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1%\documentclass[a4paper,11pt,oneside,twocolumn]{article}
2\documentclass[preprint,times,5p,twocolumn]{elsarticle}
3%\usepackage[english]{babel}
4\usepackage[ansinew]{inputenc}
5%\usepackage{abstract}
6
7\usepackage{amsmath}
8\usepackage{epic}
9\usepackage{wrapfig}
10\usepackage{eepic}
11\usepackage{latexsym}
12\usepackage{array}
13\usepackage{multicol}
14
15\usepackage{fancyhdr}
16\usepackage{verbatim}
17\addtolength{\textwidth}{1cm} \addtolength{\hoffset}{-0.5cm}
18\usepackage[colorlinks=true, pdfstartview=FitV, linkcolor=blue, citecolor=blue, urlcolor=blue, unicode]{hyperref}
19\usepackage{ifpdf}
20\usepackage{cite}
21
22\usepackage{enumitem}
23
24\newcommand{\dollar}{\$}
25
26\usepackage{graphicx}
27\graphicspath{{figures/}}
28
29
30\journal{Computer Physics Communications}
31
32\begin{document}
33
34\begin{frontmatter}
35
36\title{\textsc{Delphes}, a framework for fast simulation of a generic collider experiment}
37\author{S. Ovyn\corref{cor1}}
38\ead{severine.ovyn@uclouvain.be}
39
40%\author{X. Rouby\fnref{freiburg}}
41%\fntext[freiburg]{Now in Physikalisches Institut, Albert-Ludwigs-Universit\"at Freiburg}
42%\ead{xavier.rouby@cern.ch}
43
44\address{Center for Particle Physics and Phenomenology (CP3),
45 Universit\'e catholique de Louvain,
46 B-1348 Louvain-la-Neuve, Belgium}
47
48\author{X. Rouby}
49\ead{xavier.rouby@cern.ch}
50
51\address{Physikalisches Institut,
52 Albert-Ludwigs-Universit\"at Freiburg,
53 D-79104 Freiburg, Germany
54}
55
56\begin{abstract}
57It is always delicate to know whether theoretical predictions are visible and measurable in a high energy collider experiment due to the complexity of the related detectors, data acquisition chain and software.
58We introduce here a new \texttt{C++}-based framework, \textsc{Delphes}, for fast simulation of
59a general-purpose experiment. The simulation includes a tracking system, embedded into a magnetic field, calorimetry and a muon
60system, and possible very forward detectors arranged along the beamline.
61The framework is interfaced to standard file formats (e.g.\ Les Houches Event File or \texttt{HepMC}) and outputs observable objects for analysis, like missing transverse energy and collections of electrons or jets.
62The simulation of detector response takes into account the detector resolution, and usual reconstruction algorithms, such as \textsc{FastJet}. A simplified preselection can also be applied on processed data for trigger emulation. Detection of very forward scattered particles relies on the transport in beamlines with the \textsc{Hector} software. Finally, the \textsc{Frog} 2D/3D event display is used for visualisation of the collision final states.
63An overview of \textsc{Delphes} is given as well as a few \textsc{lhc} use-cases for illustration.\\ \\
64\textit{Preprint:} \texttt{CP3-09-01}, \texttt{arXiv:0903.2225 [hep-ph]}\\ \\
65%\includegraphics[scale=0.8]{DelphesLogoSml}\\
66\includegraphics[scale=0.8]{fig0}\\
67{\bf PROGRAM SUMMARY}\\
68\begin{small}
69\noindent
70{\em Program Title:} DELPHES \\
71{\em Current version:} 1.8 \\
72{\em Journal Reference:} \\
73 %Leave blank, supplied by Elsevier.
74{\em Catalogue identifier:} \\
75 %Leave blank, supplied by Elsevier.
76%{\em Licensing provisions:} \\
77 %enter "none" if CPC non-profit use license is sufficient.
78{\em Distribution format:} tar.gz \\
79{\em Programming language:} C++ \\
80%{\em Computer:} any computer with a C++ compiler and the ROOT environment \cite{bib:Root}
81 %Computer(s) for which program has been designed.
82%{\em Operating system:} \\
83 %Operating system(s) for which program has been designed.
84%{\em RAM:} bytes \\
85 %RAM in bytes required to execute program with typical data.
86%{\em Number of processors used:} \\
87 %If more than one processor.
88%{\em Supplementary material:} \\
89 % Fill in if necessary, otherwise leave out.
90%{\em Keywords:} Keyword one, Keyword two, Keyword three, etc. \\
91 % Please give some freely chosen keywords that we can use in a
92 % cumulative keyword index.
93%{\em Classification:} \\
94 %Classify using CPC Program Library Subject Index, see (
95 % http://cpc.cs.qub.ac.uk/subjectIndex/SUBJECT_index.html)
96 %e.g. 4.4 Feynman diagrams, 5 Computer Algebra.
97{\em External routines/libraries:} ROOT environment \\
98 % Fill in if necessary, otherwise leave out.
99{\em Subprograms used:} HepMC, STDHEP, FastJet, Hector, FROG. All provided within DELPHES distribution. \\
100{\em URL:}\href{http://www.fynu.ucl.ac.be/delphes.html}{http://www.fynu.ucl.ac.be/delphes.html}\\
101%{\em References:}
102%\begin{refnummer}
103%\item Reference 1 % This is the reference list of the Program Summary
104%\item Reference 2 % Type references in text as [1], [2], etc.
105%\item Reference 3 % This list is different from the bibliography, which
106 % you can use in the Long Write-Up.
107%\end{refnummer}
108\end{small}
109
110\begin{keyword}
111\textsc{Delphes} \sep fast simulation \sep trigger \sep event display \sep \textsc{lhc} \sep \textsc{FastJet} \sep \textsc{Hector} \sep \textsc{Frog} \sep Les Houches Event File \sep HepMC \sep \textsc{root}
112\PACS 29.85.-c \sep 07.05.Tp \sep 29.90.+r \sep 29.50.+v
113\end{keyword}
114
115\end{abstract}
116\cortext[cor1]{Corresponding author: +32.10.47.32.29.}
117\end{frontmatter}
118
119\section{Introduction}
120
121Experiments at high energy colliders are very complex systems for several reasons. Firstly, in terms of the various detector subsystems, including tracking, central calorimetry, forward calorimetry, and muon chambers. Such apparatus differ in their detection principles, technologies, geometrical acceptances, resolutions and sensitivities. Secondly, due to the requirement of a highly effective online selection (i.e.\ a \textit{trigger}), subdivided into several levels for an optimal reduction factor of ``uninteresting'' events, but based only on partially processed data. Finally, in terms of the experiment software, with different data formats (like \textit{raw} or \textit{reconstructed} data), many reconstruction algorithms and particle identification approaches.
122
123This complexity is handled by large collaborations of thousands of people, but the data and the expertise are only available to their members. Real data analyses require a full detector simulation, including transport of the primary and secondary particles through the detector material accounting for the various detector inefficiencies, the dead material, the imperfections and the geometrical details. Moreover, control of the detector calibration and alignment are crucial. Such simulation is very complicated, technical and requires a large \texttt{CPU} power. On the other hand, phenomenological studies, looking for the observability of given signals, may require only fast but realistic estimates of the expected signals and associated backgrounds.
124
125A new framework, called \textsc{Delphes}~\citep{bib:Delphes}, is introduced here, for the fast simulation of a general-purpose collider experiment.
126Using the framework, observables can be estimated for specific signal and background channels, as well as their production and measurement rates.
127Starting from the output of event generators, the simulation of the detector response takes into account the subdetector resolutions, by smearing the kinematic properties of the final-state particles\footnote{Throughout the paper, final-state particles refer as particles considered as stable by the event generator.}. Tracks of charged particles and deposits of energy in calorimetric cells (or \textit{calotowers}) are then created.
128
129\textsc{Delphes} includes the most crucial experimental features, such as (Fig.~\ref{fig:FlowChart}):
130\begin{enumerate}
131\item the geometry of both central and forward detectors,
132\item magnetic field for tracks
133\item reconstruction of photons, leptons, jets, $b$-jets, $\tau$-jets and missing transverse energy,
134\item lepton isolation,
135\item trigger emulation,
136\item an event display.
137\end{enumerate}
138
139\begin{figure*}[!ht]
140\begin{center}
141%\includegraphics[scale=0.78]{FlowDelphes}
142\includegraphics[scale=0.78]{fig1}
143\caption{Flow chart describing the principles behind \textsc{Delphes}. Event files coming from external Monte Carlo generators are read by a converter stage (top).
144The kinematics variables of the final-state particles are then smeared according to the tunable subdetector resolutions.
145Tracks are reconstructed in a simulated solenoidal magnetic field and calorimetric towers sample the energy deposits. Based on these low-level objects, dedicated algorithms are applied for particle identification, isolation and reconstruction.
146The transport of very forward particles to the near-beam detectors is also simulated.
147Finally, an output file is written, including generator-level and analysis-object data.
148If requested, a fully parametrisable trigger can be emulated. Optionally, the geometry and visualisation files for the 3D event display can also be produced.
149All user parameters are set in the \textit{Detector/Smearing Card} and the \textit{Trigger Card}. }
150\label{fig:FlowChart}
151\end{center}
152\end{figure*}
153
154Although 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.
155
156Four datafile formats can be used as input in \textsc{Delphes}\footnote{\texttt{[code] }See the \texttt{HEPEVTConverter}, \texttt{HepMCConverter}, \texttt{LHEFConverter} and \texttt{STDHEPConverter} classes.}. In order to process events from many different generators, the standard Monte Carlo event structures \texttt{StdHEP}~\citep{bib:stdhep} and \texttt{HepMC}~\citep{bib:hepmc} can be used as an input. Besides, \textsc{Delphes} can also provide detector response for events read in ``Les Houches Event Format'' (\textsc{lhef}~\citep{bib:lhe}) and \textsc{root} files obtained from \textsc{.hbook} using the \texttt{h2root} utility from the \textsc{root} framework~\citep{bib:Root}.
157%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.
158
159\textsc{Delphes} uses the \texttt{ExRootAnalysis} utility~\citep{bib:ExRootAnalysis} to create output data in a \texttt{*.root} ntuple.
160This output contains a copy of the generator-level data (\textsc{gen} tree), the analysis data objects after reconstruction (\mbox{\textsc{A}nalysis} tree), and possibly the results of the trigger emulation (\mbox{\textsc{T}rigger} tree).
161In option\footnote{\texttt{[code]} See the \texttt{FLAG\_lhco} variable in the detector datacard. This text file format is shortly described in the user manual.}, \textsc{Delphes} can produce a reduced output file in \texttt{*.lhco} text format, which is limited to the list of the reconstructed high-level objects in the final states.
162
163The program is driven by input cards. The detector card (\texttt{data/DetectorCard.dat}) allows a large spectrum of running conditions by modifying basic detector parameters, including calorimeter and tracking coverage and resolution, thresholds or jet algorithm parameters. The trigger card (\texttt{data/TriggerCard.dat}) lists the user algorithms for the simplified online
164preselection.
165
166
167\section{Detector simulation}
168
169The overall layout of the general-purpose detector simulated by \textsc{Delphes} is shown in Fig.~\ref{fig:GenDet3}.
170A central tracking system (\textsc{tracker}) is surrounded by an electromagnetic and a hadron calorimeters (\textsc{ecal} and \textsc{hcal}, resp., each with a central region and two endcaps). 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
171The fast simulation of the detector response takes into account geometrical acceptance of sub-detectors and their finite resolution, as defined in the detector data card\footnote{\texttt{[code] }See the \texttt{RESOLution} class.}.
172If no such file is provided, predefined values based on ``typical'' \textsc{cms} acceptances and resolutions are used\footnote{\texttt{[code] }Detector and trigger cards for the \textsc{atlas} and \textsc{cms} experiments are also provided in \texttt{data/} directory.}. The geometrical coverage of the various subsystems used in the default configuration are summarised in Tab.~\ref{tab:defEta}.
173
174\begin{table*}[t]
175\begin{center}
176\caption{Default extension in pseudorapidity $\eta$ of the different subdetectors.
177Full azimuthal ($\phi$) acceptance is assumed.
178The corresponding parameter name, in the detector card, is given. \vspace{0.5cm}}
179\begin{tabular}{llcc}
180\hline
181Subdetector & & $\eta$ & $\phi$ \\
182\textsc{tracker} & {\verb CEN_max_tracker } & $[-2.5; 2.5]$ & $[-\pi ; \pi]$\\
183\textsc{ecal}, \textsc{hcal} & {\verb CEN_max_calo_cen }& $[-1.7 ; 1.7]$ & $[-\pi ; \pi]$\\
184\textsc{ecal}, \textsc{hcal} endcaps & {\verb CEN_max_calo_ec }& $[-3 ; -1.7] \& [1.7 ; 3]$ & $[-\pi ; \pi]$\\
185\textsc{fcal} & {\verb CEN_max_calo_fwd } & $[-5 ; -3]$ \& $[3 ;5]$ & $[-\pi ; \pi]$\\
186\textsc{muon} & {\verb CEN_max_mu } & $[-2.4 ; 2.4]$ & $[-\pi ; \pi]$\\ \hline
187\end{tabular}
188\label{tab:defEta}
189\end{center}
190\end{table*}
191
192\begin{figure}[!h]
193\begin{center}
194%\includegraphics[width=\columnwidth]{Detector_Delphes_3}
195\includegraphics[width=\columnwidth]{fig2}
196\caption{
197Profile 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).
198It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
199The 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.
200The 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.
201}
202\label{fig:GenDet3}
203\end{center}
204\end{figure}
205
206
207\subsubsection*{Magnetic field}
208In addition to the subdetectors, the effects of a solenoidal magnetic field are simulated for the charged particles\footnote{\texttt{[code] }See the \texttt{TrackPropagation} class.}. This affects the position at which charged particles enter the calorimeters and their corresponding tracks.
209
210
211
212\subsection{Tracks reconstruction}
213Every stable charged particle with a transverse momentum above some threshold and lying inside the detector volume covered by the tracker provides a track.
214By default, a track is assumed to be reconstructed with $90\%$ probability\footnote{\texttt{[code]} The reconstruction efficiency is defined in the detector datacard by the \texttt{TRACKING\_EFF} term.} if its transverse momentum $p_T$ is higher than $0.9~\textrm{GeV}/c$ and if its pseudorapidity $|\eta| \leq 2.5$.
