Keywords:} \textsc{Delphes}, fast simulation, LHC, smearing, trigger, \textsc{FastJet}, \textsc{Hector}, \textsc{Frog}
    6262\vspace{1cm}
    63 
    64 %\saythanks
     63\end{abstract}
     64]
     65\saythanks
    6566
    6667\section{Introduction}
    … …  
    7677A new framework, called \textsc{Delphes}~\cite{bib:Delphes}, is introduced here, for the fast simulation of a general purpose collider experiment.
    7778Using the framework, observables can be estimated for specific signal and background channels, as well as their production and measurement rates, under a set of assumptions.
    78 Starting from the output of event generators, the simulation of the detector response takes into account the subdetector resolutions, by smearing the kinematical properties of the visible final particles. Tracks of charged particles and calorimetric towers are then created.
     79Starting from the output of event generators, the simulation of the detector response takes into account the subdetector resolutions, by smearing the kinematical properties of the visible final particles. Tracks of charged particles and calorimetric towers (or \textit{calotowers} are then created.
    7980
    8081\textsc{Delphes} includes the most crucial experimental features, like (1) the geometry of both central or forward detectors; (2) lepton isolation; (3) reconstruction of photons, leptons, jets, $b$-jets, $\tau$-jets and missing transverse energy; (4) trigger emulation and (5) an event display (Fig.~\ref{fig:FlowChart}).
    8182
    82 \begin{figure}[!h]
    83 \begin{center}
    84 \includegraphics[width=0.9\columnwidth]{FlowDelphes}
     83\begin{figure*}[t]
     84\begin{center}
     85%\includegraphics[width=0.9\textwidth]{FlowDelphes}
     86\includegraphics[scale=0.78]{FlowDelphes}
    8587\caption{Flow chart describing the principles behind \textsc{Delphes}. Event files coming from external Monte Carlo generators are read by a convertor stage.
    8688The kinematical variables of the final state particles are then smeared according to the subdetector resolutions.
    … …  
    9193\label{fig:FlowChart}
    9294\end{center}
    93 \end{figure}
     95\end{figure*}
    9496
    9597Although this kind of approach yields much realistic results than a simple ``parton-level" analysis, a fast simulation comes with some limitations. Detector geometry is idealised, being uniform, symmetric around the beam axis, and having no cracks nor dead material. Secondary interactions, multiple scatterings, photon conversion and bremsstrahlung are also neglected.
    … …  
    105107\section{Detector simulation}
    106108
    107 \begin{figure}[!h]
    108 \begin{center}
    109 \includegraphics[width=\columnwidth]{Detector_Delphes_1}
    110 \caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. The innermost layer, close to the interaction point, is a central tracking system (pink).
    111 It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
    112 The outer layer of the central system (red) consist of a muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
    113 The actual detector granularity and extension is defined in the user-configuration card. The detector is assumed to be strictly symmetric around the beam axis (black line). Additional forward detectors are not depicted.}
    114 \label{fig:GenDet}
    115 \end{center}
    116 \end{figure}
    117 
    118 \begin{figure}[!h]
    119 \begin{center}
    120 \includegraphics[width=0.5\columnwidth]{Detector_Delphes_3}
    121 \caption{Profile of the layout assumed in \textsc{Delphes}. The extension of the various subdetectors, as defined in Tab.~\ref{tab:defEta}, are clearly visible.
    122 Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
    123 \label{fig:GenDet3}
    124 \end{center}
    125 \end{figure}
    126 
    127 \begin{figure}[!h]
    128 \begin{center}
    129 \includegraphics[width=0.6\columnwidth]{Detector_Delphes_2b}
    130 \caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. Open 3D-view of the detector with solid volumes. Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
    131 \label{fig:GenDet2}
    132 \end{center}
    133 \end{figure}
    134 
    135 
    136 The overall layout of the general purpose detector simulated by \textsc{Delphes} is shown in figure \ref{fig:GenDet}.
     109The overall layout of the general purpose detector simulated by \textsc{Delphes} is shown in Fig.~\ref{fig:GenDet3}.
    137110A central tracking system (\textsc{tracker}) is surrounded by an electromagnetic and a hadron calorimeters (\textsc{ecal} and \textsc{hcal}, resp.). Two forward calorimeters (\textsc{fcal}) ensure a larger geometric coverage for the measurement of the missing transverse energy. Finally, a muon system (\textsc{muon}) encloses the central detector volume
    138111The fast simulation of the detector response takes into account geometrical acceptance of sub-detectors and their finite resolution, as defined in the smearing data card\footnote{\texttt{[code] }See the \texttt{RESOLution} class.}.
    139112If no such file is provided, predifined values are used. The coverage of the various subsystems used in the default configuration are summarised in table \ref{tab:defEta}.
    140113
    141 
    142 \begin{table}[!h]
     114\begin{table*}[t]
    143115\begin{center}
    144116\caption{Default extension in pseudorapidity $\eta$ of the different subdetectors.
    145117The corresponding parameter name, in the smearing card, is given. \vspace{0.5cm}}
    146 \begin{tabular}[!h]{lll}
     118\begin{tabular}{lll}
    147119\hline
    148120\textsc{tracker} & {\verb CEN_max_tracker } & $0.0 \leq |\eta| \leq 2.5$\\
    … …  
    153125\label{tab:defEta}
    154126\end{center}
    155 \end{table}
     127\end{table*}
     128
     129\begin{figure}[!h]
     130\begin{center}
     131\includegraphics[width=\columnwidth]{Detector_Delphes_3}
     132\caption{
     133Profile of layout of the generic detector geometry assumed in \textsc{Delphes}. The innermost layer, close to the interaction point, is a central tracking system (pink).
