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Changeset 560 in svn for trunk/paper


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Timestamp:
Apr 5, 2010, 12:54:57 AM (15 years ago)
Author:
Xavier Rouby
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commentaires VL: premiere vague

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trunk/paper/CommPhysComp
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  • trunk/paper/CommPhysComp/notes.tex

    r540 r560  
    3636
    3737\author{X. Rouby}
    38 %\author{X. Rouby\fnref{freiburg}}
    39 %\fntext[freiburg]{Now in Physikalisches Institut, Albert-Ludwigs-Universit\"at Freiburg}
    40 %\ead{xavier.rouby@cern.ch}
    41 
    4238\author{V. Lema\^itre}
    4339
    … …  
    4642        B-1348 Louvain-la-Neuve, Belgium}
    4743
    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-im-Breisgau, Germany}
    54 
    5544\begin{abstract}
    56 % It 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.
    57 % We introduce here a new \texttt{C++}-based framework, \textit{Delphes}, for fast simulation of
    58 % a general-purpose experiment. The simulation includes a tracking system, embedded into a magnetic field, calorimetry and a muon
    59 % system, and possible very forward detectors arranged along the beamline.
    60 % The 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.
    61 % The simulation of detector response takes into account the detector resolution, and usual reconstruction algorithms, such as 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 \textit{Hector} software. Finally, the \textsc{FROG} 2D/3D event display is used for visualisation of the collision final states.
    62 % An overview of \textit{Delphes} is given as well as a few \textsc{LHC} use-cases for illustration.\\ \\
    63 
    64 It is sometimes difficult to know whether theoretical predictions can be observed in a high energy collider experiment, especially when expected experimental signature involve jets and missing transverse energy.
    65 For this purpose, we have designed a new \texttt{C++}-based framework, \textit{Delphes}, performing a fast multipurpose detector response simulation.
    66 The simulation includes a tracking system, embedded into a magnetic field, calorimeters and a muon system, and possible very forward detectors arranged along the beamline.
     45
     46This paper presents a new \texttt{C++} framework, \textit{Delphes}, performing a
     47fast multipurpose detector response simulation.
     48The simulation includes a tracking system, embedded into a magnetic field,
     49calorimeters and a muon system, and possible very forward detectors arranged
     50along the beamline.
    6751The framework is interfaced to standard file formats (e.g.\ Les Houches Event File or \texttt{HepMC}) and outputs observables such as isolated leptons, missing transverse energy and collection of jets which can be used for dedicated analyses.
    6852The simulation of the detector response takes into account the effect of magnetic field, the granularity of the calorimeters and subdetector resolutions.
    … …  
    7256
    7357\textit{Preprint:} \texttt{CP3-09-01}, \texttt{arXiv:0903.2225 [hep-ph]}\\ \\
    74 %\includegraphics[scale=0.8]{DELPHESLogoSml}\\
    7558\includegraphics[scale=0.8]{fig0}\\
    7659{\bf PROGRAM SUMMARY}\\
    … …  
    8063{\em Current version:} 1.8                                    \\
    8164{\em Journal Reference:}                                      \\
    82   %Leave blank, supplied by Elsevier.
    8365{\em Catalogue identifier:}                                   \\
    84   %Leave blank, supplied by Elsevier.
    85 %{\em Licensing provisions:}                                   \\
    86   %enter "none" if CPC non-profit use license is sufficient.
    8766{\em Distribution format:}  tar.gz                            \\
    8867{\em Programming language:}  C++                              \\
    … …  
    128107\section{Introduction}
    129108
    130 Multipurpose detectors at high energy colliders are very complex systems. Their simulation is in general performed by means of the GEANT~\citep{bib:geant} package and final observables used for analyses usually require sophisticated reconstruction algorithms.
    131 
    132 
    133 This complexity is handled by large collaborations, and data and the expertise on reconstruction and simulation software are only available to their members. Precise 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.
    134 %\textcolor{blue}{Moreover, control of the detector calibration and alignment are crucial}.
    135 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 signal signatures and their associated backgrounds.
    136 
    137 A new framework, called \textit{Delphes}~\citep{bib:delphes}, is introduced here, for the fast simulation of a general-purpose collider experiment.
    138 Using this framework, observables such as cross-sections and efficiencies after event selection can be estimated for specific reactions.