215
216
217\subsection{Simulation of central calorimeters}
218
219The energy of each particle considered as stable in the generator particle list is smeared, with a Gaussian distribution depending on the calorimeter resolution. This resolution varies with the sub-calorimeter (\textsc{ecal}, \textsc{hcal}, \textsc{fcal}) measuring the particle.
220The response of each sub-calorimeter is parametrised as a function of the energy:
221\begin{equation}
222\frac{\sigma}{E} = \frac{S}{\sqrt{E}} \oplus \frac{N}{E} \oplus C,
223\label{eq:caloresolution}
224\end{equation}
225where $S$, $N$ and $C$ are the \textit{stochastic}, \textit{noise} and \textit{constant} terms, respectively, and $\oplus$ stands for quadratic additions.\\
226
227
228The particle four-momentum $p^\mu$ are smeared with a parametrisation directly derived from typical detector technical designs\footnote{\texttt{[code] }~\citep{bib:cmsjetresolution,bib:ATLASresolution}. The response of the detector is applied to the electromagnetic and the hadronic particles through the \texttt{SmearElectron} and \texttt{SmearHadron} functions.}.
229In the default parametrisation, the calorimeter is assumed to cover the pseudorapidity range $|\eta|<3$ and consists in an electromagnetic and hadronic parts. 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.
230Muons and neutrinos are assumed not 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 therefore be handled with care.}.
231The default values of the stochastic, noise and constant terms are given in Tab.~\ref{tab:defResol}.\\
232
233\begin{table}[!h]
234\begin{center}
235\caption{Default values for the resolution of the central and forward calorimeters. Resolution is parametrised by the \textit{stochastic} ($S$), \textit{noise} ($N$) and \textit{constant} ($C$) terms (Eq.~\ref{eq:caloresolution}).
236The corresponding parameter name, in the detector card, is given. \vspace{0.5cm}}
237\begin{tabular}[!h]{lllc}
238\hline
239\multicolumn{2}{c}{Resolution Term} & Card flag & Value\\\hline
240 \multicolumn{4}{l}{\textsc{ecal}} \\
241 & $S$ (GeV$^{1/2}$) & {\verb ELG_Scen } & $0.05$ \\
242 & $N$ (GeV)& {\verb ELG_Ncen } & $0.25$ \\
243 & $C$ & {\verb ELG_Ccen } & $0.0055$ \\
244 \multicolumn{4}{l}{\textsc{ecal}, end caps} \\
245 & $S$ (GeV$^{1/2}$) & {\verb ELG_Sec } & $0.05$ \\
246 & $N$ (GeV)& {\verb ELG_Nec } & $0.25$ \\
247 & $C$ & {\verb ELG_Cec } & $0.0055$ \\
248 \multicolumn{4}{l}{\textsc{fcal}, electromagnetic part} \\
249 & $S$ (GeV$^{1/2}$)& {\verb ELG_Sfwd } & $2.084$ \\
250 & $N$ (GeV)& {\verb ELG_Nfwd } & $0$ \\
251 & $C$ & {\verb ELG_Cfwd } & $0.107$ \\
252 \multicolumn{4}{l}{\textsc{hcal}} \\
253 & $S$ (GeV$^{1/2}$)& {\verb HAD_Scen } & $1.5$ \\
254 & $N$ (GeV)& {\verb HAD_Ncen } & $0$\\
255 & $C$ & {\verb HAD_Ccen } & $0.05$\\
256 \multicolumn{4}{l}{\textsc{hcal}, end caps} \\
257 & $S$ (GeV$^{1/2}$)& {\verb HAD_Sec } & $1.5$ \\
258 & $N$ (GeV)& {\verb HAD_Nec } & $0$\\
259 & $C$ & {\verb HAD_Cec } & $0.05$\\
260 \multicolumn{4}{l}{\textsc{fcal}, hadronic part} \\
261 & $S$ (GeV$^{1/2}$)& {\verb HAD_Sfwd } & $2.7$\\
262 & $N$ (GeV)& {\verb HAD_Nfwd } & $0$ \\
263 & $C$ & {\verb HAD_Cfwd } & $0.13$\\
264\hline
265\end{tabular}
266\label{tab:defResol}
267\end{center}
268\end{table}
269
270The energy of electrons and photons found in the particle list are smeared using the \textsc{ecal} resolution terms. Charged and neutral final-state hadrons interact with the \textsc{ecal}, \textsc{hcal} and \textsc{fcal}.
271Some long-living particles, such as the $K^0_s$ and $\Lambda$'s, with lifetime $c\tau$ smaller than $10~\textrm{mm}$ are considered as stable particles although they decay before the calorimeters. The energy smearing of such particles is performed using the expected fraction of the energy, determined according to their decay products, that would be deposited into the \textsc{ecal} ($E_{\textsc{ecal}}$) and into the \textsc{hcal} ($E_{\textsc{hcal}}$). Defining $F$ as the fraction of the energy leading to a \textsc{hcal} deposit, the two energy values are given by
272\begin{equation}
273\left\{
274\begin{array}{l}
275E_{\textsc{hcal}} = E \times F \\
276E_{\textsc{ecal}} = E \times (1-F) \\
277\end{array}
278\right.
279\end{equation}
280where $0 \leq F \leq 1$. The electromagnetic part is handled the same way for the electrons and photons.
281The resulting calorimetry energy measurement given after the application of the smearing is then $E = E_{\textsc{hcal}} + E_{\textsc{ecal}}$. For $K_S^0$ and $\Lambda$ hadrons\footnote{\texttt{[code]} To implement different ratios for other particles, see the \texttt{BlockClasses} class.}, the energy fraction is $F$ is assumed to be $0.7$.\\
282
283\subsection{Calorimetric towers}
284
285The smallest unit for geometrical sampling of the calorimeters is a \textit{tower}; it segments the $(\eta,\phi)$ plane for the energy measurement. No longitudinal segmentation is available in the simulated calorimeters. All undecayed particles, except muons and neutrinos deposit energy in a calorimetric tower, either in \textsc{ecal}, in \textsc{hcal} or \textsc{fcal}.
286As the detector is assumed to be cylindrical (e.g.\ symmetric in $\phi$ and with respect to the $\eta=0$ plane), the detector 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.
287
288\begin{figure}[!h]
289\begin{center}
290%\includegraphics[width=\columnwidth]{calosegmentation}
291\includegraphics[width=\columnwidth]{fig3}
292\caption{Default segmentation of the calorimeters in the $(\eta,\phi)$ plane. Only the central detectors (\textsc{ecal}, \textsc{hcal}) and \textsc{fcal} are considered. $\phi$ angles are expressed in radians.}
293\label{fig:calosegmentation}
294\end{center}
295\end{figure}
296
297The calorimetric towers directly enter in the calculation of the missing transverse energy (\textsc{met}), and as input for the jet reconstruction algorithms. No sharing between neighbouring towers is implemented when particles enter a tower very close to its geometrical edge. Smearing is applied directly on the accumulated electromagnetic and hadronic energies of each calorimetric tower.
298
299\subsection{Very forward detectors simulation}
300
301Most 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.
302Zero Degree Calorimeters (\textsc{zdc}) are located at zero angle, i.e.\ are aligned with the beamline axis at the interaction point, and placed beyond the point 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 pseudorapidities (e.g.\ $|\eta_{\textrm{n,}\gamma}| > 8.3$ in \textsc{atlas} and \textsc{cms}).
303Forward taggers (called here \textsc{rp220}, for ``roman pots at $220~\textrm{m}$'' and \textsc{fp420} ``for forward proton taggers at $420~\textrm{m}$'', 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 millimetres from the true beam trajectory and this distance defines their acceptance (Tab.~\ref{tab:fdetacceptance}).
304
305\begin{figure}[!h]
306\begin{center}
307%\includegraphics[width=\columnwidth]{fdets}
308\includegraphics[width=\columnwidth]{fig4}
309\caption{Default location of the very forward detectors, including \textsc{zdc}, \textsc{rp220} and \textsc{fp420} in the \textsc{lhc} beamline.
310Incoming (red) and outgoing (black) beams on one side of the interaction point ($s=0~\textrm{m}$).
311The Zero Degree Calorimeter is located in perfect alignment with the beamline axis at the interaction point, at $140~\textrm{m}$, the beam paths are separated. The forward taggers are near-beam detectors located at $220~\textrm{m}$ and $420~\textrm{m}$. Beamline simulation with \textsc{Hector}~\citep{bib:Hector}.}
312\label{fig:fdets}
313\end{center}
314\end{figure}
315
316\begin{table*}[t]
317\begin{center}
318\caption{Default parameters for the forward detectors: distance from the interaction point and detector acceptance. The \textsc{lhc} beamline is assumed around the fifth \textsc{lhc} interaction point (\textsc{ip}). For the \textsc{zdc}, the acceptance depends only on the pseudorapidity $\eta$ of the particle, which should be neutral and stable.
319The tagger acceptance is fully determined by the distance in the transverse plane of the detector to the real beam position~\citep{bib:Hector}. It is expressed in terms of the particle energy ($E$).
320\vspace{0.5cm}}
321\begin{tabular}{llcl}
322\hline
323Detector & Distance from \textsc{ip}& Acceptance & \\ \hline
324\textsc{zdc} & $140$ m & $|\eta|> 8.3$ & for $n$ and $\gamma$\\
325\textsc{rp220} & $220$ m & $E \in [6100 ; 6880]$ (GeV) & at $2~\textrm{mm}$\\
326\textsc{fp420} & $420$ m & $E \in [6880 ; 6980]$ (GeV) & at $4~\textrm{mm}$\\
327\hline
328\end{tabular}
329\label{tab:fdetacceptance}
330\end{center}
331\end{table*}
332
333
334While 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~\citep{bib:Hector}, which includes the chromaticity effects and the geometrical aperture of the beamline elements of any arbitrary collider.
335
336Some subdetectors have the ability to measure the time of flight of the particle.
337This corresponds to the delay after which the particle is observed in the detector, with respect to the bunch crossing reference time at the interaction point ($t_0$). The time of flight measurement of \textsc{zdc} and \textsc{fp420} detector is implemented here. For the \textsc{zdc}, the formula is simply
338\begin{equation}
339 t = t_0 + \frac{1}{v} \times \Big( \frac{s-z}{\cos \theta}\Big),
340\end{equation}
341where $t$ 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 $1 - \cos \theta < 10^{-4}$.
342The formula then reduces to
343\begin{equation}
344 t = \frac{1}{c} \times (s-z)
345\end{equation}
346For example, a photon takes $0.47~\mu\textrm{s}$ to reach a \textsc{zdc} located at $s=140~\textrm{m}$, neglecting $z$ and $\theta$, and assuming that $v=c$. Only neutrons and photons are currently assumed to be able to reach the \textsc{zdc}. All other particles are neglected in the \textsc{zdc}. The \textsc{zdc}s are composed of an electromagnetic and a hadronic sections, for the measurement of photons and neutrons, respectively. The energy of the observed neutral is smeared according to Eq.~\ref{eq:caloresolution} and the section resolutions (Tab.~\ref{tab:defResolZdc}). The \textsc{zdc} hits do not enter in the calorimeter tower list used for reconstruction of jets and missing transverse energy.
347
348\begin{table}[!h]
349\begin{center}
350\caption{Default values for the resolution of the zero degree calorimeters. Resolution is parametrised by the \textit{stochastic} ($S$), \textit{noise} ($N$) and \textit{constant} ($C$) terms (Eq.~\ref{eq:caloresolution}).
351The corresponding parameter name, in the detector card, is given. \vspace{0.5cm}}
352\begin{tabular}[!h]{lllc}
353\hline
354\multicolumn{2}{c}{Resolution Term} & Card flag & Value\\\hline
355 \multicolumn{4}{l}{\textsc{zdc}, electromagnetic part} \\
356 & $S$ (GeV$^{1/2}$)& {\verb ELG_Szdc } & $0.7$ \\
357 & $N$ (GeV)& {\verb ELG_Nzdc } & $0.0$ \\
358 & $C$ & {\verb ELG_Czdc } & $0.08$ \\
359 \multicolumn{4}{l}{\textsc{zdc}, hadronic part} \\
360 & $S$ (GeV$^{1/2}$)& {\verb HAD_Szdc } & $1.38$\\
361 & $N$ (GeV)& {\verb HAD_Nzdc } & $0$ \\
362 & $C$ & {\verb HAD_Czdc } & $0.13$\\
363\hline
364\end{tabular}
365\label{tab:defResolZdc}
366\end{center}
367\end{table}
368
369
370
371
372\section{High-level object reconstruction}
373
374Analysis 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}.
375In addition, some detector data are added: tracks, calorimetric towers and hits in \textsc{zdc}, \textsc{rp220} and \textsc{fp420}.
376While electrons, muons and photons are easily identified, some other objects are more difficult to measure, like jets or missing energy due to invisible particles.
377
378For most of these objects, their four-momentum 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).
379
380
381
382\subsection{Photon and charged lepton reconstruction}
383From 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.
384
385\subsubsection*{Electrons and photons}
386Electron ($e^\pm$) and photon candidates are reconstructed if they fall into the acceptance of the tracking system and have a transverse momentum above a threshold (default $p_T > 10~\textrm{GeV}/c$). A calorimetric tower will be seen in the detector, as electrons will leave in addition a track. Subsequently, electrons and photons create a candidate in the jet collection.
387Assuming a good measurement of the track parameters in the real experiment, the electron energy can be reasonably recovered. In \textsc{Delphes}, electron energy is smeared according to the resolution of the calorimetric tower where it points to, but independently from any other deposited energy is this tower. This approach is still conservative as the calorimeter resolution is worse than the tracker one.
388
389\subsubsection*{Muons}
390Generator-level muons entering the detector acceptance are considered as candidates for the analysis level.
391The acceptance is defined in terms of a transverse momentum threshold to be overpassed that should be computed using the chosen geometry of the detector and the magnetic field considered (default : $p_T > 10~\textrm{GeV}/c$) and of the pseudorapidity coverage of the muon system (default: $-2.4 \leq \eta \leq 2.4$).
392The 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. Multiple scattering is neglected. This implies that low energy muons have in \textsc{Delphes} a better resolution than in a real detector. Furthermore, muons leave no deposit in calorimeters.