     134It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
     135The outer layer of the central system (red) consist of a muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
     136The detector parameters are defined in the user-configuration card. The extension of the various subdetectors, as defined in Tab.~\ref{tab:defEta}, are clearly visible. The detector is assumed to be strictly symmetric around the beam axis (black line). Additional forward detectors are not depicted.
     137}
     138\label{fig:GenDet3}
     139\end{center}
     140\end{figure}
     141
     142
     143\subsubsection*{Magnetic field}
     144In addition to the subdetectors, the effects of a dipolar magnetic field is simulated for the charged particles\footnote{\texttt{[code] }See the \texttt{TrackPropagation} class.}. This simply modifies the corresponding particle direction before it enters the calorimeters.
     145
     146
    156147
    157148\subsection{Tracks reconstruction}
    … …  
    171162
    172163
    173 The particle 4-momentum $p^\mu$ are smeared with a parametrisation directly derived from the detector techinal designs\footnote{\texttt{[code] }The response of the detector is applied to the electromagnetic and the hadronic particles through the \texttt{SmearElectron} and \texttt{SmearHadron} functions.}.
     164The particle four-momentum $p^\mu$ are smeared with a parametrisation directly derived from the detector techinal designs\footnote{\texttt{[code] }The response of the detector is applied to the electromagnetic and the hadronic particles through the \texttt{SmearElectron} and \texttt{SmearHadron} functions.}.
    174165In the default parametrisation, the calorimeter is assumed to cover the pseudorapidity range $|\eta|<3$ and consists in an electromagnetic and an hadronic part. Coverage between pseudorapidities of $3.0$ and $5.0$ is provided by forward calorimeters, with different response to electromagnetic objects ($e^\pm, \gamma$) or hadrons.
    175166Muons and neutrinos are assumed no to interact with the calorimeters\footnote{In the current \textsc{Delphes} version, particles other than electrons ($e^\pm$), photons ($\gamma$), muons ($\mu^\pm$) and neutrinos ($\nu_e$, $\nu_\mu$ and $\nu_\tau$) are simulated as hadrons for their interactions with the calorimeters. The simulation of stable particles beyond the Standard Model should subsequently be handled with care.}.
    … …  
    221212The smallest unit for geometrical sampling of the calorimeters is a \textit{tower}; it segments the $(\eta,\phi)$ plane for the energy measurement.
    222213All undecayed particles, except muons and neutrinos produce a calorimetric tower, either in \textsc{ecal}, in \textsc{hcal} or \textsc{fcal}.
    223 As the detector is assumed to be symmetric in $\phi$ and with respect to the $\eta=0$ plane, the smearing card stores the number of calorimetric towers with $\phi=0$ and $\eta>0$ (default: $40$ towers). For a given $\eta$, the size of the $\phi$ segmentation is also specified.
    224 
    225 The calorimetric towers directly enter in the calculation of the missing transverse energy, and as input for the jet reconstruction algorithms.
    226 No longitudinal segmentation is available in the simulated calorimeters.
    227 No sharing between neighbouring towers is implemented when particles enter a tower very close to its geometrical edge.
    228 
    229 \textcolor{red}{Mettre une figure avec une grille en $(\eta,\phi)$ pour illustrer la segmentation (un peu comme une feuille quadrillée).}
    230 
    231 \begin{figure}[!h]
    232 \begin{center}
    233 \includegraphics[width=0.8\columnwidth]{calosegmentation}
     214As the detector is assumed to be symmetric in $\phi$ and with respect to the $\eta=0$ plane, the smearing card stores the number of calorimetric towers with $\phi=0$ and $\eta>0$ (default: $40$ towers). For a given $\eta$, the size of the $\phi$ segmentation is also specified. Fig.~\ref{fig:calosegmentation} illustrates the default segmentation of the $(\eta,\phi)$ plane.
     215
     216
     217
     218\begin{figure}[!h]
     219\begin{center}
     220\includegraphics[width=\columnwidth]{calosegmentation}
    234221\caption{Default segmentation of the calorimeters in the $(\eta,\phi)$ plane. Only the central detectors (\textsc{ecal}, \textsc{hcal} and \textsc{fcal}) are considered.}
    235222\label{fig:calosegmentation}
    … …  
    237224\end{figure}
    238225
     226The calorimetric towers directly enter in the calculation of the missing transverse energy, and as input for the jet reconstruction algorithms. No longitudinal segmentation is available in the simulated calorimeters. No sharing between neighbouring towers is implemented when particles enter a tower very close to its geometrical edge.
    239227
    240228\subsection{Very forward detectors simulation}
    … …  
    246234\begin{figure}[!h]
    247235\begin{center}
    248 \includegraphics[width=0.8\columnwidth]{fdets}
     236\includegraphics[width=\columnwidth]{fdets}
    249237\caption{Default location of the very forward detectors, including \textsc{zdc}, \textsc{rp220} and \textsc{fp420} in the \textsc{lhc} beamline.
    250238Incoming (red) and outgoing (black) beams on one side of the interaction point ($s=0~\textrm{m}$).