    139 Starting from the output of event generators, the simulation of the detector response takes into account the subdetector resolutions, by smearing the kinematics of final-state particles (i.e. those considered as stable by the event generator
    140 \footnote{In the current \textit{Delphes} version, particles other than electrons ($e^\pm$), photons ($\gamma$), muons ($\mu^\pm$), neutrinos ($\nu_e$, $\nu_\mu$ and $\nu_\tau$) and neutralinos 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~\citep{qr:invisibleparticles}.}).
    141 % Tracks of charged particles and deposits of energy in calorimetric cells (or \textit{calotowers}) are then created. These two types of quantities are used for the reconstruction of jets and the isolation of leptons.
    142 
    143 \textit{Delphes} includes the most crucial experimental features, such as (Fig.~\ref{fig:FlowChart}):
     109Multipurpose detectors at high energy colliders are very complex systems.
     110Precise data analyses require a full detector simulation, including transport of
     111the primary and secondary particles through the detector material accounting for
     112the various detector inefficiencies, the dead material, the imperfections and
     113the geometrical details. Their simulation is in general performed by means of
     114the GEANT~\citep{bib:geant} package and final observables used for analyses
     115usually require sophisticated reconstruction algorithms.
     116
     117
     118This complexity can only be handled by large collaborations. Such simulation is
     119very complicated, technical and requires a large \texttt{CPU} power.
     120Phenomenological studies, looking for the observability of given signals,
     121require in general only fast but realistic estimates of the expected signal
     122signatures and their associated backgrounds.
     123
     124In this context, a new framework, called \textit{Delphes}~\citep{bib:delphes},
     125has been developped, for a fast simulation of a general-purpose collider
     126experiment.
     127Using this framework, observables such as cross-sections and efficiencies after
     128event selection can be estimated for specific reactions.
     129Starting from the output of event generators, the simulation of the detector
     130response takes into account the subdetector resolutions, by smearing the
     131kinematics of final-state particles (i.e. those considered as stable by the
     132event generator
     133\footnote{In the current \textit{Delphes} version, particles other than
     134electrons ($e^\pm$), photons ($\gamma$), muons ($\mu^\pm$), neutrinos ($\nu_e$,
     135$\nu_\mu$ and $\nu_\tau$) and neutralinos are simulated as hadrons for their
     136interactions with the calorimeters. The simulation of stable particles beyond
     137the Standard Model should therefore be handled with
     138care~\citep{qr:invisibleparticles}.}).
     139
     140
     141\textit{Delphes} includes the most crucial experimental features, such as
     142(Fig.~\ref{fig:FlowChart}):
    144143\begin{enumerate}
    145144\item the geometry of both central and forward detectors,
    146145\item the effect of magnetic field on tracks,
    147 \item the reconstruction of photons, leptons, jets, $b$-jets, $\tau$-jets and missing transverse energy,
     146\item the reconstruction of photons, leptons, jets, $b$-jets, $\tau$-jets and
     147missing transverse energy,
    148148\item a lepton isolation,
    149149\item a trigger emulation,
    … …  
    155155%\includegraphics[scale=0.78]{FlowDELPHES}
    156156\includegraphics[scale=0.78]{fig1}
    157 \caption{Flow chart describing the principles behind \textit{Delphes}. Event files coming from external Monte Carlo generators are read by a converter stage (top).
    158 The kinematics variables of the final-state particles are then smeared according to the tunable subdetector resolutions.
    159 Tracks are reconstructed in a simulated solenoidal magnetic field and calorimetric cells sample the energy deposits. Based on these low-level objects, dedicated algorithms are applied for particle identification, isolation and reconstruction.
    160 The transport of very forward particles to the near-beam detectors is also simulated.
    161 Finally, an output file is written, including generator-level and analysis-object data.
    162 If requested, a fully parametrisable trigger can be emulated. Optionally, the geometry and visualisation files for the 3D event display can also be produced.
    163 All user parameters are set in the \textit{Detector/Smearing Card} and the \textit{Trigger Card}. }
     157\caption{Flow chart describing the principles behind \textit{Delphes}. Event
     158files coming from external Monte Carlo generators are read by a converter stage
     159(top).
     160The kinematics variables of the final-state particles are then smeared
     161according to the tunable subdetector resolutions.
     162Tracks are reconstructed in a simulated solenoidal magnetic field and
     163calorimetric cells sample the energy deposits. Based on these low-level objects,
     164dedicated algorithms are applied for particle identification, isolation and
     165reconstruction.