393
394\subsubsection*{Charged lepton isolation}
395\label{sec:isolation}
396
397To improve the quality of the contents of the charged lepton collections, additional criteria can be applied such as 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 $p_T>2~\textrm{GeV}/c$ within a cone of $\Delta R = \sqrt{\Delta \eta^2 + \Delta \phi^2} <0.5$ around the lepton.
398The result (i.e.\ \textit{isolated} or \textit{not}) is added to the charged lepton measured properties.
399In addition, the sum $P_T$ of the transverse momenta of all tracks but the lepton one within the isolation cone is
400provided\footnote{\texttt{[code] }See the \texttt{IsolFlag} and \texttt{IsolPt} values in the \texttt{Electron} or \texttt{Muon} collections in the \texttt{Analysis} tree, as well as the \texttt{ISOL\_PT} and \texttt{ISOL\_Cone} variables in the detector card.}:
401$$ P_T = \sum_{i \neq \mu}^\textrm{tracks} p_T(i)$$
402
403No calorimetric isolation is applied, but the muon collection contains also the ratio $\rho_\mu$ between (1) the sum of the transverse energies in all calotowers in a $N \times N$ grid around the muon, and (2) the muon transverse
404momentum\footnote{\texttt{[code] }Calorimetric isolation parameters in the detector card are \texttt{ISOL\_Calo\_ET} and \texttt{ISOL\_Calo\_Grid}.}:
405$$ \rho_\mu = \frac{\Sigma_i E_T(i)}{p_T(\mu)}~,~ i\textrm{ in }N \times N \textrm { grid centred on }\mu.$$
406
407
408\subsubsection*{Forward neutrals}
409
410The zero degree calorimeter hits correspond to neutral particles with a lifetime long enough to reach these detectors (default: $c \tau \geq 140~\textrm{m}$) and very large pseudorapidities (default: $|\eta|>8.3$). In current versions of \textsc{Delphes}, only photons and neutrons are considered. Photons are identified thanks to the electromagnetic section of the calorimeter, and if their energy overpasses a given threshold (def. $20$~GeV). Similarly, neutrons are reconstructed according to the resolution of the hadronic section, if their energy exceeds a threshold\footnote{\texttt{[code]} These thresholds are defined by the \texttt{ZDC\_gamma\_E} and \texttt{ZDC\_n\_E} variables in the detector card.} (def. $50$~GeV).
411
412
413
414\subsection{Jet reconstruction}
415
416A realistic analysis requires a correct treatment of particles which have hadronised. Therefore, the most widely currently used jet algorithms have been integrated into the \textsc{Delphes} framework using the \textsc{FastJet} tools~\citep{bib:FastJet}.
417Six different jet reconstruction schemes are available\footnote{\texttt{[code] }The choice is done by allocating the \texttt{JET\_jetalgo } input parameter in the detector card.}. The first three belong to the cone algorithm class while the last three are using a sequential recombination scheme. For all of them, the towers are used as input for the jet clustering. Jet algorithms differ in their sensitivity to soft particles or collinear splittings, and in their computing speed performances.
418By default, reconstruction uses a cone algorithm with $\Delta R=0.7$.
419Jets are stored if their transverse energy is higher\footnote{\texttt{[code] PTCUT\_jet }variable in the detector card.} than $20~\textrm{GeV}$.
420
421\subsubsection*{Cone algorithms}
422
423\begin{enumerate}
424
425\item {\it CDF Jet Clusters}~\citep{bib:jetclu}: Algorithm forming jets by associating together towers lying within a circle (default radius $\Delta R=0.7$) in the $(\eta$, $\phi)$ space.
426This so-called \textsc{Jetclu} cone jet algorithm is used by the \textsc{cdf} experiment in Run II.
427All 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.
428The existing \textsc{FastJet} code has been modified to allow easy modification of the tower pattern in $(\eta, \phi)$ space.
429In 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 detector card.}.
430
431\item {\it CDF MidPoint}~\citep{bib:midpoint}: Algorithm developed for the \textsc{cdf} Run II to reduce infrared and collinear sensitivities compared to purely seed-based cone by adding `midpoints' (energy barycentres) in the list of cone seeds.
432
433\item {\it Seedless Infrared Safe Cone}~\citep{bib:SIScone}: The \textsc{SISCone} algorithm is simultaneously insensitive to additional soft particles and collinear splittings, and fast enough to be used in experimental analysis.
434
435\end{enumerate}
436
437\subsubsection*{Recombination algorithms}
438
439The three sequential recombination jet algorithms are safe with respect to soft radiations (\textit{infrared}) and collinear splittings. They rely on recombination schemes where calorimeter tower 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 $i$.
440
441The 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 towers are left in the input list. 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:
442
443\begin{enumerate}[start=4]
444
445\item {\it Longitudinally invariant $k_t$ jet}~\citep{bib:ktjet}:
446\begin{equation}
447\begin{array}{l}
448 d_{ij} = \min(k_{ti}^2,k_{tj}^2)\Delta R_{ij}^2/R^2 \\
449 d_{iB}=k_{ti}^2 \\
450\end{array}
451\end{equation}
452
453\item {\it Cambridge/Aachen jet}~\citep{bib:aachen}:
454\begin{equation}
455\begin{array}{l}
456d_{ij} = \Delta R_{ij}^2/R^2\\
457d_{iB}=1 \\
458\end{array}
459\end{equation}
460
461\item {\it Anti $k_t$ jet}~\citep{bib:antikt}: where hard jets are exactly circular in the $(y,\phi)$ plane
462\begin{equation}
463\begin{array}{l}
464d_{ij} = \min(1/k_{ti}^2,1/k_{tj}^2)\Delta R_{ij}^2/R^2 \\
465d_{iB}=1/k_{ti}^2 \\
466\end{array}
467\end{equation}
468\end{enumerate}
469
470\subsubsection*{Energy flow}
471
472In jets, several particle can leave their energy into a given calorimetric tower, which broadens the jet energy resolution. However, the energy of charged particles associated to jets can be deduced from their reconstructed track, thus providing a way to identify some of the components of towers with multiple hits. When the \textit{energy flow} is switched on in \textsc{Delphes}\footnote{\texttt{[code]} Set \texttt{JET\_Eflow} to $1$ or $0$ in the detector card in order to switch on or off the energy flow for jet reconstruction.}, the energy of tracks pointing to calotowers is extracted and smeared separately, before running the chosen jet reconstruction algorithm. This option allows a better jet $E$ reconstruction.
473
474\subsection{$b$-tagging}
475
476A 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. By default, 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{BTAG\_b}, \texttt{BTAG\_mistag\_c} and \texttt{BTAG\_mistag\_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.}.
477The (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 equal to the one used to reconstruct the jet (default: $\Delta R$ of $0.7$). In current version of \textsc{Delphes}, the displacement of secondary vertices is not simulated.
478
479\subsection{\texorpdfstring{$\tau$}{\texttau} identification}
480
481Jets originating from $\tau$-decays are identified using a procedure consistent with the one applied in a full detector simulation~\citep{bib:cmsjetresolution}.
482The tagging relies on two properties of the $\tau$ lepton. First, $77\%$ of the $\tau$ hadronic decays contain only one charged hadron associated to a few neutrals (Tab.~\ref{tab:taudecay}). Tracks are useful for this criterion. Secondly, the particles arisen from the $\tau$ lepton produce narrow jets in the calorimeter (this is defined as the jet \textit{collimation}).
483
484
485\begin{table}[!h]
486\begin{center}
487\caption{ Branching ratios for $\tau^-$ lepton~\citep{bib:pdg}. $h^\pm$ and $h^0$ refer to charged and neutral hadrons, respectively. $n \geq 0$ and $m \geq 0$ are integers.
488\vspace{0.5cm} }
489\begin{tabular}[!h]{ll}
490\hline
491 \multicolumn{2}{l}{\textbf{Leptonic decays}}\\
492 $ \tau^- \rightarrow e^- \ \bar \nu_e \ \nu_\tau$ & $17.9\% $ \\
493 $ \tau^- \rightarrow \mu^- \ \bar \nu_\mu \ \nu_\tau$ & $17.4\%$ \\
494 \multicolumn{2}{l}{\textbf{Hadronic decays}}\\
495 $ \tau^- \rightarrow h^-\ n\times h^\pm \ m\times h^0\ \nu_\tau$ & $64.7\%$ \\
496 $ \tau^- \rightarrow h^-\ m\times h^0 \ \nu_\tau$ & $50.1\%$ \\
497 $ \tau^- \rightarrow h^-\ h^+ h^- m\times h^0 \ \nu_\tau$ & $14.6\%$ \\
498\hline
499\end{tabular}
500\label{tab:taudecay}
501\end{center}
502\end{table}
503
504\begin{figure}[!h]
505\begin{center}
506%\includegraphics[width=0.6\columnwidth]{Tau}
507\includegraphics[width=0.80\columnwidth]{fig5}
508\caption{Illustration of the identification of $\tau$-jets ($1-$prong). The jet cone is narrow and contains only one track. The small cone serves to apply the \textit{electromagnetic collimation}, while the broader cone is used to reconstruct the jet originating from the $\tau$-decay.}
509\label{h_WW_ss_cut1}
510\end{center}
511\end{figure}
512
513
514\begin{table}[!h]
515\begin{center}
516\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.
517\vspace{0.5cm} }
518\begin{tabular}[!h]{lll}
519\hline
520Parameter & Card flag & Value\\\hline
521\multicolumn{3}{l}{\textbf{Electromagnetic collimation}} \\
522$R^\textrm{em}$ & \texttt{TAU\_energy\_scone } & $0.15$\\
523min $E_{T}^\textrm{tower}$ & {\verb JET_M_seed } & $1.0$~GeV\\
524$C_{\tau}$ & \texttt{TAU\_energy\_frac} & $0.95$\\
525\multicolumn{3}{l}{\textbf{Tracking isolation}} \\
526$R^\textrm{tracks}$ & \texttt{TAU\_track\_scone} & $0.4$\\
527min $p_T^\textrm{tracks}$ & \texttt{PTAU\_track\_pt } & $2$ GeV$/c$\\
528\multicolumn{3}{l}{\textbf{$\tau$-jet candidate}} \\
529$\min p_T$ & \texttt{TAUJET\_pt} & $10$ GeV$/c$\\
530\hline
531\end{tabular}
532\label{tab:tauRef}
533\end{center}
534\end{table}
535
536
537\subsubsection*{Electromagnetic collimation}
538
539To use the narrowness of the $\tau$-jet, the \textit{electromagnetic collimation} $C_{\tau}$ 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.
540To be taken into account, a calorimeter tower should have a transverse energy $E_T^\textrm{tower}$ above a given threshold.
541A large fraction of the jet energy is expected in this small cone. This fraction, or \textit{collimation factor}, is represented in Fig.~\ref{fig:tau2} for the default values (see Tab.~\ref{tab:tauRef}).
542
543\begin{figure}[!h]
544\begin{center}
545%\includegraphics[width=\columnwidth]{Tau2}
546\includegraphics[width=\columnwidth]{fig6}
547\caption{Distribution of the electromagnetic collimation $C_\tau$ variable for true $\tau$-jets, normalised to unity. This distribution is shown for associated $WH$ photoproduction~\citep{bib:whphotoproduction}, where the Higgs boson decays into a $W^+ W^-$ pair. Each $W$ boson decays into a $\ell \nu_\ell$ pair, where $\ell = e, \mu, \tau$.
548Events generated with \textsc{MadGraph/MadEvent}~\citep{bib:mgme}.
549Final state hadronisation is performed by \textsc{Pythia}~\citep{bib:pythia}.
550Histogram entries correspond to true $\tau$-jets, matched with generator-level data. }
551\label{fig:tau2}
552\end{center}
553\end{figure}
554
555\subsubsection*{Tracking isolation}
556
557The tracking isolation for the $\tau$ identification requires that the number of tracks associated to particles with significant transverse momenta is one and only one in a cone of radius $R^\textrm{tracks}$ ($3-$prong $\tau$-jets are dropped).
558This cone should be entirely incorporated into the tracker to be taken into account. Default values of these parameters are given in Tab.~\ref{tab:tauRef}.
559
560
561
562\begin{figure}[!h]
563\begin{center}
564%\includegraphics[width=\columnwidth]{Tau1}
565\includegraphics[width=\columnwidth]{fig7}
566\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}.
567Histogram entries correspond to true $\tau$-jets, matched with generator-level data.}
568\label{fig:tau1}
569\end{center}
570\end{figure}
571
572
573\subsubsection*{Purity}
574Once 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 $66\%$.
575
576\subsection{Missing transverse energy}
577In an ideal detector, momentum conservation imposes the transverse momentum of the observed final state $\overrightarrow{p_T}^\textrm{obs}$ to be equal to the $\overrightarrow{p_T}$ vector sum of the invisible particles, written $\overrightarrow{p_T}^\textrm{miss}$.
578\begin{equation}
579\overrightarrow{p_T} = \left(
580\begin{array}{c}
581p_x\\
582p_y\\
583\end{array}
584\right)
585~ \textrm{and} ~
586\left\{
587\begin{array}{l}
588 p_x^\textrm{miss} = - p_x^\textrm{obs} \\
589 p_y^\textrm{miss} = - p_y^\textrm{obs} \\
590\end{array}
591\right.
592\end{equation}
593The \textit{true} missing transverse energy, i.e.\ at generator-level, is calculated as the opposite of the vector sum of the transverse momenta of all visible particles -- or equivalently, to the vector sum of invisible particle transverse momenta.
594In a real experiment, calorimeters measure energy and not momentum. Any problem affecting the detector (dead channels, misalignment, noisy towers, cracks) worsens directly the measured missing transverse energy $\overrightarrow {E_T}^\textrm{miss}$. In this document, \textsc{met} is based on the calorimetric towers and only muons and neutrinos are not taken into account for its evaluation\footnote{However, as tracks and calorimetric towers are available in the output file, the missing transverse energy can always be reprocessed a posteriori }:
595\begin{equation}
596\overrightarrow{E_T}^\textrm{miss} = - \sum^\textrm{towers}_i \overrightarrow{E_T}(i)
597\end{equation}
598
599
600\section{Trigger emulation}
601
602New physics in collider experiment are often characterised in phenomenology by low cross-section values, compared to the Standard Model (\textsc{sm}) processes. %For instance at the \textsc{lhc} ($\sqrt{s}=14~\textrm{TeV}$), the cross-section of inclusive production of $b \bar b$ pairs is expected to be $10^7~\textrm{nb}$, or inclusive jets at $100~\textrm{nb}$ ($p_T > 200~\textrm{GeV}/c$), while Higgs boson cross-section within the \textsc{sm} can be as small as $2 \times 10^{-3}~\textrm{nb}$ ($pp \rightarrow WH$, $m_H=115~\textrm{GeV}/c^2$).