    … …  
    254242\end{figure}
    255243
    256 \begin{table}[!h]
     244\begin{table*}[t]
    257245\begin{center}
    258246\caption{Default parameters for the forward detectors: distance from the interaction point and detector acceptance. The \textsc{lhc} beamline is assumed around the fifth interaction point. For the \textsc{zdc}, the acceptance depends only on the pseudorapidity $\eta$ of the particle, which should be neutral and stable.
    259247The tagger acceptance is fully determined by the distance in the transverse plane of the detector to the real beam position~\cite{bib:Hector}. It is expressed in terms of the particle energy.
    260248\vspace{0.5cm}}
    261 \begin{tabular}[!h]{llcl}
     249\begin{tabular}{llcl}
    262250\hline
    263251Detector & Distance & Acceptance & \\ \hline
    … …  
    269257\label{tab:fdetacceptance}
    270258\end{center}
    271 \end{table}
     259\end{table*}
    272260
    273261
    … …  
    292280In addition, some detector data are added: tracks, calorometric towers and hits in \textsc{zdc}, \textsc{rp220} and \textsc{fp420}.
    293281While electrons, muons and photons are easily identified, some other objects are more difficult to measure, like jets or missing energy due to invisible particles.
     282
     283For most of these objects, their four-momentum $p^\mu$ and related quantities are directly accessible in \textsc{Delphes} output ($E$, $\vec{p}$, $p_T$, $\eta$ and $\phi$). Additional properties are available for specific objects (like the charge and the isolation status for $e^\pm$ and $\mu^\pm$, the result of application of $b$-tag for jets and time-of-flight for some detector hits).
    294284 
    295285
    … …  
    303293
    304294Generator level muons entering the detector acceptance are considered as candidates for the analysis level.
    305 The acceptance is defined in terms of a transverse momentum threshold to overpass (default : $p_T > 0~\textrm{GeV}$) and of the pseudorapidity coverage of the muon system of the detector (default: $-2.4 \leq \eta \leq 2.4$).
    306 The application of the detector resolution on the muon momentum depends on a Gaussian smearing of the $p_T$ variable\footnote{\texttt{[code]} See the \texttt{SmearMuon} method.}. Neither $\eta$ nor $\phi$ variables are modified. Multiple scattering is thus neglected, while low energy muons have a worst resolution in a real detector.
     295The acceptance is defined in terms of a transverse momentum threshold to overpass (default : $p_T > 10~\textrm{GeV}$) and of the pseudorapidity coverage of the muon system of the detector (default: $-2.4 \leq \eta \leq 2.4$).
     296The application of the detector resolution on the muon momentum depends on a Gaussian smearing of the $p_T$ variable\footnote{\texttt{[code]} See the \texttt{SmearMuon} method.}. Neither $\eta$ nor $\phi$ variables are modified beyond the calorimeters: no additional magnetic field is applied. In addition, multiple scattering is also neglected. This implies that low energy muons have in \textsc{Delphes} a better resolution than in a real detector.
    307297
    308298\subsubsection*{Charged lepton isolation}
    309299
    310 To improve the quality of the contents of the charged lepton collections, additional criteria are applied to impose some isolation. This requires that the electron or muon candidate is isolated in the detector from any other particle, within a small cone. In \textsc{Delphes}, charged lepton isolation demands that there is no other charged particle with $p_T>2~\textrm{GeV}$ within a cone of $\Delta R<0.5$ around the lepton.\\
     300To improve the quality of the contents of the charged lepton collections, additional criteria can be applied to impose some isolation. This requires that electron or muon candidates are isolated in the detector from any other particle, within a small cone. In \textsc{Delphes}, charged lepton isolation demands that there is no other charged particle with $p_T>2~\textrm{GeV}$ within a cone of $\Delta R = \sqrt{\Delta \eta^2 + \Delta \phi^2} <0.5$ around the lepton. The result (i.e. \textit{isolated} or \textit{not}) is added to the charged lepton measured properties\footnote{\texttt{[code] }See the \texttt{IsolFlag} output of the \texttt{Electron} or \texttt{Muon} collections in the \texttt{Analysis} tree.}.\\
    311301
    312302
    … …  
    321311Six different jet reconstruction schemes are available\footnote{\texttt{[code] }The choice is done by allocating the \texttt{JET\_jetalgo } input parameter in the smearing card.}. The first three belong to the cone algorithm class while the last three are using a sequential recombinaison scheme. For all of them, the towers are used as input of the jet clustering. Jet algorithms also differ with their sensitivity to soft particles or collinear splittings, and with their computing speed performance.
    322312 
    323 \begin{itemize}
    324  
    325 \item \textbf{Cone algorithms:}
     313\subsubsection*{Cone algorithms}
    326314 
    327315\begin{enumerate}
    328316 
    329 \item {\it CDF JetClu}: Algorithm forming jets by associating together towers lying within a circle (default radius $R=0.7$) in the $(\eta$, $\phi)$ space.
     317\item {\it CDF Jet Clusters}: Algorithm forming jets by associating together towers lying within a circle (default radius $\Delta R=0.7$) in the $(\eta$, $\phi)$ space.
    330318The so-called \textsc{jetclu} cone jet algorithm that was used by \textsc{cdf} in Run II is used.
    331319All towers with a transverse energy $E_T$ higher than a given threshold (default: $E_T > 1~\textrm{GeV}$) are used to seed the jet candidates.
    332320The existing \textsc{FastJet} code as been modified to allow easy modification or the tower pattern in $\eta$, $\phi$ space.