     166The transport of very forward particles to the near-beam detectors is also
     167simulated.
     168Finally, an output file is written, including generator-level and
     169analysis-object data.
     170If requested, a fully parametrisable trigger can be emulated. Optionally, the
     171geometry and visualisation files for the 3D event display can also be produced.
     172All user parameters are set in the \textit{Detector/Smearing Card} and the
     173\textit{Trigger Card}. }
    164174\label{fig:FlowChart}
    165175\end{center}
    166176\end{figure*}
    167177
    168 Although \textit{Delphes} yields much realistic results than a simple ``parton-level" analysis, it has 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.
    169 
    170 Several common datafile formats can be used as input in \textit{Delphes} \citep{qr:inputformat},
    171 %\footnote{\texttt{[code] }See the \texttt{HEPEVTConverter}, \texttt{HepMCConverter}, \texttt{LHEFConverter} and \texttt{STDHEPConverter} classes.}.
    172 in order to process events from many different generators.
    173 % The standard Monte Carlo event structures \texttt{StdHEP}~\citep{bib:stdhep} and \texttt{HepMC}~\citep{bib:hepmc} can be used as an input. Besides, \textit{Delphes} can also provide detector response for events read in ``Les Houches Event Format'' (\textsc{LHEF}~\citep{bib:lhe}) and \texttt{*.root} files obtained from \texttt{*.hbook} using the \texttt{h2root} utility from the \textsc{ROOT} framework~\citep{bib:Root}.
    174 %Afterwards, \textit{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.
    175 \textit{Delphes} creates output data in a ROOT ntuple \citep{bib:Root}.
    176 This output contains a copy of the generator-level data, the analysis data objects after reconstruction, and possibly the results of the trigger emulation \citep{qr:outputformat}.
    177 In option
    178 %\footnote{\texttt{[code]} See the \texttt{FLAG\_LHCO} variable in the detector datacard. This text file format is shortly described in the user manual.},
    179 \textit{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~\citep{qr:lhco}.
     178Although \textit{Delphes} yields much realistic results than a simple
     179``parton-level" analysis, it has some limitations. Detector geometry is
     180idealised, being uniform, symmetric around the beam axis, and having no cracks
     181nor dead material. Secondary interactions, multiple scatterings, photon
     182conversion and bremsstrahlung are also neglected.
     183
     184Several common datafile formats can be used as input in \textit{Delphes}
     185\citep{qr:inputformat}, in order to process events from many different
     186generators. \textit{Delphes} creates output data in a ROOT ntuple
     187\citep{bib:Root}. This output contains a copy of the generator-level data, the
     188analysis data objects after reconstruction, and possibly the results of the
     189trigger emulation \citep{qr:outputformat}.
     190In option \textit{Delphes} can produce a reduced output file in \texttt{*.lhco}
     191text format, which is limited to the list of the reconstructed high-level
     192objects in the final states~\citep{qr:lhco}.
    180193
    181194
    … …  
    183196\section{Simulation of the detector response}
    184197
    185 The overall layout of the multipurpose detector simulated by \textit{Delphes} is shown in Fig.~\ref{fig:GenDet3}.
    186 It consists in a central tracking system (\textsc{TRACKER}) surrounded by an electromagnetic and a hadron calorimeters (\textsc{ECAL} and \textsc{HCAL}, each with a central region and two endcaps) and two forward calorimeters (\textsc{FCAL}).
    187 %  ensure a larger geometric coverage for the measurement of the missing transverse energy.
    188 Finally, a muon system (\textsc{MUON}) encloses the central detector volume.
    189 
    190 A detector card \citep{qr:detectorcard} allows a large spectrum of running conditions by modifying basic detector parameters, including calorimeter and tracking coverage and resolution, thresholds or jet algorithm parameters.
    191 Even if \textit{Delphes} has been developped for the simulation of general-purpose detectors at the \textsc{LHC} (namely, \textsc{CMS} and \textsc{ATLAS}), this input parameter file interfaces a flexible parametrisation for other cases, e.g.\ at future linear colliders~\citep{qr:datacards}.
    192 If no detector card is provided, predefined values based on ``typical'' \textsc{CMS} acceptances and resolutions are used.
    193 %\footnote{\texttt{[code] }Detector and trigger cards for the \textsc{ATLAS} and \textsc{CMS} experiments are also provided in \texttt{data/} directory.}.