603
604%High statistics are required for data analyses, consequently imposing high luminosity, i.e.\ a high collision rate.
605As only a tiny fraction of the observed events can be stored for subsequent \textit{offline} analyses, a very large data rejection factor should be applied directly as the events are produced.
606This data selection is supposed to reject only well-known \textsc{sm} events\footnote{However, some bandwidth is allocated to minimum-bias and/or zero-bias (``random'') triggers that stores a small fraction of the events without any selection criteria.}.
607Dedicated algorithms of this \textit{online} selection, or \textit{trigger}, should be fast and very efficient for data rejection, in order to preserve the experiment output bandwidth. They must also be as inclusive as possible to avoid loosing interesting events.
608
609Most of the usual trigger algorithms select events containing objects (i.e.\ jets, particles, \textsc{met}) with an energy scale above some threshold. This is often expressed in terms of a cut on the transverse momentum of one or several objects of the measured event. Logical combinations of several conditions are also possible. For instance, a trigger path could select events containing at least one jet and one electron such as $p_T^\textrm{jet} > 100~\textrm{GeV}/c$ and $p_T^e > 50~\textrm{GeV}/c$.
610
611A trigger emulation is included in \textsc{Delphes}, using a fully parametrisable \textit{trigger table}\footnote{\texttt{[code] }The trigger card is the \texttt{data/TriggerCard.dat} file.}. When enabled, this trigger is applied on analysis-object data.
612In a real experiment, the online selection is often divided into several steps (or \textit{levels}).
613This splits the overall reduction factor into a product of smaller factors, corresponding to the different trigger levels.
614This is related to the architecture of the experiment data acquisition chain, with limited electronic buffers requiring a quick decision for the first trigger level.
615First-level triggers are then fast and simple but based only on partial data as not all detector front-ends are readable within the decision latency.
616Higher level triggers are more complex, of finer-but-not-final quality and based on full detector data.
617
618Real triggers are thus intrinsically based on reconstructed data with a worse resolution than final analysis data.
619On the contrary, same data are used in \textsc{Delphes} for trigger emulation and for final analyses.
620
621\section{Validation}
622
623\textsc{Delphes} performs a fast simulation of a collider experiment.
624Its performances in terms of computing time and data size are directly proportional to the number of simulated events and on the considered physics process. As an example, $10,000$ $pp \rightarrow t \bar t X$ events are processed in $110~\textrm{s}$ on a regular laptop and use less than $250~\textrm{MB}$ of disk space.
625The quality and validity of the output are assessed by comparing to resolution of the reconstructed data to the \textsc{cms} detector expectations.
626
627Electrons and muons are by construction equal to the experiment designs, as the Gaussian smearing of their kinematics properties is defined according to their resolutions.
628Similarly, the $b$-tagging efficiency (for real $b$-jets) and misidentification rates (for fake $b$-jets) are taken from the expected values of the experiment.
629Unlike these simple objects, jets and missing transverse energy should be carefully cross-checked.
630
631\subsection{Jet resolution}
632
633The 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 for its validation, both for \textsc{cms}- and \textsc{atlas}-like detectors.
634This validation is based on $pp \rightarrow gg$ events produced with \textsc{MadGraph/MadEvent} and hadronised using \textsc{Pythia}~\citep{bib:mgme,bib:pythia}.
635
636For a \textsc{cms}-like detector, a similar procedure as the one explained in public results is applied here.
637The events were arranged in $14$ bins of gluon transverse momentum $\hat{p}_T$. In each $\hat{p}_T$ bin, every jet in \textsc{Delphes} is matched to the closest jet of generator-level particles, using the spatial separation between the two jet axes
638\begin{equation}
639\Delta R = \sqrt{ \big(\eta^\textrm{rec} - \eta^\textrm{MC} \big)^2 + \big(\phi^\textrm{rec} - \phi^\textrm{MC} \big)^2}<0.25.
640\end{equation}
641The jets made of generator-level particles, here referred as \textit{MC jets}, are obtained by applying the algorithm to all particles considered as stable after hadronisation.
642Jets produced by \textsc{Delphes} and satisfying the matching criterion are called hereafter \textit{reconstructed jets}.
643All jets are computed with the clustering algorithm (\textsc{jetclu}) with a cone radius $R$ of $0.7$.
644
645The ratio of the transverse energies of every reconstructed jet $E_T^\textrm{rec}$ to its corresponding \textsc{mc} jet $E_T^\textrm{MC}$ is calculated in each $\hat{p}_T$ bin.
646The $E_T^\textrm{rec}/E_T^\textrm{MC}$ histogram is fitted with a Gaussian distribution in the interval \mbox{$\pm 2$~\textsc{rms}} centred around the mean value.
647The resolution in each $\hat{p}_T$ bin is obtained by the fit mean $\langle x \rangle$ and variance $\sigma^2(x)$:
648\begin{equation}
649%\frac{\sigma(R_{jet})}{\langle R_{jet} \rangle }=
650\frac{\sigma \Big (\frac{E_T^\textrm{rec}}{E_T^\textrm{MC}} \Big)_\textrm{fit}}{ \Big \langle \frac{E_T^\textrm{rec}}{E_T^\textrm{MC}} \Big \rangle_\textrm{fit}}~
651\Big( \hat{p}_T(i) \Big)\textrm{, for all }i.
652\end{equation}
653
654\begin{figure}[!h]
655\begin{center}
656%\includegraphics[width=\columnwidth]{resolutionJet}
657\includegraphics[width=\columnwidth]{fig8}
658\caption{Resolution of the transverse energy of reconstructed jets $E_T^\textrm{rec}$ as a function of the transverse energy of the closest jet of generator-level particles $E_T^\textrm{MC}$, in a \textsc{cms}-like detector. The jets events are reconstructed with the \textsc{jetclu} clustering algorithm with a cone radius of $0.7$. The maximum separation between the reconstructed and \textsc{mc}-jets is $\Delta R= 0.25$. Dotted line is the fit result for comparison to the \textsc{cms} resolution~\citep{bib:cmsjetresolution}, in blue. The $pp \rightarrow gg$ dijet events have been generated with \textsc{MadGraph/MadEvent} and hadronised with \textsc{Pythia}.}
659\label{fig:jetresolcms}
660\end{center}
661\end{figure}
662
663The resulting jet resolution as a function of $E_T^\textrm{MC}$ is shown in Fig.~\ref{fig:jetresolcms}.
664This distribution is fitted with a function of the following form:
665\begin{equation}
666\frac{a}{E_T^\textrm{MC}}\oplus \frac{b}{\sqrt{E_T^\textrm{MC}}}\oplus c,
667\label{eq:fitresolution}
668\end{equation}
669where $a$, $b$ and $c$ are the fit parameters.
670It is then compared to the resolution published by the \textsc{cms} collaboration~\citep{bib:cmsjetresolution}. The resolution curves from \textsc{Delphes} and \textsc{cms} are in good agreement.
671
672Similarly, the jet resolution is evaluated for an \textsc{atlas}-like detector. The $pp \rightarrow gg$ events are here arranged in $8$ adjacent bins in $p_T$. A $k_T$ reconstruction algorithm with $R=0.6$ is chosen and the maximal matching distance between the \textsc{mc}-jets and the reconstructed jets is set to $\Delta R=0.2$. The relative energy resolution is evaluated in each bin by:
673\begin{equation}
674\frac{\sigma(E)}{E} = \sqrt{~~ \Bigg \langle ~\Bigg( \frac{E^\textrm{rec} - E^\textrm{MC}}{E^\textrm{rec}} \Bigg)^2 ~ \Bigg \rangle ~ - ~ \Bigg \langle \frac{E^\textrm{rec} - E^\textrm{MC}}{ E^\textrm{rec} } \Bigg \rangle^2}.
675\end{equation}
676
677Figure~\ref{fig:jetresolatlas} shows a good agreement between the resolution obtained with \textsc{Delphes}, the result of the fit with Equation~\ref{eq:fitresolution} and the corresponding curve provided by the \textsc{atlas} collaboration~\citep{bib:ATLASresolution}.
678
679\begin{figure}[!h]
680\begin{center}
681\includegraphics[width=\columnwidth]{fig8b}
682\caption{Relative energy resolution of reconstructed jets as a function of the energy of the closest jet of generator-level particles $E^\textrm{MC}$, in an \textsc{atlas}-like detector. The jets are reconstructed with the $k_T$ algorithm with a radius $R=0.6$. The maximal matching distance between \textsc{mc}- and reconstructed jets is $\Delta R=0.2$. Only central jets are considered ($|\eta|<0.5$). Dotted line is the fit result for comparison to the \textsc{atlas} resolution~\citep{bib:ATLASresolution}, in blue. The $pp \rightarrow gg$ di-jet events have been generated with \textsc{MadGraph/MadEvent} and hadronised with \textsc{Pythia}.}
683\label{fig:jetresolatlas}
684\end{center}
685\end{figure}
686
687
688\subsection{MET resolution}
689
690All major detectors at hadron colliders have been designed to be as much hermetic as possible in order to detect the presence of one or more neutrinos and/or new weakly interacting particles through apparent missing transverse energy.
691The resolution of the $\overrightarrow{E_T}^\textrm{miss}$ variable, as obtained with \textsc{Delphes}, is then crucial.
692
693The samples used to study the \textsc{met} performance are identical to those used for the jet validation.
694It is worth noting that the contribution to $E_T^\textrm{miss}$ from muons is negligible in the studied sample.
695The input samples are divided in five bins of scalar $E_T$ sums $(\Sigma E_T)$. This sum, called \textit{total visible transverse energy}, is defined as the scalar sum of transverse energy in all towers.
696The quality of the \textsc{met} reconstruction is checked via the resolution on its horizontal component $E_x^\textrm{miss}$.
697
698The $E_x^\textrm{miss}$ resolution is evaluated in the following way.
699The distribution of the difference between $E_x^\textrm{miss}$ in \textsc{Delphes} and at generator-level is fitted with a Gaussian function in each $(\Sigma E_T)$ bin. The fit \textsc{rms} gives the \textsc{met} resolution in each bin.
700The resulting value is plotted in Fig.~\ref{fig:resolETmis} as a function of the total visible transverse
701energy, for \textsc{cms}- and \textsc{atlas}-like detectors.
702
703\begin{figure}[!h]
704\begin{center}
705%\includegraphics[width=\columnwidth]{resolutionETmis}
706\includegraphics[width=\columnwidth]{fig9}
707\includegraphics[width=\columnwidth]{fig9b}
708\caption{$\sigma(E^\textrm{mis}_{x})$ as a function on the scalar sum of all towers ($\Sigma E_T$) for $pp \rightarrow gg$ events, for a \textsc{cms}-like detector (top) and an \textsc{atlas}-like detector (bottom), for di-jet events produced with \textsc{MadGraph/MadEvent} and hadronised with \textsc{Pythia}.}
709\label{fig:resolETmis}
710\end{center}
711\end{figure}
712
713The resolution $\sigma_x$ of the horizontal component of \textsc{met} is observed to behave like
714\begin{equation}
715\sigma_x = \alpha ~\sqrt{E_T}~~~(\mathrm{GeV}^{1/2}),
716\end{equation}
717where the $\alpha$ parameter depends on the resolution of the calorimeters.
718
719The \textsc{met} resolution expected for the \textsc{cms} detector for similar events is $\sigma_x = (0.6-0.7) ~ \sqrt{E_T} ~ \mathrm{GeV}^{1/2}$ with no pile-up\footnote{\textit{Pile-up} events are extra simultaneous $pp$ collision occurring at high-luminosity in the same bunch crossing.}~\citep{bib:cmsjetresolution}, which compares very well with the $\alpha = 0.63$ obtained with \textsc{Delphes}. Similarly, for an \textsc{atlas}-like detector, a value of $0.53$ is obtained by \textsc{Delphes} for the $\alpha$ parameter, while the experiment expects it in the range $[0.53~ ;~0.57]$~\citep{bib:ATLASresolution}.
720
721\subsection{\texorpdfstring{$\tau$}{\texttau}-jet efficiency}
722Due to the complexity of their reconstruction algorithm, $\tau$-jets have also to be checked.
723Table~\ref{tab:taurecoefficiency} lists the reconstruction efficiencies for the hadronic $\tau$-jets in the \textsc{cms} experiment and in \textsc{Delphes}. Agreement is good enough to validate also this reconstruction.
724
725\begin{table}[!h]
726\begin{center}
727\caption{Reconstruction efficiencies of $\tau$-jets in decays from $Z$ or $H$ bosons, in \textsc{Delphes} and in the \textsc{cms} experiment~\citep{bib:cmstauresolution}.\vspace{0.5cm}}
728\begin{tabular}{lll}
729\hline
730\multicolumn{2}{c}{\textsc{cms}} & \\
731$Z \rightarrow \tau^+ \tau^-$ & $38 \%$ & \\
732$H \rightarrow \tau^+ \tau^-$ & $36 \%$ & $m_H = 150~\textrm{GeV}/c^2$ \\
733$H \rightarrow \tau^+ \tau^-$ & $47 \%$ & $m_H = 300~\textrm{GeV}/c^2$ \\
734\multicolumn{2}{c}{\textsc{Delphes}} & \\
735$H \rightarrow \tau^+ \tau^-$ &$42 \%$ & $m_H = 140~\textrm{GeV}/c^2$ \\
736\hline
737\end{tabular}
738\label{tab:taurecoefficiency}
739\end{center}
740\end{table}
741
742
743\section{Visualisation}
744
745When performing an event analysis, a visualisation tool is useful to convey information about the detector layout and the event topology in a simple way. The \textit{Fast and Realistic OpenGL Displayer} \textsc{frog}~\citep{bib:Frog} has been interfaced in \textsc{Delphes}, allowing an easy display of the defined detector configuration\footnote{\texttt{[code] } To prepare the visualisation, the \texttt{FLAG\_frog} parameter should be equal to $1$.}.