    333 In the following versions of \textsc{Delphes}, a new dedicated plugin will be created on this purpose\footnote{\texttt{[code] }\texttt{JET\_coneradius} and \texttt{JET\_seed} variables in the smearing card.}.
     321In the following versions of \textsc{Delphes}, a new dedicated plug-in will be created on this purpose\footnote{\texttt{[code] }\texttt{JET\_coneradius} and \texttt{JET\_seed} variables in the smearing card.}.
    334322 
    335323\item {\it CDF MidPoint}: Algorithm developped for the \textsc{cdf} Run II to reduce infrared and collinear sensitivity compared to purely seed-based cone by adding `midpoints' (energy barycenters) in the list of cone seeds.
    … …  
    339327\end{enumerate}
    340328 
    341 \item {\bf Recombination algorithms:}
    342  
    343 The three following infrared and collinear safe algorithms rely on recombination schemes where neighbouring calotower pairs are successively merged. The definitions of the jet algorithms are identical except for the distance used during the merging procedure. The jet reconstruction stars by finding the minimum value $d_{min}$ of all the distances $d_{ij}$ between each pair of towers and all `beam distance' $d_{iB}$. If the minimum distance is a $d_{ij}$ the towers are merged into a single tower, summing their four-momenta using the E-scheme recombination. If the minimum value is a $d_{iB}$, the object is declared as a final jet and is removed from the input list. This procedure is repeated until no input towers are left. More information on these jet can be found here.
     329\subsubsection*{Recombination algorithms}
     330 
     331The three following jet algorithms are safe for soft radiations (\textit{infrared}) and collinear splittings. They rely on recombination schemes where neighbouring calotower pairs are successively merged. The definitions of the jet algorithms are similar except for the definition of the \textit{distances} $d$ used during the merging procedure. Two such variables are defined: the distance $d_{ij}$ between each pair of towers $(i,j)$, and a variable $d_{iB}$ (\textit{beam distance}) depending on the transverse momentum of the tower $i$.
     332
     333The jet reconstruction algorithm browses the calotower list. It starts by finding the minimum value $d_\textrm{min}$ of all the distances $d_{ij}$ and $d_{iB}$. If $d_\textrm{min}$ is a $d_{ij}$, the towers $i$ and $j$ are merged into a single tower with a four-momentum $p^\mu = p^\mu (i) + p^\mu (j)$ (\textit{E-scheme recombination}). If $d_\textrm{min}$ is a $d_{iB}$, the tower is declared as a final jet and is removed from the input list. This procedure is repeated until no input towers are left. Further information on these jet algorithms is given here below, using $k_{ti}$, $y_{i}$ and $\phi_i$ as the transverse momentum, rapidity and azimuth of calotower $i$ and $\Delta R_{ij}= \sqrt{(y_i-y_j)^2+(\phi_i-\phi_j)^2}$ as the jet-radius parameter:
    344334 
    345335\begin{enumerate}[start=4]
    … …  
    347337\item {\it Longitudinally invariant $k_t$ jet}:
    348338\begin{equation}
    349 d_{ij} = min(k_{ti}^2,k_{tj}^2)\Delta R_{ij}^2/R^2,
    350 \end{equation}
    351 with $\Delta R_{ij}^2= (y_i-y_j)^2+(\phi_i)-\phi_j)^2$, $k_{ti}$, $y_{i}$ and $\phi_i$ are the transverse momentum, rapidity and azimuth of calotower i and $R$ is the jet-radius parameter defined in the datacard. The beam distance is defined as $d_{iB}=k_{ti}^2$.
     339\begin{array}{l}
     340  d_{ij} = \min(k_{ti}^2,k_{tj}^2)\Delta R_{ij}^2/R^2 \\
     341  d_{iB}=k_{ti}^2 \\
     342\end{array}
     343\end{equation}
    352344 
    353345\item {\it Cambridge/Aachen jet}:
    354346 
    355347\begin{equation}
    356 d_{ij} = \Delta R_{ij}^2/R^2,~d_{iB}=1.
    357 \end{equation}
    358  
    359 \item {\it Anti $k_t$ jet}: hard jets are exactly circular on Behaves like
    360  
    361 \begin{equation}
    362 d_{ij} =  min(1/k_{ti}^2,1/k_{tj}^2)\Delta R_{ij}^2/R^2,~d_{iB}=1/k_{ti}^2
    363 \end{equation}
    364  \end{enumerate}
    365 \end{itemize}
    366  
    367 The reconstructed jets are conserved in the jet list if their transverse energy is bigger than {\verb PTCUT_jet }.
    368 By default, jets are reconstructed using a cone algorithm with $R=0.7$ and use the calorimetric towers. The reconstructed jets are required to have a transverse momentum above $20~\textrm{GeV}$ and $|\eta|<3.0$.
     348\begin{array}{l}
     349d_{ij} = \Delta R_{ij}^2/R^2\\
     350d_{iB}=1 \\
     351\end{array}
     352\end{equation}
     353 
     354\item {\it Anti $k_t$ jet}: where hard jets are exactly circular
     355 
     356\begin{equation}
     357\begin{array}{l}
     358d_{ij} =  \min(1/k_{ti}^2,1/k_{tj}^2)\Delta R_{ij}^2/R^2 \\
     359d_{iB}=1/k_{ti}^2 \\
     360\end{array}
     361\end{equation}
     362\end{enumerate}
     363 
     364By default, reconstruction uses a cone algorithm with $\Delta R=0.7$. Jets are stored if their transverse energy is higher\footnote{\texttt{[code] PTCUT\_jet }variable in the smearing card.} than $20~\textrm{GeV}$.