    194 The geometrical coverage of the various subsystems used in the default configuration are summarised in Tab.~\ref{tab:defEta}.
    195 The detector is assumed to be strictly symmetric around the beam axis.
     198The overall layout of the multipurpose detector simulated by \textit{Delphes}
     199is shown in Fig.~\ref{fig:GenDet3}. It consists in a central tracking system
     200(\textsc{TRACKER}) surrounded by an electromagnetic and a hadron calorimeters
     201(\textsc{ECAL} and \textsc{HCAL}, each with a central region and two endcaps)
     202and two forward calorimeters (\textsc{FCAL}). Finally, a muon system
     203(\textsc{MUON}) encloses the central detector volume.
     204
     205A detector card \citep{qr:detectorcard} allows a large spectrum of running
     206conditions by modifying basic detector parameters, including calorimeter and
     207tracking coverage and resolution, thresholds or jet algorithm parameters.
     208Even if \textit{Delphes} has been developped for the simulation of
     209general-purpose detectors at the \textsc{LHC} (namely, \textsc{CMS} and
     210\textsc{ATLAS}), this input parameter file interfaces a flexible parametrisation
     211for other cases, e.g.\ at future linear colliders~\citep{qr:datacards}.
     212If no detector card is provided, predefined values based on ``typical''
     213\textsc{CMS} acceptances and resolutions are used. The geometrical coverage of
     214the various subsystems used in the default configuration are summarised in
     215Tab.~\ref{tab:defEta}. The detector is assumed to be strictly symmetric around
     216the beam axis.
    196217
    197218\begin{table}[t]
    198 % \begin{table*}[t]
    199219\begin{center}
    200220\caption{Default extension in pseudorapidity $\eta$ of the different subdetectors.
    201221Full azimuthal ($\phi$) acceptance is assumed.
    202222 \vspace{0.5cm}}
    203 % \begin{tabular}{llcc}
    204 % \hline
    205 % Subdetector & & $\eta$ & $\phi$ \\
    206 % \textsc{TRACKER}      & {\verb CEN_max_tracker }      & $[-2.5; 2.5]$         & $[-\pi ; \pi]$\\
    207 % \textsc{ECAL}, \textsc{HCAL} & {\verb CEN_max_calo_cen }& $[-1.7 ; 1.7]$      & $[-\pi ; \pi]$\\
    208 % \textsc{ECAL}, \textsc{HCAL} endcaps & {\verb CEN_max_calo_ec }& $[-3 ; -1.7] \& [1.7 ; 3]$   & $[-\pi ; \pi]$\\
    209 % \textsc{FCAL}                 & {\verb CEN_max_calo_fwd }     & $[-5 ; -3]$ \& $[3 ;5]$     & $[-\pi ; \pi]$\\
    210 % \textsc{MUON}                 & {\verb CEN_max_mu }           & $[-2.4 ; 2.4]$        & $[-\pi ; \pi]$\\ \hline
    211 % \end{tabular}
    212223\begin{tabular}{lcc}
    213224\hline
    … …  
    221232\label{tab:defEta}
    222233\end{center}
    223 % \end{table*}
    224234\end{table}
    225235
    … …  
    229239\includegraphics[width=\columnwidth]{fig2}
    230240\caption{
    231 Profile of layout of the generic detector geometry assumed in \textit{Delphes}. The innermost layer, close to the interaction point, is a central tracking system (pink).
    232 It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
    233 The outer layer of the central system (red) is muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
    234 % The 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).
     241Profile of layout of the generic detector geometry assumed in \textit{Delphes}.
     242The innermost layer, close to the interaction point, is a central tracking
     243system (pink). It is surrounded by a central calorimeter volume (green) with
     244both electromagnetic and hadronic sections. The outer layer of the central
     245system (red) is muon system. In addition, two end-cap calorimeters (blue) extend
     246the pseudorapidity coverage of the central detector.
    235247Additional forward detectors are not depicted.
    236248}
    … …  
    241253
    242254\subsection{Magnetic field}
    243 In addition to the subdetectors, the effects of a solenoidal magnetic field are simulated for the charged particles~\citep{qr:magneticfield}
    244 %\footnote{\texttt{[code] }See the \texttt{TrackPropagation} class.}
    245 . This affects the position at which charged particles enter the calorimeters and their corresponding tracks. The field extension is limited to the tracker volume and is in particular not applied for muon chambers. Howerver, this is not a limiting factor as the resolution applied for muon reconstruction is the one expected by the experiment, which consequently includes the effects of the magnetic field within the muon system.
