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trunk/paper/notes.tex
r119 r120 6 6 \usepackage{amsmath} 7 7 \usepackage{epic} 8 8 \usepackage{wrapfig} 9 9 \usepackage{eepic} 10 10 \usepackage{color} … … 19 19 \usepackage{ifpdf} 20 20 \usepackage{cite} 21 22 \usepackage{enumitem} 21 23 22 24 \newcommand{\dollar}{\$} … … 95 97 %The simulation package proceeds in two stages. The first part is executed on the generated events. ``Particle-level" informations are read from input files and stored in a {\it \textsc{gen}} \textsc{root} tree. 96 98 97 Three formats of input files can currently be used as input in \textsc{Delphes}\footnote{\texttt{[code] }See the \texttt{HEPEVTConverter}, \texttt{LHEFConverter} and \texttt{STDHEPConverter} classes.}. In order to process events from many different generators, the standard Monte Carlo event structure \mbox{\textsc{s}td\textsc{hep}} can be used as an input. Besides, \textsc{Delphes} can also provide detector response for events read in ``Les Houches Event Format'' (\textsc{lhef}) and \textsc{root} files obtained using the \textbf{h2root} utility from the \textsc{root} framework~\cite{bib: root}.99 Three formats of input files can currently be used as input in \textsc{Delphes}\footnote{\texttt{[code] }See the \texttt{HEPEVTConverter}, \texttt{LHEFConverter} and \texttt{STDHEPConverter} classes.}. In order to process events from many different generators, the standard Monte Carlo event structure \mbox{\textsc{s}td\textsc{hep}} can be used as an input. Besides, \textsc{Delphes} can also provide detector response for events read in ``Les Houches Event Format'' (\textsc{lhef}) and \textsc{root} files obtained using the \textbf{h2root} utility from the \textsc{root} framework~\cite{bib:Root}. 98 100 %Afterwards, \textsc{Delphes} performs a simple trigger simulation and reconstruct "high-level objects". These informations are organised in classes and each objects are ordered with respect to the transverse momentum. 99 101 … … 101 103 102 104 103 \section{ Central detector simulation}105 \section{Detector simulation} 104 106 105 107 \begin{figure}[!h] … … 137 139 If 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}. 138 140 139 \textcolor{red}{No smearing is applied on particle direction. (???)}\\140 141 141 142 \begin{table}[!h] … … 153 154 \end{center} 154 155 \end{table} 156 157 \subsection{Tracks reconstruction} 158 Every stable charged particle with a transverse momentum above some threshold and lying inside the fiducial volume of the tracker provides a track. 159 By default, a track is assumed to be reconstructed with $90\%$ probability\footnote{\texttt{[code]} The reconstruction efficiency is defined in the smearing datacard by the \texttt{TRACKING\_EFF} term.} if its transverse momentum $p_T$ is higher than $0.9~\textrm{GeV}$ and if its pseudorapidity $|\eta| \leq 2.5$. 160 155 161 156 162 \subsection{Simulation of calorimeters} … … 223 229 \textcolor{red}{Mettre une figure avec une grille en $(\eta,\phi)$ pour illustrer la segmentation (un peu comme une feuille quadrillée).} 224 230 225 \subsection{Muon smearing} 231 \begin{figure}[!h] 232 \begin{center} 233 \includegraphics[width=0.8\columnwidth]{calosegmentation} 234 \caption{Default segmentation of the calorimeters in the $(\eta,\phi)$ plane. Only the central detectors (\textsc{ecal}, \textsc{hcal} and \textsc{fcal}) are considered.} 235 \label{fig:calosegmentation} 236 \end{center} 237 \end{figure} 238 239 240 \subsection{Very forward detectors simulation} 241 242 Most of the recent experiments in beam colliders have additional instrumentation along the beamline. These extend the $\eta$ coverage to higher values, for the detection of very forward final-state particles. 243 Zero Degree Calorimeters (\textsc{zdc}) are located at zero angle, i.e. are aligned with the beamline axis at the interaction point, and placed at the distance where the paths of incoming and outgoing beams separate (Fig.~\ref{fig:fdets}). These allow the measurement of stable neutral particles ($\gamma$ and $n$) coming from the interaction point, with large pseudorapirities (e.g. $|\eta_{\textrm{n,}\gamma}| > 8.3$ in \textsc{cms}). 244 Forward taggers (called here \textsc{rp220} and \textsc{fp420} as at the \textsc{lhc}) are meant for the measurement of particles following very closely the beam path. To be able to reach these detectors, such particles must have a charge identical to the beam particles, and a momentum very close to the nominal value for the beam. These taggers are near-beam detectors located a few millimeters from the true beam trajectory and this distance defines their acceptance (Table~\ref{tab:fdetacceptance}). 