    369365
    370366 
    371367\subsection{$b$-tagging}
    372368
    373 A jet is tagged as $b$-jets if its direction lies in the acceptance of the tracker 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\footnote{\texttt{[code] }Corresponding to the \texttt{TAGGING\_B}, \texttt{MISTAGGING\_C} and \texttt{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.}
     369A jet is tagged as $b$-jets if its direction lies in the acceptance of the tracker 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 jets (i.e. originating in $u$,$d$,$s$ quarks or in gluons), a fake $b$-tagging efficiency of $10 \%$ and $1 \%$ respectively is assumed\footnote{\texttt{[code] }Corresponding to the \texttt{TAGGING\_B}, \texttt{MISTAGGING\_C} and \texttt{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 mistagging a light jet ($u$,$d$,$s$,$g$) as a $b$-jet.}
    374370%(Fig.~\ref{fig:btag})
    375371.
    376 The (mis)tagging relies on the true particle \textsc{id} of the most energetic particle within a cone around the observed $(\eta,\phi)$ region, with a radius $R = \sqrt{\Delta \eta^2 + \Delta \phi^2}$ of $0.7$.
     372The (mis)tagging relies on the true particle identity (\textsc{pid}) of the most energetic particle within a cone around the observed $(\eta,\phi)$ region, with a radius $\Delta R$ of $0.7$.
    377373
    378374%\begin{figure}[!h]
    … …  
    388384
    389385Jets originating from $\tau$-decays are identified using an identification procedure consistent with the one applied in a full detector simulation~\cite{bib:cmstaus}.
    390 
    391 
    392 \begin{wrapfigure}{l}{0.3\columnwidth}
    393 \includegraphics[width=0.3\columnwidth]{Tau}
    394 \caption{Illustration of the identification of $\tau$ jets.}
     386The tagging rely on two properties of the $\tau$ lepton. First, $77\%$ of the $\tau$ hadronic decays contain only one charged hadron associated to a few neutrals (table~\ref{tab:taudecay}). Tracks are useful for this criterium. Secondly, the particles arisen from the $\tau$ lepton produce narrow jets in the calorimeter (\textit{collimation}).
     387
     388\begin{table}[!h]
     389\begin{center}
     390\caption{ Branching rations for $\tau^-$ lepton~\cite{bib:pdg}. $h^\pm$ and $h^0$ refer to charged and neutral hadrons, respectively. $n \geq 0$ and $m \geq 0$ are integers.
     391\vspace{0.5cm}  }
     392\begin{tabular}[!h]{ll}
     393\hline
     394 \multicolumn{2}{l}{\textbf{Leptonic decays}}\\
     395 $ \tau^- \rightarrow e^- \ \bar \nu_e \ \nu_\tau$ & $17.85\% $ \\
     396 $ \tau^- \rightarrow \mu^- \ \bar \nu_\mu  \ \nu_\tau$ & $17.36\%$ \\
     397 \multicolumn{2}{l}{\textbf{Hadronic decays}}\\
     398 $ \tau^- \rightarrow h^-\ n\times h^\pm \ m\times h^0\  \nu_\tau$  & $64.79\%$ \\
     399 $ \tau^- \rightarrow h^-\ m\times h^0 \ \nu_\tau$  & $50.15\%$ \\
     400 $ \tau^- \rightarrow h^-\ h^+ h^-  m\times h^0 \ \nu_\tau$  & $15.18\%$ \\
     401\hline
     402\end{tabular}
     403\label{tab:taudecay}
     404\end{center}
     405\end{table}
     406
     407
     408%\begin{wrapfigure}{l}{0.3\columnwidth}
     409\begin{figure}[!h]
     410\begin{center}
     411\includegraphics[width=0.6\columnwidth]{Tau}
     412\caption{Illustration of the identification of $\tau$-jets. The jet cone is narrow and contains only one track.}
    395413\label{h_WW_ss_cut1}
    396 \end{wrapfigure}
    397 
    398 The tagging rely on two properties of the $\tau$ lepton. First, in roughly $75 \%$ of the time, the hadronic $\tau$-decay products contain only one charged hadron and a number of $\pi^0$. Secondly, the particles arisen from the $\tau$ lepton produce narrow jets in the calorimeter.
     414\end{center}
     415\end{figure}
     416%\end{wrapfigure}
     417
    399418
    400419\subsubsection*{Electromagnetic collimation}
    401420
    402 To use the narrowness of the $\tau$-jet, the \textit{electromagnetic collimation} ($C_{\tau}^{em}$) is defined as the sum of the energy in a cone with $\Delta R = ${\verb TAU_energy_scone } around the jet axis divided by the energy of the reconstructed jet. The energy in the small cone is calculated using the towers objects. To be taken into account a calorimeter tower should have a transverse energy above a given threshold {\verb JET_M_seed }. A large fraction of the jet energy, denominated here with {\verb TAU_energy_frac } is expected in this small cone. The quantity is represented in figure \ref{fig:tau1} for the default values (see table \ref{tab:tauRef}).
    403 
    404 \begin{figure}[!h]
    405 \begin{center}
    406 \includegraphics[width=0.8\columnwidth]{figures/Tau2}
    407 \caption{\textcolor{red}{Distribution of the $\tau \bar \tau$ events} with respect to the electromagnetic collimation factor $C_\tau$. }
     421To use the narrowness of the $\tau$-jet, the \textit{electromagnetic collimation} $C_{\tau}^{em}$ is defined as the sum of the energy of towers in a small cone of radius $R^\textrm{em}$ around the jet axis, divided by the energy of the reconstructed jet.