746
747% \begin{figure}[!h]
748% \begin{center}
749% \includegraphics[width=\columnwidth]{Detector_Delphes_1}
750% \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), embedded into a solenoidal magnetic field.
751% It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
752% The outer layer of the central system (red) consist of a muon system.
753% In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
754% The actual detector granularity and extension is defined in the detector card.
755% The detector is assumed to be strictly symmetric around the beam axis (black line).
756% Additional forward detectors are not depicted.}
757% \label{fig:GenDet}
758% \end{center}
759% \end{figure}
760
761Two and three-dimensional representations of the detector configuration can be used for communication purposes, as they clearly illustrate the geometric coverage of the different detector subsystems.
762As an example, the generic detector geometry assumed in this paper is shown in Fig.~\ref{fig:GenDet3}
763%, \ref{fig:GenDet}
764 and~\ref{fig:GenDet2}.
765The extensions of the central tracking system, the central calorimeters and both forward calorimeters are visible.
766Note that only the geometrical coverage is depicted and that the calorimeter segmentation is not taken into account in the drawing of the detector. Moreover, both the radius and the length of each sub-detectors are just display parameters and are not relevant for the physics simulation.
767
768\begin{figure}[!h]
769\begin{center}
770%\includegraphics[width=\columnwidth]{Detector_Delphes_2b}
771\includegraphics[width=\columnwidth]{fig10}
772\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:GenDet3} are applied. Additional forward detectors are not depicted.}
773\label{fig:GenDet2}
774\end{center}
775\end{figure}
776
777Deeper understanding of interesting physics processes is possible by displaying the events themselves.
778The visibility of each set of objects ($e^\pm$, $\mu^\pm$, $\tau^\pm$, jets, transverse missing energy) is enhanced by a colour coding.
779Moreover, kinematics information of each object is visible by a simple mouse action.
780As an illustration, an associated photoproduction of a $W$ boson and a $t$ quark is shown in Fig.~\ref{fig:wt}.
781This corresponds to a $pp(\gamma p \rightarrow Wt)pX$ process, where the $Wt$ couple is induced by an incoming photon emitted by one of the colliding proton~\citep{bib:wtphotoproduction}.
782This leading proton survives after photon emission and is present in the final state.
783As the energy and virtuality of the emitted photon are low, the surviving proton does not leave the beam and escapes from the central detector without being detected.
784The experimental signature is a lack of hadronic activity in the forward hemisphere where the surviving proton escapes.
785The $t$ quark decays into a $W$ boson and a $b$ quark.
786Both $W$ bosons decay into leptons ($W \rightarrow \mu \nu_\mu$ and $W \rightarrow e \nu_e$).
787The balance between the missing transverse energy and the charged lepton pair is clear, as well as the presence of an empty forward region. It is interesting to notice that the reconstruction algorithms build a fake $\tau$-jet around the electron.
788
789\begin{figure}[!h]
790\begin{center}
791%%\includegraphics[width=\columnwidth]{Events_Delphes_1}
792%\includegraphics[width=\columnwidth]{DisplayWt}
793\includegraphics[width=\columnwidth]{fig11}
794\caption{Example of $pp(\gamma p \rightarrow Wt)pY$ event display in different orientations, with $t \rightarrow Wb$.
795One $W$ boson decays into a $\mu \nu_\mu$ pair and the second one into a $e \nu_e$ pair.
796The surviving proton leaves a forward hemisphere with no hadronic activity.
797The isolated muon is shown as the dark blue vector.
798Around the electron, in red, is reconstructed a fake $\tau$-jet (green vector surrounded by a blue cone), while the reconstructed missing energy (in grey) is very small. One jet is visible in one forward region, along the beamline axis, opposite to the direction of the escaping proton.}
799\label{fig:wt}
800\end{center}
801\end{figure}
802
803For comparison, Fig.~\ref{fig:gg} depicts an inclusive gluon pair production $pp \rightarrow ggX$.
804The event final state contains more jets, in particular along the beam axis, which is expected as the interacting protons are destroyed by the collision. Two muon candidates and large missing transverse energy are also visible.
805
806\begin{figure}[!h]
807\begin{center}
808%%\includegraphics[width=\columnwidth]{Events_Delphes_1}
809%\includegraphics[width=\columnwidth]{Displayppgg}
810\includegraphics[width=\columnwidth]{fig12}
811\caption{Example of inclusive gluon pair production $pp \rightarrow ggX$. Many jets are visible in the event, in particular along the beam axis. Two muons (in blue) are produced and the missing transverse energy is significant in this event (grey vector).}
812\label{fig:gg}
813\end{center}
814\end{figure}
815
816
817\section{Conclusion and perspectives}
818
819% \subsection{version 1}
820% We have described here the major features of the \textsc{Delphes} framework, introduced for the fast simulation of a collider experiment.
821% It has already been used for several phenomenological studies, in particular in photon interactions at the \textsc{lhc}.
822%
823% \textsc{Delphes} takes the output of event generators, in various formats, and yields analysis-object data.
824% The simulation applies the resolutions of central and forward detectors by smearing the kinematical properties of final state particles.
825% It yields tracks in a solenoidal magnetic field and calorimetric towers.
826% Realistic reconstruction algorithms are run, including the \textsc{FastJet} package, to produce collections of $e^\pm$, $\mu^\pm$, jets and $\tau$-jets. $b$-tag and missing transverse energy are also evaluated.
827% The output is validated by comparing to the \textsc{cms} expected performances.
828% A trigger stage can be emulated on the output data.
829% At last, event visualisation is possible through the \textsc{Frog} 3D event display.
830%
831%
832% \textsc{Delphes} has been developped using the parameters of the \textsc{cms} experiment but can be easily extended to \textsc{atlas} and other non-\textsc{lhc} experiments, as at Tevatron or at the \textsc{ilc}. Further developments include a more flexible design for the subdetector assembly and possibly the implementation of an event mixing module for pile-up event simulation.
833%
834%
835% \subsection{version 2}
836We have described here the major features of the \textsc{Delphes} framework, introduced for the fast simulation of a collider experiment. This framework is a tool meant for feasibility studies in phenomenology, gauging the observability of model predictions in collider experiments.
837
838\textsc{Delphes} takes as an input the output of event-generators and yields analysis-object data in the form of \texttt{TTree} in a \textsc{root} file.
839The simulation includes central and forward detectors to produce realistic observables using standard reconstruction algorithms.
840Moreover, the framework allows trigger emulation and 3D event visualisation.
841
842\textsc{Delphes} has been developed using the parameters of the \textsc{cms} experiment but can be easily extended to \textsc{atlas} and other non-\textsc{lhc} experiments, as at Tevatron or at the \textsc{ilc}. Further developments include a more flexible design for the subdetector assembly and possibly the implementation of an event mixing module for pile-up event simulation.
843
844This framework has already been used for several analyses, in particular in photon-induced interactions at the \textsc{lhc}~\citep{bib:wtphotoproduction, bib:papierquisortirajamais, bib:papiersimon}.
845
846
847\section*{Acknowledgements}
848\addcontentsline{toc}{section}{Acknowledgements}
849The authors would like to thank very warmly Vincent Lemaître for the interesting suggestions during the development of the software, as well as Jer\^ome de Favereau, Christophe Delaere, Muriel Vander Donckt and David d'Enterria for useful discussions and comments, and Loic Quertenmont for support in interfacing \textsc{Frog}. We are also really grateful to Alice Dechambre and Simon de Visscher for being beta testers of the complete package.
850Part of this work was supported by the Belgian Federal Office for Scientific, Technical and Cultural Affairs through the Interuniversity Attraction Pole P6/11.
851
852
853\begin{thebibliography}{99}
854\addcontentsline{toc}{section}{References}
855
856\bibitem{bib:Delphes} \textsc{Delphes}, \href{http://www.fynu.ucl.ac.be/delphes.html}{www.fynu.ucl.ac.be/delphes.html}
857%hepforge:
858\bibitem{bib:stdhep} L.A. Garren, M. Fischler, \href{http://cepa.fnal.gov/psm/stdhep/c++}{cepa.fnal.gov/psm/stdhep/c++}
859\bibitem{bib:hepmc} M. Dobbs and J.B. Hansen, \textbf{Comput. Phys. Commun.} \href{http://dx.doi.org/10.1016/S0010-4655(00)00189-2}{134 (2001) 41}.
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861\bibitem{bib:Root} %\textsc{Root}, \textit{An Object Oriented Data Analysis Framework},
862R. Brun, F. Rademakers, Nucl. Inst. \& Meth. in \textbf{Phys. Res. A} \href{http://dx.doi.org/10.1016/S0168-9002(97)00048-X}{389 (1997) 81-86}.
863\bibitem{bib:ExRootAnalysis} %\textit{The} \textsc{ExRootAnalysis} \textit{analysis steering utility},
864P. Demin, (2006), unpublished. Now part of \textsc{MadGraph/MadEvent}.
865\bibitem{bib:cmsjetresolution} The CMS Collaboration, \textbf{CERN/LHCC} \href{http://documents.cern.ch/cgi-bin/setlink?base=lhcc&categ=public&id=lhcc-2006-001}{2006-001}.
866\bibitem{bib:ATLASresolution} The ATLAS Collaboration, \textbf{CERN-OPEN} 2008-020, arXiv:\href{http://arxiv.org/abs/arxiv:0901.0512}{0901.0512v1}[hep-ex].
867\bibitem{bib:Hector} %\textsc{Hector}, \textit{a fast simulator for the transport of particles in beamlines},
868X. Rouby, J. de Favereau, K. Piotrzkowski, \textbf{JINST} \href{http://www.iop.org/EJ/abstract/1748-0221/2/09/P09005}{2 P09005 (2007)}.
869\bibitem{bib:FastJet} %\textit{The} \textsc{FastJet} \textit{package},
870M. Cacciari, G.P. Salam, \textbf{Phys. Lett. B} \href{http://dx.doi.org/10.1016/j.physletb.2006.08.037}{641 (2006) 57}.
871\bibitem{bib:jetclu} %\textsc{cdf} Run I legacy algorithm,
872F. Abe et al. (CDF Coll.), \textbf{Phys. Rev. D} \href{http://link.aps.org/doi/10.1103/PhysRevD.45.1448}{45 (1992) 1448}.
873\bibitem{bib:midpoint} %Run II Jet Physics: Proceedings of the Run II QCD and Weak Boson Physics Workshop,
874G.C. Blazey, et al., arXiv:\href{http://arxiv.org/abs/hep-ex/0005012}{0005012}[hep-ex].
875\bibitem{bib:SIScone} %\textsc{SIScone}, \textit{A practical Seedless Infrared-Safe Cone jet algorithm},
876G.P. Salam, G. Soyez, \textbf{JHEP} \href{http://dx.doi.org/10.1088/1126-6708/2007/05/086}{05 (2007) 086}.
877\bibitem{bib:ktjet} S. Catani, Y.L. Dokshitzer, M.H. Seymour, B.R. Webber, \textbf{Nucl. Phys. B} \href{http://dx.doi.org/10.1016/0550-3213(93)90166-M}{406 (1993) 187}; S.D. Ellis, D.E. Soper, \textbf{Phys. Rev. D} \href{http://link.aps.org/doi/10.1103/PhysRevD.48.3160}{48 (1993) 3160}.
878\bibitem{bib:aachen} Y.L. Dokshitzer, G.D. Leder, S. Moretti, B.R. Webber, \textbf{JHEP} \href{http://dx.doi.org/10.1088/1126-6708/1998/01/011}{08} \href{http://dx.doi.org/10.1088/1126-6708/1998/01/011}{(1997) 001}; M. Wobisch, T. Wengler, arXiv:\href{http://arxiv.org/abs/hep-ph/9907280}{9907280}[hep-ph].
879\bibitem{bib:antikt} %\textit{The anti-kt jet clustering algorithm},
880M. Cacciari, G.P. Salam, G. Soyez, \textbf{JHEP} \href{http://dx.doi.org/10.1088/1126-6708/2008/04/063}{04 (2008) 063}.
881\bibitem{bib:pdg} C. Amsler et al. (Particle Data Group), \textbf{Phys. Lett. B} \href{http://dx.doi.org/10.1016/j.physletb.2008.07.018}{667 (2008) 1}.
882\bibitem{bib:whphotoproduction} S. Ovyn, \textbf{Nucl. Phys. Proc. Suppl.} \href{http://dx.doi.org/10.1016/j.nuclphysbps.2008.07.034}{179-180 (2008) 269-276}.
883\bibitem{bib:mgme} %\textsc{MadGraph/MadEvent v4}, \textit{The New Web Generation},
884J. Alwall, et al., \textbf{JHEP} \href{http://dx.doi.org/10.1088/1126-6708/2007/09/028}{09 (2007) 028}.
885\bibitem{bib:pythia} %\textsc{Pythia 6.4}, \textit{Physics and Manual},
886T. Sjostrand, S. Mrenna, P. Skands, \textbf{JHEP} \href{http://dx.doi.org/10.1088/1126-6708/2006/05/026}{05 (2006) 026}.
887\bibitem{bib:cmstauresolution} %\textit{Study of $\tau$-jet identification in CMS},
888R. Kinnunen, A.N. Nikitenko, \textbf{CMS NOTE} \href{http://cdsweb.cern.ch/record/687274}{1997/002}.
889\bibitem{bib:Frog} L. Quertenmont, V. Roberfroid, \textbf{CMS CR} \href{http://cms.cern.ch/iCMS/jsp/openfile.jsp?type=CR&year=2009&files=CR2009_028.pdf}{2009/028}, arXiv:\href{http://arxiv.org/abs/0901.2718}{0901.2718v1}[hep-ex].
890\bibitem{bib:wtphotoproduction} J. de Favereau de Jeneret, S. Ovyn, \textbf{Nucl. Phys. Proc. Suppl.} \href{http://dx.doi.org/10.1016/j.nuclphysbps.2008.07.040}{179-180 (2008)} \href{http://dx.doi.org/10.1016/j.nuclphysbps.2008.07.040}{277-284}; S. Ovyn, J. de Favereau de Jeneret, \href{http://dx.doi.org/10.1393/ncb/i2008-10684-5}{Nuovo Cimento B}, arXiv:0806.4841[hep-ph].