245 246 \begin{figure}[!h] 247 \begin{center} 248 \includegraphics[width=0.8\columnwidth]{fdets} 249 \caption{Default location of the very forward detectors, including \textsc{zdc}, \textsc{rp220} and \textsc{fp420} in the \textsc{lhc} beamline. 250 Incoming (red) and outgoing (black) beams on one side of the interaction point ($s=0~\textrm{m}$). 251 The Zero Degree Calorimeter is located in perfect alignment with the beamline axis at the interaction point, at $140~\textrm{m}$, where the beam paths are separated. The forward taggers are near-beam detectors located at $220~\textrm{m}$ and $420~\textrm{m}$.} 252 \label{fig:fdets} 253 \end{center} 254 \end{figure} 255 256 \begin{table}[!h] 257 \begin{center} 258 \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. 259 The 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. 260 \vspace{0.5cm}} 261 \begin{tabular}[!h]{llcl} 262 \hline 263 Detector & Distance & Acceptance & \\ \hline 264 \textsc{zdc} & $140$ m & $|\eta|> 8.3$ & for $n$ and $\gamma$\\ 265 \textsc{rp220} & $220$ m & $E \in [6100 ; 6880]$ (GeV) & at $2~\textrm{mm}$\\ 266 \textsc{fp420} & $420$ m & $E \in [6880 ; 6980]$ (GeV) & at $4~\textrm{mm}$\\ 267 \hline 268 \end{tabular} 269 \label{tab:fdetacceptance} 270 \end{center} 271 \end{table} 272 273 274 While neutral particles propagate along a straight line to the \textsc{zdc}, a dedicated simulation of the transport of charged particles is needed for \textsc{rp220} and \textsc{fp420}. This fast simulation uses the \textsc{Hector} software~\cite{bib:Hector}, which includes the chromaticity effects and the geometrical aperture of the beamline elements. 275 276 Some subdetectors have the ability to measure the time of flight of the particle. 277 This corresponds to the delay after which the particle is observed in the detector, after the bunch crossing. The time of flight measurement of \textsc{zdc} and \textsc{fp420} detector is implemented here. For the \textsc{zdc}, the formula is simply 278 \begin{equation} 279 t = t_0 + \frac{1}{v} \times \Big( \frac{s-z}{\cos \theta}\Big), 280 \end{equation} 281 where $t$ is the time of flight, $t_0$ is the true time coordinate of the vertex from which the particle originates, $v$ the particle velocity, $s$ is the \textsc{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 \textsc{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 $1 - \cos \theta < 10^{-4}$. 282 The formula then reduces to 283 \begin{equation} 284 t = \frac{1}{c} \times (s-z) 285 \end{equation} 286 Only neutrons and photons are currently assumed to be able to reach the \textsc{zdc}. All other particles are neglected in the \textsc{zdc}. 287 To fix the ideas, if the \textsc{zdc} is located at $s=140~\textrm{m}$, neglecting $z$ and $\theta$, and assuming that $v=c$, one gets $t=0.47~\mu\textrm{s}$. 288 289 \section{High-level object reconstruction} 290 291 Analysis object data contain the final collections of particles ($e^\pm$, $\mu^\pm$, $\gamma$) or objects (light jets, $b$-jets, $\tau$-jets, $E_T^\textrm{miss}$) and are stored\footnote{\texttt{[code] }All these processed data are located under the \texttt{Analysis} tree.} in the output file created by \textsc{Delphes}. 292 In addition, some detector data are added: tracks, calorometric towers and hits in \textsc{zdc}, \textsc{rp220} and \textsc{fp420}. 293 While electrons, muons and photons are easily identified, some other objects are more difficult to measure, like jets or missing energy due to invisible particles. 294 295 296 297 \subsection{Photon and charged lepton reconstruction} 298 From here onwards, \textit{electrons} refer to both positrons ($e^+$) and electrons ($e^-$), and $\textit{charged leptons}$ refer to electrons and muons ($\mu^\pm$), leaving out the $\tau^\pm$ leptons as they decay before being detected. 299 \subsubsection*{Electrons and photons} 300 Photon and electron ($e^\pm$) candidates are reconstructed if they fall into the acceptance of the tracking system and have a transverse momentum above a threshold (default $p_T > 10~\textrm{GeV}$). A calorimetric tower will be seen in the detector, an electrons leave in addition a track. Consequently, electrons and photons creates as usual a candidate in the jet collection. 301 302 \subsubsection*{Muons} 226 303 227 304 Generator level muons entering the detector acceptance are considered as candidates for the analysis level. 228 305 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: $-2.4 \leq \eta \leq 2.4$). 229 230 The application of the detector resolution on the muon 4-momentum $p^\mu$ depends on a Gaussian smearing of the $p_T$ function\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. 231 232 \subsection{Tracks reconstruction} 233 Every stable charged particle with a transverse momentum above some threshold and lying inside the fiducial volume of the tracker provides a track. 