     422To be taken into account, a calorimeter tower should have a transverse energy $E_T^\textrm{tower}$ above a given threshold.
     423A large fraction of the jet energy is expected in this small cone. This fraction, or collimation factor, is represented in Fig.~\ref{fig:tau2} for the default values (see table \ref{tab:tauRef}).
     424
     425\begin{figure}[!h]
     426\begin{center}
     427\includegraphics[width=\columnwidth]{Tau2}
     428\caption{Distribution of the electromagnetic collimation $C_\tau$ variable for true $\tau$-jets, normalised to unity. This distribution is shown for associated $WH$ photoproduction~\cite{bib:whphotoproduction}, where the Higgs boson decays into a $W^+ W^-$ pair. Each $W$ boson decays into a $\ell \nu_\ell$ pair, where $\ell = e, \mu, \tau$.
     429Events generated with MadGraph/MadEvent~\cite{bib:mgme}.
     430Histogram entries correspond to true $\tau$-jets, matched with generator level data. }
     431\label{fig:tau2}
     432\end{center}
     433\end{figure}
     434
     435\subsubsection*{Tracking isolation}
     436
     437The tracking isolation for the $\tau$ identification requires that the number of tracks associated to a particle with a significant transverse momentum is one and only one in a cone of radius $R^\textrm{tracks}$.
     438This cone should be entirely pointing to the tracker to be taken into account. Default values of these parameters are given in table~\ref{tab:tauRef}.
     439
     440
     441
     442\begin{figure}[!h]
     443\begin{center}
     444\includegraphics[width=\columnwidth]{Tau1}
     445\caption{Distribution of the number of tracks $N^\textrm{tracks}$ within a small jet cone for true $\tau$-jets, normalised to unity. Photoproduced $WH$ events, where $W$ bosons decay leptonically ($e,\mu,\tau$), as in Fig.~\ref{fig:tau2}.
     446Histogram entries correspond to true $\tau$-jets, matched with generator level data.}
    408447\label{fig:tau1}
    409448\end{center}
    410449\end{figure}
    411450
    412 \subsubsection*{$\tau$ selection using tracks}
    413 
    414 \begin{figure}[!h]
    415 \begin{center}
    416 \includegraphics[width=0.8\columnwidth]{figures/Tau1}
    417 \caption{\textcolor{red}{Distribution of the...}}
    418 \label{h_WW_ss_cut1}
    419 \end{center}
    420 \end{figure}
    421 
    422 The tracking isolation for the $\tau$ identification requires that the number of tracks associated to a particle with $p_T >$ {\verb TAU_track_pt } is one and only one in a cone with $\Delta R =$ {\verb TAU_track_scone }. This cone should be entirely included in the tracker to be taken into account. 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 {\verb TAUJET_pt } (default value: $10~\textrm{GeV}$).\\
    423451
    424452\begin{table}[!h]
    425453\begin{center}
    426 \begin{tabular}[!h]{llc}
    427 \hline
    428 Tau definition  & Card flag & Value\\\hline
    429 $\Delta R^{for~em}$     & {\verb TAU_energy_scone } & 0.15\\
    430 min $E_{T}^{tower}$     & {\verb JET_M_seed }  & 1.0~GeV\\
    431 $C_{\tau}^{em}$         & {\verb TAU_energy_frac } & 0.95.\\
    432 $\Delta R^{for~tracks}$ & {\verb TAU_track_scone } & 0.4\\
    433 min $p_T^{tracks}$      & {\verb PTAU_track_pt } & 2 GeV\\\hline
     454\caption{Default values for parameters used in $\tau$-jet reconstruction algorithm. Electromagnetic collimation requirements involve the inner \textit{small} cone radius $R^\textrm{em}$, the minimum transverse energy for calotowers $E_T^\textrm{tower}$ and the collimation factor $C_\tau$. Tracking isolation constrains the number of tracks with a significant transverse momentum $p_T^\textrm{tracks}$ in a cone of radius $R^\textrm{tracks}$.  Finally, the $\tau$-jet collection is purified by the application of a cut on the $p_T$ of $\tau$-jet candidates.
     455\vspace{0.5cm}  }
     456\begin{tabular}[!h]{lll}
     457\hline
     458Parameter  & Card flag & Value\\\hline
     459\multicolumn{3}{l}{\textbf{Electromagnetic collimation}} \\
     460$R^\textrm{em}$     & \texttt{TAU\_energy\_scone } & $0.15$\\
     461min $E_{T}^\textrm{tower}$     & {\verb JET_M_seed }  & $1.0$~GeV\\
     462$C_{\tau}$         & \texttt{TAU\_energy\_frac} & $0.95$\\
     463\multicolumn{3}{l}{\textbf{Tracking isolation}} \\
     464$R^\textrm{tracks}$ & \texttt{TAU\_track\_scone} & $0.4$\\
     465min $p_T^{tracks}$      & \texttt{PTAU\_track\_pt } & $2$ GeV\\
     466\multicolumn{3}{l}{\textbf{$\tau$-jet candidate}} \\
     467$\min p_T$ & \texttt{TAUJET\_pt} & $10$ GeV\\
     468\hline
    434469\end{tabular}
    435470\label{tab:tauRef}
    … …  
    437472\end{table}
    438473
     474\subsubsection*{Purity}
     475Once both electromagnetic collimation and tracking isolation are applied, a threshold on the $p_T$ of the $\tau$-jet candidate is requested to purify the collection. This procedure selects $\tau$ leptons decaying hadronically with a typical efficiency of $60\%$.