891
892\bibitem{bib:papierquisortirajamais}J. de Favereau~et~al, \textbf{CP3-08-04} (2008), to be published in EPJ.
893
894%\bibitem{bib:papiersimon} ``Phenomenology of a twisted two-Higgs-doublet model'', Simon de Visscher, Jean-Marc Gerard, Michel Herquet, Vincent Lema\^itre, Fabio Maltoni, to be published.
895\bibitem{bib:papiersimon} S. de Visscher, J.M. Gerard, M. Herquet, V. Lema\^itre, F. Maltoni, arXiv:\href{http://arxiv.org/abs/0904.0705}{0904.0705}[hep-ph].
896
897\bibitem{bib:mcfio} P. Lebrun, L. Garren, Copyright (c) 1994-1995 Universities Research Association, Inc.
898
899
900\end{thebibliography}
901
902\onecolumn
903\appendix
904
905\section{User manual}
906
907The available \texttt{C++}-code is compressed in a zipped tar file which contains everything needed to run the \textsc{Delphes} package, assuming a running \textsc{root} installation. The package includes \texttt{ExRootAnalysis}~\citep{bib:ExRootAnalysis}, \textsc{Hector}~\citep{bib:Hector}, \textsc{FastJet}~\citep{bib:FastJet}, and \textsc{Frog}~\citep{bib:Frog}, as well as the conversion codes to read standard \mbox{\textsc{s}td\textsc{hep}} input files (\texttt{mcfio} and \texttt{stdhep})~\citep{bib:mcfio} and \textsc{HepMC}~\citep{bib:hepmc}.
908In order to visualise the events with the \textsc{Frog} software, a few additional external libraries may be required, as explained in \href{http://projects.hepforge.org/frog/}{http://projects.hepforge.org/frog/}.
909
910\subsection{Getting started}
911
912In order to run \textsc{Delphes} on your system, first download its sources and compile them:\\
913\texttt{wget http://www.fynu.ucl.ac.be/users/s.ovyn/Delphes/files/Delphes\_V\_*.tar.gz}\\
914Replace the \texttt{*} symbol by the proper version number\footnote{Refer to the download page on the \textsc{Delphes} website \href{http://www.fynu.ucl.ac.be/users/s.ovyn/Delphes/download.html}{http://www.fynu.ucl.ac.be/users/s.ovyn/Delphes/download.html}. Current version of \textsc{Delphes} for this manual is V 1.8 (July 2009)}.
915
916\begin{quote}
917\begin{verbatim}
918me@mylaptop:~$ tar -xvf Delphes_V_*.tar.gz
919me@mylaptop:~$ cd Delphes_V_*.*
920me@mylaptop:~$ ./genMakefile.tcl > Makefile
921me@mylaptop:~$ make
922\end{verbatim}
923\end{quote}
924Due to the large number of external utilities, the number of printed lines during the compilation can be high. The user should not pay attention to possible warning messages, which are due to the external packages used by \textsc{Delphes}. When compilation is completed, the following message is printed:
925\begin{quote}
926\begin{verbatim}
927me@mylaptop:~$ Delphes has been compiled
928me@mylaptop:~$ Ready to run
929\end{verbatim}
930\end{quote}
931
932\subsection{Running \textsc{Delphes} on your events}
933
934In this sub-appendix, we will explain how to use \textsc{Delphes} to perform a fast simulation of a general-purpose detector on your event files. The first step to use \textsc{Delphes} is to create the list of input event files (e.g.\ {\verb inputlist.list }). It is important to notice that all the files comprised in the list file should have the same of extension (\texttt{*.hep}, \texttt{*.lhe}, \texttt{*.hepmc} or \texttt{*.root}). In the simplest way to run \textsc{Delphes}, you need this input file and you need to specify the name of the output file that will contain the generator-level data (\texttt{GEN} tree), the analysis data objects after reconstruction (\texttt{Analysis} tree), and the results of the trigger emulation (\texttt{Trigger} tree).
935
936\begin{quote}
937\begin{verbatim}
938me@mylaptop:~$ ./Delphes inputlist.list OutputRootFileName.root
939\end{verbatim}
940\end{quote}
941
942\subsubsection{Setting up the configuration}
943
944The program is driven by two datacards (default cards are {\verb data/DetectorCard.dat } and {\verb data/TriggerCard.dat }) which allow the user to choose among a large spectrum of running conditions. Please note that if the user does not provide these datacards, the running will be done using the default parameters defined in the constructor of the class \texttt{RESOLution} (see next). If you choose a different detector or running configuration, you will need to edit the datacards accordingly. Detector and trigger cards are provided in the \texttt{data/} subdirectory for the \textsc{cms} and \textsc{atlas} experiments.
945
946\begin{enumerate}
947\item{\bf The detector card }
948It contains all pieces of information needed to run \textsc{Delphes}:
949\begin{itemize}
950 \item detector parameters, including calorimeter and tracking coverage and resolutions, transverse energy thresholds for object reconstruction and jet algorithm parameters.
951 \item six flags ({\verb FLAG_bfield }, {\verb FLAG_vfd }, {\verb FLAG_RP }, {\verb FLAG_trigger }, {\verb FLAG_frog } and {\verb FLAG_lhco }), should be set in order to configure the magnetic field propagation, the very forward detectors simulation, the use of very forward taggers, the trigger selection, the preparation for \textsc{Frog} display and the creation of an output file in \texttt{*.lhco} text format (respectively).
952 \end{itemize}
953
954If no datacard is provided by the user, the default smearing and running parameters are used:
955\begin{quote}
956\begin{verbatim}
957# Detector extension, in pseudorapidity units (|eta|)
958CEN_max_tracker 2.5 // Maximum tracker coverage
959CEN_max_calo_cen 1.7 // central calorimeter coverage
960CEN_max_calo_ec 3.0 // calorimeter endcap coverage
961CEN_max_calo_fwd 5.0 // forward calorimeter pseudorapidity coverage
962CEN_max_mu 2.4 // muon chambers pseudorapidity coverage
963
964# Energy resolution for electron/photon in central/endcap/fwd/zdc calos
965# \sigma/E = C + N/E + S/\sqrt{E}, E in GeV
966ELG_Scen 0.05 // S term for central ECAL
967ELG_Ncen 0.25 // N term
968ELG_Ccen 0.005 // C term
969ELG_Sec 0.05 // S term for ECAL endcap
970ELG_Nec 0.25 // N term
971ELG_Cec 0.005 // C term
972ELG_Sfwd 2.084 // S term for FCAL
973ELG_Nfwd 0. // N term
974ELG_Cfwd 0.107 // C term
975ELG_Szdc 0.70 // S term for ZDC
976ELG_Nzdc 0. // N term
977ELG_Czdc 0.08 // C term
978
979# Energy resolution for hadrons in central/endcap/fwd/zdc calos
980# \sigma/E = C + N/E + S/\sqrt{E}, E in GeV
981HAD_Scen 1.5 // S term for central HCAL
982HAD_Ncen 0. // N term
983HAD_Ccen 0.05 // C term
984HAD_Sec 1.5 // S term for HCAL endcap
985HAD_Nec 0. // N term
986HAD_Cec 0.05 // C term
987HAD_Sfwd 2.7 // S term for FCAL
988HAD_Nfwd 0. // N term
989HAD_Cfwd 0.13 // C term
990HAD_Szdc 1.38 // S term for ZDC
991HAD_Nzdc 0. // N term
992HAD_Czdc 0.13 // C term
993
994# Time resolution for ZDC/RP220/RP420
995ZDC_T_resolution 0 // in s
996RP220_T_resolution 0 // in s
997RP420_T_resolution 0 // in s
998
999# Muon smearing
1000MU_SmearPt 0.01 // transverse momentum Pt in GeV/c
1001
1002# Tracking efficiencies
1003TRACK_ptmin 0.9 // minimal pT
1004TRACK_eff 90 // efficiency associated to the tracking (%)
1005\end{verbatim}
1006\end{quote}
1007
1008\begin{quote}
1009\begin{verbatim}
1010# Calorimetric towers
1011TOWER_number 40
1012### list of the edges of each tower in eta for eta>0 assuming
1013###a symmetric detector in eta<0
1014### the list starts with the lower edge of the most central tower
1015### the list ends with the higher edged of the most forward tower
1016### there should be NTOWER+1 values
1017TOWER_eta_edges 0. 0.087 0.174 0.261 0.348 0.435 0.522 0.609 0.696 0.783
1018 0.870 0.957 1.044 1.131 1.218 1.305 1.392 1.479 1.566 1.653
1019 1.740 1.830 1.930 2.043 2.172 2.322 2.500 2.650 2.868 2.950
1020 3.125 3.300 3.475 3.650 3.825 4.000 4.175 4.350 4.525 4.700
1021 5.000
1022
1023### list of the tower size in phi (in degrees), assuming that all
1024### towers are similar in phi for a given eta value
1025### the list starts with the phi-size of the most central tower (eta=0)
1026### the list ends with the phi-size of the most forward tower
1027### there should be NTOWER values
1028TOWER_dphi 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10
1029 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 20 20
1030\end{verbatim}
1031\end{quote}
1032
1033\begin{quote}
1034\begin{verbatim}
1035# Thresholds for reconstructed objects, in GeV/c
1036PTCUT_elec 10.0
1037PTCUT_muon 10.0
1038PTCUT_jet 20.0
1039PTCUT_gamma 10.0
1040PTCUT_taujet 10.0
1041
1042# Thresholds for reconstructed objects in ZDC, E in GeV
1043ZDC_gamma_E 20
1044ZDC_n_E 50
1045
1046# Charged lepton isolation. Pt and Et in GeV
1047ISOL_PT 2.0 //minimal pt of tracks for isolation criteria
1048ISOL_Cone 0.5 //Cone for isolation criteria
1049ISOL_Calo_Cone 0.4 //Cone for calorimetric isolation
1050ISOL_Calo_ET 2.0 //minimal tower E_T for isolation criteria. 1E99 means "off"
1051ISOL_Calo_Grid 3 //Grid size (N x N) for calorimetric isolation
1052
1053# General jet variable
1054JET_coneradius 0.7 // generic jet radius
1055JET_jetalgo 1 // 1 for Cone algorithm,
1056 // 2 for MidPoint algorithm,
1057 // 3 for SIScone algorithm,
1058 // 4 for kt algorithm
1059 // 5 for Cambridge/Aachen algorithm
1060 // 6 for anti-kt algorithm
1061JET_seed 1.0 // minimum seed to start jet reconstruction, in GeV
1062JET_Eflow 1 // Energy flow: perfect energy assumed in the tracker coverage.
1063 // 1 is 'on' ; 0 is 'off'
1064\end{verbatim}
1065\end{quote}
1066
1067\begin{quote}
1068\begin{verbatim}
1069# Tagging definition
1070BTAG_b 40 // b-tag efficiency (%)
1071BTAG_mistag_c 10 // mistagging (%)
1072BTAG_mistag_l 1 // mistagging (%)
1073
1074# FLAGS
1075FLAG_bfield 1 //1 to run the bfield propagation else 0
1076FLAG_vfd 1 //1 to run the very forward detectors else 0
1077FLAG_RP 1 //1 to run the very forward detectors else 0
1078FLAG_trigger 1 //1 to run the trigger selection else 0
1079FLAG_frog 1 //1 to run the FROG event display
1080FLAG_lhco 1 //1 to run the LHCO
1081
1082# In case BField propagation allowed
1083TRACK_radius 129 // radius of the BField coverage, in cm
1084TRACK_length 300 // length of the BField coverage, in cm
1085TRACK_bfield_x 0 // X component of the BField, in T
1086TRACK_bfield_y 0 // Y component of the BField, in T
1087TRACK_bfield_z 3.8 // Z component of the BField, in T
1088
1089# Very forward detector extension, in pseudorapidity
1090# if allowed
1091VFD_min_zdc 8.3 // Zero-Degree neutral Calorimeter
1092VFD_s_zdc 140 // distance of the ZDC, from the IP, in [m]
1093\end{verbatim}
1094\end{quote}
1095
1096
1097\begin{quote}
1098\begin{verbatim}
1099#Hector parameters
1100RP_220_s 220 // distance of the RP to the IP, in meters
1101RP_220_x 0.002 // distance of the RP to the beam, in meters
1102RP_420_s 420 // distance of the RP to the IP, in meters
1103RP_420_x 0.004 // distance of the RP to the beam, in meters
1104RP_beam1Card data/LHCB1IR5_v6.500.tfs // beam optics file, beam 1
1105RP_beam2Card data/LHCB2IR5_v6.500.tfs // beam optics file, beam 2
1106RP_IP_name IP5 // tag for IP in Hector ; 'IP1' for ATLAS
1107RP_offsetEl_x 0.097 // horizontal separation between both beam, in meters
1108RP_offsetEl_y 0 // vertical separation between both beam, in meters
1109RP_offsetEl_s 120 // distance of beam separation point, from IP
1110RP_cross_x -500 // IP offset in horizontal plane, in micrometers
1111RP_cross_y 0 // IP offset in vertical plane, in micrometers
1112RP_cross_ang_x 142.5 // half-crossing angle in horizontal plane, in microrad
1113RP_cross_ang_y 0 // half-crossing angle in vertical plane, in microrad
1114
1115
1116# In case FROG event display allowed
1117NEvents_Frog 100
1118# Number of events to process
1119NEvents -1 // -1 means 'all'
1120
1121
1122# input PDG tables
1123PdgTableFilename data/particle.tbl // table with particle pid,mass,charge,...
1124\end{verbatim}
1125\end{quote}
1126
1127In general, energies, momenta and masses are expressed in GeV, GeV$/c$, GeV$/c^2$ respectively, and magnetic fields in T.
1128Geometrical extension are often referred in terms of pseudorapidity $\eta$, as the detectors are supposed to be symmetric in $\phi$. From version 1.8 onwards, the number of events to run is also be included in the detector card (\texttt{NEvents}). For version 1.7 and earlier, the parameters related to the calorimeter endcaps (\texttt{CEN\_max\_calo\_ec}, \texttt{ELG\_Sec}, \texttt{ELG\_Nec}, \texttt{ELG\_Cec}, \texttt{HAD\_Sec}, \texttt{HAD\_Nec} and \texttt{HAD\_Cec}) did not exist in the detector cards; in addition, some other variables had different names (\texttt{HAD\_Scen} was \texttt{HAD\_Sfcal}, \texttt{HAD\_Ncen} was \texttt{HAD\_Nfcal}, \texttt{HAD\_Ccen} was \texttt{HAD\_Cfcal}, \texttt{HAD\_Sfwd} was \texttt{HAD\_Shf}, \texttt{HAD\_Nfwd} was \texttt{HAD\_Nhf}, \texttt{HAD\_Cfwd} was \texttt{HAD\_Chf}). However, these cards are still completely compatible with new versions of \textsc{Delphes}. In such a case, the calorimeter endcaps are simply assumed to be located at the edge of the central calorimeter volumes, with the same resolution values.