234 By default, a track is assumed to be reconstructed with $90\%$ probability\footnote{\texttt{[code]} The reconstruction efficiency is defined in the smearing datacard by the \texttt{TRACKING\_EFF} term.} if its transverse momentum $p_T$ is higher than $0.9~\textrm{GeV}$ and if its pseudorapidity $|\eta| \leq 2.5$. 235 236 237 \subsection{Isolated lepton reconstruction} 238 239 Photon and electron candidates are reconstructed if they fall into the acceptance of the tracking system and have a transverse momentum above a threshold (default $p_T > 10~\textrm{GeV}$). 240 Lepton isolation (for $e^\pm$ and $\mu^\pm$) demands that there is no other charged particles with $p_T>2~\textrm{GeV}$ within a cone of $\Delta R<0.5$ around the lepton.\\ 241 242 \subsection{Very forward detectors simulation} 243 244 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 \textsc{zdc} and \textsc{fp420} detector is implemented here. For the \textsc{zdc}, the formula is simply 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. 307 308 \subsubsection*{Charged lepton isolation} 309 310 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.\\ 311 312 313 314 315 316 317 318 \subsection{Jet reconstruction} 319 320 A realistic analysis requires a correct treatment of final state particles which hadronise. Therefore, the most widely currently used jet algorithms have been integrated into the \textsc{Delphes} framework using the \textsc{FastJet} tools~\cite{bib:FastJet}. 321 Six 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. 322 323 \begin{itemize} 324 325 \item \textbf{Cone algorithms:} 326 327 \begin{enumerate} 328 329 \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. 330 The so-called \textsc{jetclu} cone jet algorithm that was used by \textsc{cdf} in Run II is used. 331 All 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. 332 The 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.}. 334 335 \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. 336 337 \item {\it SISCone}: Seedless Infrared Safe Cone~\cite{bib:SIScone}: Cone algorithm simultaneously insensitive to additional soft particles and collinear splittings, and fast enough to be used in experimental analysis. 338 339 \end{enumerate} 340 341 \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. 344 345 \begin{enumerate}[start=4] 346 347 \item {\it Longitudinally invariant $k_t$ jet}: 245 348 \begin{equation} 246 t_2 = t_1 + \frac{1}{v} \times \big( \frac{s-z}{\cos \theta}\big), 247 \end{equation} 248 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 \textsc{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 \textsc{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 $1 - \cos \theta < 10^{-4}$. 249 The formula then reduces to 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 $d_{iB}=k_{ti}^2$. 352 353 \item {\it Cambridge/Aachen jet}: 354 250 355 \begin{equation} 251 t_2 = \frac{1}{c} \times (s-z) 252 \end{equation} 253 Only neutrons and photons are currently assumed to be able to reach the \textsc{zdc}. All other particles are neglected 254 To fix the ideas, if the \textsc{zdc} is located at $s=140~\textrm{m}$, neglecting $z$ and $\theta$, and assuming that $v=c$, one gets $t=0.47~\mu\textrm{s}$. 255 256 \section{High-level object reconstruction} 257 258 Final state particles which hadronise or invisible ones are more difficult to measure. For instance, light jets or jets originating from $b$ quarks or $\tau$ leptons require dedicated algorithms for their measurement. 259 The \textsc{FastJet} tools~\cite{bib:FastJet} have been integrated into the \textsc{Delphes} framework for a fast jet reconstruction, using several algorithms, like Cone or $k_T$ ones. 260 261 \textcolor{red}{More on jet algorithms?} 262 263 \subsection{Jet reconstruction} 264 356 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 }. 265 368 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 $|\eta|<3.0$. 266 369 370 267 371 \subsection{$b$-tagging} 268 372 … … 292 396 \end{wrapfigure} 293 397 294 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.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. 295 399 296 400 \subsubsection*{Electromagnetic collimation} … … 463 567 \bibitem{bib:Delphes} \textsc{Delphes}, hepforge: 464 568 \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}, 465 571 \bibitem{bib:Frog} \textsc{Frog}, 466 572 \bibitem{bib:CMSresolution} CMS IN 2007/053 467 \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}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} 468 574 \bibitem{bib:cmstaus} Tau reconstruction in CMS 469 575 \end{thebibliography}
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