     476
    439477\subsection{Transverse missing energy}
    440 In an ideal detector, the transverse missing energy is simply computed as the missing term which would balance the transverse momentum in the observed event. Its value is then computed as the opposite of the sum of the momentum of all observed particles. In a real experiment, any problem affecting the detector (dead channels, misalignment, noisy towers, cracks) is directly worsening the measured missing transverse energy. In this document, the missing transverse energy (\textcolor{red}{symbol???}) is based on the calorimetric towers and only muons and neutrinos are not taken into account for its evaluation.
     478In an ideal detector, the transverse momentum of the observed final state $p_T^\textrm{obs}$ should be equal to the $p_T$ sum of the invisible particles, written $p_T^\textrm{miss}$.
     479\begin{equation}
     480 p_T^\textrm{miss} = - p_T^\textrm{obs}
     481\end{equation}
     482
     483the transverse missing energy would simply be computed as the term which balances the transverse momentum sum in the observed event. Its value is then computed as the opposite of the sum of the momentum of all observed particles. In a real experiment, any problem affecting the detector (dead channels, misalignment, noisy towers, cracks) is directly worsening the measured missing transverse energy. In this document, the missing transverse energy (\textcolor{red}{symbol???}) is based on the calorimetric towers and only muons and neutrinos are not taken into account for its evaluation.
    441484
    442485\section{Trigger emulation}
    … …  
    448491\section{Validation}   
    449492
     493\subsection{Jet resolution}
     494 
     495The majority of interesting processes at the \textsc{lhc} contain jets in the final state. The jet resolution obtained using \textsc{Delphes} is therefore a crucial point of the validation. While \textsc{Delphes} contains six jet reconstruction algorithms, only the jet clustering algorithm with $R=0.7$ is used to validate the jet collection. Cross-check has been made with the results obtained using the \textsc{cms} detector. This validation employs $pp \rightarrow gg$ events produced using \textsc{mg/me} and hadronized using \textsc{pythia}. The events were divided into 14 bins of $\hat{p_T}$ of the gluons. Each \textsc{Delphes} jet is matched to the closest {\it particle-level} jet using the spatial separation in $\eta - \phi$ between the two jet axis $\Delta R<0.25$, otherwise they are discarded. The particle-level jets are obtained by applying the same clustering algorithm to all particles considered as stable by \textsc{pythia}.
     496 
     497For each $\hat{p}_T$ bin, the  \textsc{Delphes} jet transverse energy ($E_T^{rec}$) of all jets satisfying the matching criteria is compaired to the {\it particle level} transverse energy ($E_T^{MC}$). The obtained histograms of the $E_T^{rec}/E_T^{MC}$ response have been fitted with a Gaussian function in the interval $\pm 2.RMS$ centered around the mean value. The final jet resolution is obtained using the following formula:
     498 
     499\begin{equation}
     500\frac{\sigma(R_{jet})}{<R_{jet}>}=\frac{\sigma(\frac{E_T^{rec}}{E_T^{MC}})_{fit}}{<\frac{E_T^{rec}}{E_T^{MC}}>_{fit}}.
     501\end{equation}
     502 
     503\begin{figure}[!h]
     504\begin{center}
     505\includegraphics[width=\columnwidth]{resolutionJet}
     506\caption{Distribution of the jet transverse energy resolution as a function of the {\it particle-level}  jet transverse energy. The maximum allowed separation between the \textsc{Delphes} and the {\it partile-level} jets is $\Delta R<0.25$.}
     507\label{fig:jetresol}
     508\end{center}
     509\end{figure}
     510 
     511The resulting jet resolution, plotted as a function of $E_T^{GEN}$ is shown in figure \ref{fig:jetresol}. The plots were then fitted with a function of the following form:
     512 
     513\begin{equation}
     514\frac{a}{E_T^{GEN}}\oplus \frac{b}{\sqrt{E_T^{GEN}}}\oplus c,
     515\end{equation}
     516 
     517where a, b, and c are the fit parameters. The obtained resolution is compared to the one obtained with a recent version of the simulation package of the CMS detector. Overall, the resolution curve of \textsc{Delphes} matches relatively well to those of \textsc{cms}.
     518 
     519\subsection{$E_T^{mis}$ resolution}
     520 
     521Because all major detectors at hadron colliders have been designed to be as mutch hermetic as possible in order to detect the presence of one or more neutrinos through apparent missing transverse energy, the resolution of the $E_T^{miss}$ obtained with \textsc{Delphes} is a crucial point. The samples used to study the transverse missing energy performance are identical to those used for the jet validation. The {\it particle-level} true transverse missing energy is calculated as the vector sum of the transverse momenta of all visible particles (or equivalently, to the vector sum of invisible particles). It should be noticed that the contribution to the transverse missing energy from muons is negligeable in the sample we are interested in.
     522 
     523In order to obtain the x-component missing energy resolution ($E_x^{miss}$), the distribution of the difference between the \textsc{Delphes} and the {\it particle-level} $E_x^{miss}$ has been fitted with a Gaussian function. The resulting $E_x^{mis}$ is plotted in figure \ref{fig:resolETmis} as a function of the total visible transverse energy, defined as the scalar sum of transverse energy in all towers ($\Sigma E_T$).