1129
1130\item{\bf The trigger card }
1131
1132This card contains the definitions of all trigger-bits. Cuts can be applied on the transverse momentum $p_T$ of electrons, muons, jets, $\tau$-jets, photons and the missing transverse energy. The following codes should be used so that \textsc{Delphes} can correctly translate the input list of trigger-bits into selection algorithms:
1133
1134\begin{quote}
1135\begin{tabular}{ll}
1136{\it Trigger code} & {\it Corresponding object}\\
1137{\verb ELEC_PT } & electron \\
1138{\verb IElec_PT } & isolated electron \\
1139{\verb MUON_PT } & muon \\
1140{\verb IMuon_PT } & isolated muon \\
1141{\verb JET_PT } & jet \\
1142{\verb TAU_PT } & $\tau$-jet \\
1143{\verb ETMIS_PT } & missing transverse energy \\
1144{\verb GAMMA_PT } & photon \\
1145{\verb Bjet_PT } & $b$-jet \\
1146\end{tabular}
1147\end{quote}
1148
1149Each line in the trigger datacard is allocated to exactly one trigger-bit and starts with the name of the corresponding trigger.
1150Logical combination of several conditions is also possible. If the trigger-bit requires the presence of multiple identical objects, the order of their $p_T$ thresholds is very important: they must be defined in \textit{decreasing} order. The transverse momentum $p_T$ is expressed in \mbox{GeV/$c$}. Finally, the different requirements on the objects must be separated by a {\verb && } flag.
1151The default trigger card can be found in the data repository of \textsc{Delphes} (\texttt{data/TriggerCard.dat}), as well as for both \textsc{cms} and \textsc{atlas} experiments at the \textsc{lhc}.
1152An example of trigger table consistent with the previous rules is given here:
1153\begin{quote}
1154\begin{verbatim}
1155SingleJet >> JET_PT: '200'
1156DoubleElec >> ELEC_PT: '20' && ELEC_PT: '10'
1157SingleElec and Single Muon >> ELEC_PT: '20' && MUON_PT: '15'
1158\end{verbatim}
1159\end{quote}
1160\end{enumerate}
1161
1162\subsubsection{Running the code}
1163
1164First, create the detector and trigger cards (\texttt{data/DetectorCard.dat} and \texttt{data/TriggerCard.dat}). \\
1165Then, create a text file containing the list of input files that will be used by \textsc{Delphes} (with extension \texttt{*.lhe}, \texttt{*.hepmc}, \texttt{*.root} or \texttt{*.hep}).
1166To run the code, type the following command (in one line)
1167\begin{quote}
1168\begin{verbatim}
1169me@mylaptop:~$ ./Delphes inputlist.list OutputRootFileName.root
1170 data/DetectorCard.dat data/TriggerCard.dat
1171\end{verbatim}
1172\end{quote}
1173As a reminder, typing the \texttt{./Delphes} command simply displays the correct usage:
1174
1175\begin{quote}
1176\begin{verbatim}
1177me@mylaptop:~$ ./Delphes
1178 Usage: ./Delphes input_file output_file [detector_card] [trigger_card]
1179 input_list - list of files in Ntpl, StdHep, HepMC or LHEF format,
1180 output_file - output file.
1181 detector_card - Card containing resolution variables for detector simulation (optional)
1182 trigger_card - Card containing the trigger algorithms (optional)
1183\end{verbatim}
1184\end{quote}
1185
1186
1187\subsection{Getting the \textsc{Delphes} information}
1188
1189\subsubsection{Contents of the \textsc{Delphes} ROOT trees}
1190
1191The \textsc{Delphes} output file (\texttt{*.root}) is subdivided into three \textit{trees}, corresponding to generator-level data, analysis-object data and trigger output. These \textit{trees} are structures that organise the output data into \textit{branches} containing data (or \textit{leaves}) related with each others, like the kinematics properties ($E$, $p_x$, $\eta$, $\ldots$) of a given particle.
1192
1193Here is the exhaustive list of \textit{branches} availables in these \textit{trees}, together with their corresponding physical objet and \texttt{ExRootAnalysis} C++ class name:
1194\begin{quote}
1195\begin{tabular}{lll}
1196{\bf GEN \textsc{tree}} & &\\
1197~~~Particle & generator particles from \textsc{hepevt} & {\verb GenParticle }\\
1198\multicolumn{3}{l}{}\\
1199{\bf Trigger \textsc{tree}} & &\\
1200~~~TrigResult & Acceptance of different trigger-bits & {\verb TRootTrigger }\\
1201\multicolumn{3}{l}{}\\
1202{\bf Analysis \textsc{tree}} & & \\
1203~~~Tracks & Collection of tracks & {\verb TRootTracks }\\
1204~~~CaloTower & Calorimetric towers & {\verb TRootCalo }\\
1205~~~Electron & Collection of electrons & {\verb TRootElectron }\\
1206~~~Photon & Collection of photons & {\verb TRootPhoton }\\
1207~~~Muon & Collection of muons & {\verb TRootMuon }\\
1208~~~Jet & Collection of jets & {\verb TRootJet }\\
1209~~~TauJet & Collection of jets tagged as $\tau$-jets & {\verb TRootTauJet }\\
1210~~~ETmis & Transverse missing energy information & {\verb TRootETmis }\\
1211~~~ZDChits & Hits in the Zero Degree Calorimeters & {\verb TRootZdcHits }\\
1212~~~RP220hits & Hits in the first proton taggers & {\verb TRootRomanPotHits }\\
1213~~~FP420hits & Hits in the next proton taggers & {\verb TRootRomanPotHits }\\
1214\end{tabular}
1215\end{quote}
1216The third column shows the names of the corresponding classes to be written in a \textsc{root} tree.
1217The bin number in the unique leaf in the \texttt{trigger} tree (namely, \texttt{TrigResult.Accepted}) corresponds to the trigger number in the provided list. In addition, the result of the global trigger decision upon each event (i.e.\ the logical \texttt{OR} of all trigger conditions) is stored in the first bin (number 0) of this leaf.
1218In \texttt{Analysis} tree, all classes except \texttt{TRootTracks}, \texttt{TRootCalo}, \texttt{TRootTrigger}, \texttt{TRootETmis} and \texttt{TRootRomanPotHits} inherit from the class \texttt{TRootParticle} which includes the following data members (stored as \textit{leaves} in \textit{branches} of the \textit{trees}):
1219\begin{quote}
1220\begin{tabular}{ll}
1221\multicolumn{2}{l}{\textbf{Most common leaves}}\\
1222 \texttt{~~~float E; }&\texttt{ // particle energy in GeV }\\
1223 \texttt{~~~float Px; }&\texttt{ // particle momentum vector (x component) in GeV$/c$ }\\
1224 \texttt{~~~float Py; }&\texttt{ // particle momentum vector (y component) in GeV$/c$ }\\
1225 \texttt{~~~float Pz; }&\texttt{ // particle momentum vector (z component) in GeV$/c$ }\\
1226 \texttt{~~~float PT; }&\texttt{ // particle transverse momentum in GeV$/c$ }\\
1227 \texttt{~~~float Eta; }&\texttt{ // particle pseudorapidity }\\
1228 \texttt{~~~float Phi; }&\texttt{ // particle azimuthal angle in rad }\\
1229\end{tabular}
1230\end{quote}
1231
1232In addition to their kinematics, some additional properties are available for specific objects:
1233\begin{quote}
1234\begin{tabular}{ll}
1235\multicolumn{2}{l}{{\bf Leaves in the \texttt{Particle} branch (\texttt{GEN} tree)}} \\
1236 \texttt{~~~int PID; }&\texttt{ // particle HEP ID number }\\
1237 \texttt{~~~int Status; }&\texttt{ // particle status }\\
1238 \texttt{~~~int M1; }&\texttt{ // particle 1st mother }\\
1239 \texttt{~~~int M2; }&\texttt{ // particle 2nd mother }\\
1240 \texttt{~~~int D1; }&\texttt{ // particle 1st daughter }\\
1241 \texttt{~~~int D2; }&\texttt{ // particle 2nd daughter }\\
1242 \texttt{~~~float Charge; }&\texttt{ // electrical charge in units of e}\\
1243 \texttt{~~~float T; }&\texttt{ // particle vertex position (t component, in mm$/c$) }\\
1244 \texttt{~~~float X; }&\texttt{ // particle vertex position (x component, in mm) }\\
1245 \texttt{~~~float Y; }&\texttt{ // particle vertex position (y component, in mm) }\\
1246 \texttt{~~~float Z; }&\texttt{ // particle vertex position (z component, in mm) }\\
1247 \texttt{~~~float M; }&\texttt{ // particle mass in GeV$/c^2$}\\
1248\end{tabular}
1249\end{quote}
1250\begin{quote}
1251\begin{tabular}{ll}
1252\multicolumn{2}{l}{\textbf{Additional leaves in \texttt{Electron} and \texttt{Muon} branches} (\texttt{Analysis} tree)} \\
1253 \texttt{~~~int Charge } &\texttt{ // particle Charge }\\
1254 \texttt{~~~bool IsolFlag } &\texttt{ // stores the result of the tracking isolation test }\\
1255 \texttt{~~~float IsolPt } &\texttt{ // sum of all track pt in isolation cone (GeV/c) }\\
1256 \texttt{~~~float EtaCalo } &\texttt{ // particle pseudorapidity when entering the calo }\\
1257 \texttt{~~~float PhiCalo } &\texttt{ // particle azimuthal angle in rad when entering the calo }\\
1258 \texttt{~~~float EHoverEE }&\texttt{ // hadronic energy over electromagnetic energy }\\
1259 \texttt{~~~float EtRatio } &\texttt{ // calo Et in NxN-tower grid around the muon over the muon Et }\\
1260\end{tabular}
1261\end{quote}
1262\begin{quote}
1263\begin{tabular}{ll}
1264\multicolumn{2}{l}{\textbf{Additional leaf in the \texttt{Jet} branch (\texttt{Analysis} tree)}} \\
1265 \texttt{~~~bool Btag } &\texttt{ // stores the result of the b-tagging }\\
1266 \texttt{~~~int NTracks }&\texttt{ // number of tracks associated to the jet }\\
1267 \texttt{~~~float EHoverEE }&\texttt{ // hadronic energy over electromagnetic energy }\\
1268\end{tabular}
1269\end{quote}
1270\begin{quote}
1271\begin{tabular}{ll}
1272\multicolumn{2}{l}{\textbf{Leaves in the \texttt{Tracks} branch (\texttt{Analysis} tree)}}\\
1273 \texttt{~~~float Eta } &\texttt{ // pseudorapidity at the beginning of the track }\\
1274 \texttt{~~~float Phi } &\texttt{ // azimuthal angle at the beginning of the track }\\
1275 \texttt{~~~float EtaOuter }&\texttt{ // pseudorapidity at the end of the track }\\
1276 \texttt{~~~float PhiOuter }&\texttt{ // azimuthal angle at the end of the track }\\
1277 \texttt{~~~float PT } &\texttt{ // track transverse momentum in GeV$/c$ }\\
1278 \texttt{~~~float E } &\texttt{ // track energy in GeV }\\
1279 \texttt{~~~float Px } &\texttt{ // track momentum vector (x component) in GeV$/c$ }\\
1280 \texttt{~~~float Py } &\texttt{ // track momentum vector (x component) in GeV$/c$ }\\
1281 \texttt{~~~float Pz } &\texttt{ // track momentum vector (x component) in GeV$/c$ }\\
1282 \texttt{~~~float Charge } &\texttt{ // track charge in units of $e$ }\\
1283\end{tabular}
1284\end{quote}
1285\begin{quote}
1286\begin{tabular}{ll}
1287\multicolumn{2}{l}{\textbf{Leaves in the \texttt{CaloTower} branch (\texttt{Analysis} tree)}}\\
1288 \texttt{~~~float Eta } &\texttt{ // pseudorapidity of the tower }\\
1289 \texttt{~~~float Phi } &\texttt{ // azimuthal angle of the tower in rad }\\
1290 \texttt{~~~float E } &\texttt{ // tower energy in GeV }\\
1291 \texttt{~~~float E\_em } &\texttt{ // electromagnetic component of the tower energy in GeV}\\
1292 \texttt{~~~float E\_had } &\texttt{ // hadronic component of the tower energy in GeV}\\
1293 \texttt{~~~float ET } &\texttt{ // tower transverse energy in GeV }\\
1294& \\
1295\multicolumn{2}{l}{\textbf{Leaves in the \texttt{ETmis} branch (\texttt{Analysis} tree)}}\\
1296 \texttt{~~~float Phi } &\texttt{ // azimuthal angle of the transverse missing energy in rad }\\
1297 \texttt{~~~float ET } &\texttt{ // transverse missing energy in GeV }\\
1298 \texttt{~~~float Px } &\texttt{ // x component of the transverse missing energy in GeV }\\
1299 \texttt{~~~float Py } &\texttt{ // y component of the transverse missing energy in GeV }\\
1300\end{tabular}
1301\end{quote}
1302
1303The hits in very forward detector (\textsc{zdc, rp220, fp420}) have some common data. In particular, the \texttt{side} variable tells in which detector (left:-1 or right:+1 of the interaction point) the hit has been seen. Moreover, some generator level data is provided for information, as the correspondance with the contents of the \texttt{GEN} tree is not possible. These generator-level data correspond to the particle kinematics (energy, momentum, angle) and identification (pid).