     524 
     525\begin{figure}[!h]
     526\begin{center}
     527\includegraphics[width=\columnwidth]{figures/resolutionETmis}
     528\caption{$\sigma(E^{miss}_{x})$ as a function on the scalar sum of all towers ($\Sigma E_T$) for $pp \rightarrow gg$ events.}
     529\label{fig:resolETmis}
     530\end{center}
     531\end{figure}
     532 
     533The resolution is observed to follow the form
     534\begin{equation}
     535\sigma_X = \alpha ~\Sigma E_T ~\mathrm{GeV}^{1/2},
     536\end{equation}
     537whith $\alpha$ is depending on the resolution of the calorimeters. Knowing that the expected transverse missing energy resolution expected using the \textsc{cms} detector for similar events is $\sigma_X = (0.6-0.7) ~ \Sigma E_T ~ \mathrm{GeV}^{1/2}$ with no pile-up (no extra simultaneous $pp$ collision occuring at the same bunch crossing), we can conclude that the resolution obtained by \textsc{Delphes} ( $\sigma_X = 0.68~ \Sigma E_T ~\mathrm{GeV}^{1/2}$) is in excellent agreement with the expectations of a general purpose detector.
     538
     539\subsection{$tau$-jet efficiency}
     540with an efficiciency of about $50\%$ for the $\tau$-jets in CMS~\cite{bib:cmstauresolution}.
     541
    450542\section{Visualisation}
     543
     544\begin{figure}[!h]
     545\begin{center}
     546\includegraphics[width=\columnwidth]{Detector_Delphes_1}
     547\caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. The innermost layer, close to the interaction point, is a central tracking system (pink).
     548It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
     549The outer layer of the central system (red) consist of a muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
     550The actual detector granularity and extension is defined in the user-configuration card. The detector is assumed to be strictly symmetric around the beam axis (black line). Additional forward detectors are not depicted.}
     551\label{fig:GenDet}
     552\end{center}
     553\end{figure}
     554
     555
     556\begin{figure}[!h]
     557\begin{center}
     558\includegraphics[width=0.6\columnwidth]{Detector_Delphes_2b}
     559\caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. Open 3D-view of the detector with solid volumes. Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
     560\label{fig:GenDet2}
     561\end{center}
     562\end{figure}
    451563
    452564
    … …  
    462574
    463575
     576
     577
    464578\section{Conclusion and perspectives}
    465579
    466 
    467 \newpage
    468 
     580\begin{thebibliography}{99}
     581 
     582\bibitem{bib:Delphes} \textsc{Delphes}, hepforge:
     583\bibitem{bib:FastJet} \textsc{Fast-Jet},
     584\bibitem{bib:SIScone} A practical Seedless Infrared-Safe Cone jet algorithm, G.P. Salam, G. Soyez, JHEP0705:086,2007.
     585\bibitem{bib:Hector} \textsc{Hector},
     586\bibitem{bib:Frog} \textsc{Frog},
     587\bibitem{bib:CMSresolution} CMS IN 2007/053
     588\bibitem{bib:Root} \textsc{Root} - An Object Oriented Data Analysis Framework, R. Brun and F. Rademakers, Nucl. Inst. \& Meth. in Phys. Res. A 389 (1997) 81-86, \url{http://root.cern.ch}
     589\bibitem{bib:cmstaus} Tau reconstruction in CMS
     590\bibitem{bib:whphotoproduction} WH photoproduction, S. Ovyn
     591\bibitem{bib:mgme} Madgraph/Madevent
     592\bibitem{bib:pdg} C. Amsler et al. (Particle Data Group), PL B667, 1 (2008) (URL: http://pdg.lbl.gov)
     593\bibitem{bib:cmstauresolution} R. Kinnunen, \textit{Study of $\tau$-jet identification in CMS}, CMS NOTE 1997/002.
     594\end{thebibliography}
     595
     596\onecolumn
    469597\appendix
    470598
    … …  
    557685\subsection{Running the \textsc{Frog} event display}
    558686
     687
     688
     689
    559690\begin{itemize}
    560691\item If the { \verb FLAG_frog } was switched on, two files were created during the run of \textsc{Delphes}: {\verb DelphesToFrog.vis } and {\verb DelphesToFrog.geom }. They contain all the needed information to run frog.
    … …  
    563694\end{itemize}
    564695
    565 \begin{thebibliography}{99}
    566  
    567 \bibitem{bib:Delphes} \textsc{Delphes}, hepforge:
    568 \bibitem{bib:FastJet} \textsc{Fast-Jet},
    569 \bibitem{bib:SIScone} A practical Seedless Infrared-Safe Cone jet algorithm, G.P. Salam, G. Soyez, JHEP0705:086,2007.
    570 \bibitem{bib:Hector} \textsc{Hector},
    571 \bibitem{bib:Frog} \textsc{Frog},
    572 \bibitem{bib:CMSresolution} CMS IN 2007/053
    573 \bibitem{bib:Root} \textsc{Root} - An Object Oriented Data Analysis Framework, R. Brun and F. Rademakers, Nucl. Inst. \& Meth. in Phys. Res. A 389 (1997) 81-86, \url{http://root.cern.ch}
    574 \bibitem{bib:cmstaus} Tau reconstruction in CMS
    575 \end{thebibliography}
    576696
    577697In the list of input files, all files should have the same type
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