1304
1305\begin{quote}
1306\begin{tabular}{ll}
1307\multicolumn{2}{l}{\textbf{Common leaves for ZDC, RP220, FP420}}\\
1308 \texttt{~~~float T } &\texttt{ // time of flight in s }\\
1309 \texttt{~~~float E } &\texttt{ // measured/smeared energy in GeV }\\
1310 \texttt{~~~int side }&\texttt{ // -1 or +1 }\\
1311\multicolumn{2}{l}{Generator level data}\\
1312 \texttt{~~~int pid; }&\texttt{ // particle ID }\\
1313 \texttt{~~~float genPx; }&\texttt{ // particle momentum vector (x component) in GeV$/c$ }\\
1314 \texttt{~~~float genPy; }&\texttt{ // particle momentum vector (y component) in GeV$/c$ }\\
1315 \texttt{~~~float genPz; }&\texttt{ // particle momentum vector (z component) in GeV$/c$ }\\
1316 \texttt{~~~float genPT; }&\texttt{ // particle transverse momentum in GeV$/c$ }\\
1317 \texttt{~~~float genEta; }&\texttt{ // particle pseudorapidity }\\
1318 \texttt{~~~float genPhi; }&\texttt{ // particle azimuthal angle in rad }\\
1319\end{tabular}
1320\end{quote}
1321
1322\begin{quote}
1323\begin{tabular}{ll}
1324\multicolumn{2}{l}{\textbf{Additional leaves in the \texttt{ZDChits} branch (\texttt{Analysis} tree)}}\\
1325 \texttt{~~~int hadronic\_hit } &\texttt{ // 0(is not hadronic) or 1(is hadronic) }
1326\end{tabular}
1327\end{quote}
1328
1329\begin{quote}
1330\begin{tabular}{ll}
1331\multicolumn{2}{l}{\textbf{Additional leaves in the \texttt{RP220hits} and \texttt{FP420hits} branches (\texttt{Analysis} tree)}}\\
1332 \texttt{~~~flaot S } &\texttt{ // detector position from IP in m } \\
1333 \texttt{~~~float X } &\texttt{ // hit horizontal position in m } \\
1334 \texttt{~~~float Y } &\texttt{ // hit vertical position in m } \\
1335 \texttt{~~~float TX } &\texttt{ // hit horizontal angle in rad } \\
1336 \texttt{~~~float TY } &\texttt{ // hit vertical angle in rad } \\
1337 \texttt{~~~float q2 } &\texttt{ // reconstructed momentum transfer in GeV$^2$ }
1338\end{tabular}
1339\end{quote}
1340The hit position is computed from the center of the beam position, not from the edge of the detector.
1341
1342
1343\subsection{Running an analysis on your \textsc{Delphes} events}
1344
1345To analyse the \textsc{root} ntuple produced by \textsc{Delphes}, the simplest way is to use the {\verb Analysis_Ex.cpp } code which is coming in the {\verb Examples } repository of \textsc{Delphes}. Note that all of this is optional and done to facilitate the analyses, as the output from \textsc{Delphes} is viewable with the standard \textsc{root} \texttt{TBrowser} and can be analysed using the \texttt{MakeClass} facility.
1346As an example, here is a simple overview of a \texttt{myoutput.root} file created by \textsc{Delphes}:
1347\begin{quote}
1348\begin{verbatim}
1349me@mylaptop:~$ root -l myoutput.root
1350root [0]
1351Attaching file myoutput.root as _file0...
1352root [1] .ls
1353TFile** myoutput.root
1354 TFile* myoutput.root
1355 KEY: TTree GEN;1 Analysis tree
1356 KEY: TTree Analysis;1 Analysis tree
1357 KEY: TTree Trigger;1 Analysis tree
1358root [2] TBrowser t;
1359root [3] Analysis->GetEntries()
1360(const Long64_t)200
1361root [4] GEN->GetListOfBranches()->ls()
1362OBJ: TBranchElement Event Event_ : 0 at: 0x9108f30
1363OBJ: TBranch Event_size Event_size/I : 0 at: 0x910cfd0
1364OBJ: TBranchElement Particle Particle_ : 0 at: 0x910c6b0
1365OBJ: TBranch Particle_size Particle_size/I : 0 at: 0x9111c58
1366root [5] Trigger->GetListOfLeaves()->ls()
1367OBJ: TLeafElement TrigResult_ TrigResult_ : 0 at: 0x90f90a0
1368OBJ: TLeafElement TrigResult.Accepted Accepted[TrigResult_] : 0 at: 0x90f9000
1369OBJ: TLeafI TrigResult_size TrigResult_size : 0 at: 0x90fb860
1370\end{verbatim}
1371\end{quote}
1372The \texttt{.ls} command lists the current keys available and in particular the three \textit{tree} names.
1373\mbox{\texttt{TBrowser t}} launches a browser and the \texttt{GetEntries()} method outputs the number of data in the corresponding \textit{tree}.
1374The list of \textit{branches} or \textit{leaves} can be displayed with the \texttt{GetListOfBranches()} and \texttt{GetListOfLeaves()} methods, pointing to the \texttt{ls()} one. In particular, it is possible to shown only parts of the output, using wildcard characters (\texttt{*}):
1375\begin{quote}
1376\begin{verbatim}
1377root [6] Analysis->GetListOfLeaves()->ls("*.E")
1378OBJ: TLeafElement Jet.E E[Jet_] : 0 at: 0xa08bc68
1379OBJ: TLeafElement TauJet.E E[TauJet_] : 0 at: 0xa148910
1380OBJ: TLeafElement Electron.E E[Electron_] : 0 at: 0xa1d8a50
1381OBJ: TLeafElement Muon.E E[Muon_] : 0 at: 0xa28ac80
1382OBJ: TLeafElement Photon.E E[Photon_] : 0 at: 0xa33cd88
1383OBJ: TLeafElement Tracks.E E[Tracks_] : 0 at: 0xa3cced0
1384OBJ: TLeafElement CaloTower.E E[CaloTower_] : 0 at: 0xa4ba188
1385OBJ: TLeafElement ZDChits.E E[ZDChits_] : 0 at: 0xa54a3c8
1386OBJ: TLeafElement RP220hits.E E[RP220hits_] : 0 at: 0xa61e648
1387OBJ: TLeafElement FP420hits.E E[FP420hits_] : 0 at: 0xa6d0920
1388\end{verbatim}
1389\end{quote}
1390
1391To draw a particular leaf, either double-click on the corresponding name in the \texttt{TBrowser} or use the \texttt{Draw} method of the corresponding \textit{tree}.
1392\begin{quote}
1393\begin{verbatim}
1394root [7] Trigger->Draw("TrigResult.Accepted");
1395\end{verbatim}
1396\end{quote}
1397Mathematical operations on several \textit{leaves} are possible within a given \textit{tree}, following the C++ syntax:
1398\begin{quote}
1399\begin{verbatim}
1400root [8] Analysis->Draw("Muon.Px * Muon.Px");
1401root [9] Analysis->Draw("sqrt(pow(Muon.E,2) - pow(Muon.Pz,2) + pow(Muon.PT,2))");
1402\end{verbatim}
1403\end{quote}
1404Finally, to prepare an deeper analysis, the \texttt{MakeClass} method is useful. It creates two files (\texttt{*.h} and \texttt{*.C}) with automatically generated code that allows the access to all branches and leaves of the corresponding tree:
1405\begin{quote}
1406\begin{verbatim}
1407root [10] Trigger->MakeClass()
1408Info in <TTreePlayer::MakeClass>: Files: Trigger.h and
1409 Trigger.C generated from TTree: Trigger
1410\end{verbatim}
1411\end{quote}
1412For more information, refer to ROOT documentation. Moreover, an example of code (based on the output of \begin{verbatim}MakeClass\end{verbatim}) is provided in the \texttt{Examples/} directory.
1413
1414To run the \texttt{Examples/Analysis\_Ex.cpp} code, the two following arguments are required: a text file containing the input \textsc{Delphes} \textsc{root} files to run, and the name of the output \textsc{root} file.
1415 \begin{quote}
1416\begin{verbatim}
1417me@mylaptop:~$ ./Analysis_Ex input_file.list output_file.root
1418\end{verbatim}
1419 \end{quote}
1420One can easily edit, modify and compile (\texttt{make}) changes in this file.
1421
1422\subsubsection{Adding the trigger information}
1423The \texttt{Examples/Trigger\_Only.cpp} code permits to run the trigger selection separately from the general detector simulation on output \textsc{Delphes} root files. A \textsc{Delphes} root file is mandatory as an input argument for the \texttt{Trigger\_Only} routine. The new \textit{tree} containing the trigger result data will be appended to this file.
1424The trigger datacard is also necessary. To run the code:
1425 \begin{quote}
1426\begin{verbatim}
1427me@mylaptop:~$ ./Trigger_Only input_file.root data/TriggerCard.dat
1428\end{verbatim}
1429 \end{quote}
1430
1431\subsection{Running the FROG event display}
1432
1433\begin{itemize}
1434\item If the { \verb FLAG_frog } was switched on in the smearing card, two files have been created during the running of \textsc{Delphes}: {\verb DelphesToFrog.vis } and {\verb DelphesToFrog.geom }. They contain all the needed pieces of information to run \textsc{frog}.
1435\item To display the events and the geometry, you first need to compile \textsc{Frog}. Go to the {\verb Utilities/FROG } and type {\verb make }. This compilation is done once for all, with this geometry (i.e.\ as long as the \texttt{*vis} and \texttt{*geom} files do not change).
1436\item Go back into the main directory and type
1437\begin{quote}
1438\texttt{me@mylaptop:~\$ ./Utilities/FROG/frog}
1439\end{quote}
1440\end{itemize}
1441
1442\subsection{LHCO file format}
1443 The \texttt{*lhco} file format is a text-\textsc{ascii} data format briefly discussed here. An exhaustive description is provided on \href{http://v1.jthaler.net/olympicswiki}{http://v1.jthaler.net/olympicswiki}. This section is based on this webpage.
1444Only final high-level objects are available in the \texttt{lhco} format, and their properties are arranged in columns. Each row corresponds to an object in the event and all events are written after each other. Comment-lines starts with a hash \texttt{\#} symbol.
1445
1446\begin{verbatim}
1447 # typ eta phi pt jmas ntrk btag had/em dum1 dum2
1448 0 57 0
1449 1 0 1.392 -2.269 19.981 0.000 0.000 0.000 4.605 0.000 0.000
1450 2 3 1.052 2.599 29.796 3.698 -1.000 0.000 0.320 0.000 0.000
1451 3 4 1.542 -2.070 84.308 41.761 7.000 0.000 1.000 0.000 0.000
1452 4 4 1.039 0.856 58.992 34.941 1.000 0.000 1.118 0.000 0.000
1453 5 4 1.052 2.599 29.796 3.698 0.000 0.000 0.320 0.000 0.000
1454 6 4 0.431 -2.190 22.631 3.861 0.000 0.000 1.000 0.000 0.000
1455 7 6 0.000 0.845 62.574 0.000 0.000 0.000 0.000 0.000 0.000
1456\end{verbatim}
1457Each row in an event starts with a unique number (i.e.\ in first column).
1458Row \texttt{0} contains the event number (here: \texttt{57}) and some trigger information (here: \texttt{0}. This very particular trigger encoding is not implemented in \textsc{Delphes}.).
1459Subsequent rows list the reconstructed high-level objects.
1460Each row is organised in columns, which details the object kinematics as well as more specific information, such as isolation criteria or $b$-tagging.
1461
1462\paragraph{1st column (\texttt{\#})}
1463The first column is the line number in the event. Each event starts with a 0 and contains as many lines as needed to list all high-level objects.
1464
1465\paragraph{2nd column (\texttt{typ})}
1466The second column gives the object identification code, or \textit{type}.
1467The different object types are:\\
1468\begin{tabular}{ll}
1469 \texttt{0}& for a photon ($\gamma$)\\
1470 \texttt{1}& for an electron ($e^\pm$)\\
1471 \texttt{2}& for a muon ($\mu^\pm$)\\
1472 \texttt{3}& for a hadronically-decaying tau ($\tau$-jet)\\
1473 \texttt{4}& for a jet\\
1474 \texttt{6}& for a missing transverse energy ($E_T^\textrm{miss}$)\\
1475\end{tabular}\\
1476Object type \texttt{5} is not defined.
1477An event always ends with the row corresponding to the missing transverse energy (type \texttt{6}).
1478
1479\paragraph{3rd (\texttt{eta}) and 4th (\texttt{phi}) columns}
1480The third and forth columns gives the object pseudorapidity $\eta$ and azimuth $\phi$. This latter quantity is expressed in radians, ranging from $-\pi$ to $\pi$.
1481
1482\paragraph{5th (\texttt{pt}) and 6th (\texttt{jmass}) columns}
1483The fifth column provides the object transverse momentum ($p_T$ in GeV$/c$) or energy ($E_T$ in GeV), while the invariant mass ($M$ in GeV/$c^2$) is in the sixth column.
1484
1485\paragraph{7th column (\texttt{ntrk})}
1486The seventh column reports the total number of tracks associated to the objects. This is \texttt{0} for photons, \texttt{$\pm$ 1} for charged leptons including taus (where the sign reports the lepton measured charge) and a positive number (\texttt{$\geq$ 0}) for jets.
1487
1488\paragraph{8th column (\texttt{btag})}
1489The eighth column tells whether a jet is tagged as a $b$-jet (\texttt{1}) or not (\texttt{0}).
1490This is always \texttt{0} for electrons, photons and missing transverse energy.
1491For muons, the closest jet in searched for, in terms of $\Delta R$. The integer-part of the quoted number is the row-number (column 1) of this jet.
1492
1493\paragraph{9th column (\texttt{had/em})}
1494For jets, electrons and photons, the ninth column is the ration between hadronic and electromagnetic energies in the calorimetric towers associated to the object. This is always \texttt{0} for missing transverse energy.
1495For muons, this number (\texttt{aaa.bb}) reports two values related to the muon isolation (section \ref{sec:isolation}). The integer part (\texttt{aaa}) is transverse momentum sum $P_T$ (in GeV/$c$) and the fractional part (\texttt{bb}) is the energy ratio $\rho_\mu$.
1496
1497
1498\paragraph{10th and 11th columns (\texttt{dum1} and \texttt{dum2})}
1499The last two columns are currently not used.
1500
1501\paragraph{Warning}
1502Inherently to the data format itself, the \texttt{*lhco} output contains only a fraction of the available data. Moreover, dealing with text file may have various drawbacks, such as the output file size and the time needed for its creation. Whenever possible, working on the \texttt{*root} output file should be preferred.
1503
1504\end{document}
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