     255In addition to the subdetectors, the effects of a solenoidal magnetic field are
     256simulated for the charged particles~\citep{qr:magneticfield}. This affects the
     257position at which charged particles enter the calorimeters and their
     258corresponding tracks. The field extension is limited to the tracker volume and
     259is in particular not applied for muon chambers. Howerver, this is not a limiting
     260factor as the resolution applied for muon reconstruction is the one expected by
     261the experiment, which consequently includes the effects of the magnetic field
     262within the muon system.
    246263
    247264
    248265\subsection{Tracks reconstruction}
    249266Every stable charged particle with a transverse momentum above some threshold and lying inside the detector volume covered by the tracker provides a track.
    250 By default, a track is assumed to be reconstructed with $90\%$ probability
    251 %\footnote{\texttt{[code]} The reconstruction efficiency is defined in the detector datacard by the \texttt{TRACKING\_EFF} term.}
    252 if its transverse momentum $p_T$ is higher than $0.9~\textrm{GeV}/c$ and if its pseudorapidity
    253 $|\eta| \leq 2.5$~\citep{qr:tracks}. No smearing is currently applied on tracks.
     267By default, a track is assumed to be reconstructed with $90\%$ probability if
     268its transverse momentum $p_T$ is higher than $0.9~\textrm{GeV}/c$ and if its
     269pseudorapidity $|\eta| \leq 2.5$~\citep{qr:tracks}. No smearing is currently
     270applied on tracks.
    254271
    255272
    256273\subsection{Calorimetric cells}
    257274
    258 The response of the calorimeters to energy deposits of incoming particles depends on their segmentation and resolution, as well as on the nature of the particles themselves. In CMS and ATLAS detectors, for instance, the calorimeter characteristics are not identical in every direction, with typically finer resolution and granularity in the central regions~\citep{bib:cmsjetresolution,bib:ATLASresolution}. It is thus very important to compute the exact coordinates of the entry point of the particles into the calorimeters, via the magnetic field calculations.
    259 
    260 The smallest unit for geometrical sampling of the calorimeters is a \textit{cell}; it segments the $(\eta,\phi)$ plane for the energy measurement. No longitudinal segmentation is available in the simulated calorimeters. \textit{Delphes} assumes that ECAL and HCAL have the same segmentations and that the detector is symmetric in $\phi$ and with respect to the $\eta=0$ plane~\citep{qr:calorimetriccells}.
    261 Fig.~\ref{fig:calosegmentation} illustrates the default calorimeter segmentation.
     275The response of the calorimeters to energy deposits of incoming particles
     276depends on their segmentation and resolution, as well as on the nature of the
     277particles themselves. In CMS and ATLAS detectors, for instance, the calorimeter
     278characteristics are not identical in every direction, with typically finer
     279resolution and granularity in the central
     280regions~\citep{bib:cmsjetresolution,bib:ATLASresolution}. It is thus very
     281important to compute the exact coordinates of the entry point of the particles
     282into the calorimeters, via the magnetic field calculations.
     283
     284The smallest unit for geometrical sampling of the calorimeters is a
     285\textit{cell}; it segments the $(\eta,\phi)$ plane for the energy measurement.
     286No longitudinal segmentation is available in the simulated
     287calorimeters. \textit{Delphes} assumes that ECAL and HCAL have the same
     288segmentations and that the detector is symmetric in $\phi$ and with respect to
     289the $\eta=0$ plane~\citep{qr:calorimetriccells}.
     290Fig.~\ref{fig:calosegmentation} illustrates the default calorimeter
     291segmentation.
    262292
    263293\begin{figure}[!ht]
    … …  
    284314\begin{table}[!h]
    285315\begin{center}
    286 \caption{Default values for the resolution of the central and forward calorimeters (for both electromagnetic and hadronic parts). Resolution is parametrised by the \textit{stochastic} ($S$), \textit{noise} ($N$) and \textit{constant} ($C$) terms (Eq.~\ref{eq:caloresolution})~\citep{qr:resolutionterms}.
    287 %The corresponding parameter name, in the detector card, is given.
     316\caption{Default values for the resolution of the central and forward
     317calorimeters (for both electromagnetic and hadronic parts). Resolution is
     318parametrised by the \textit{stochastic} ($S$), \textit{noise} ($N$) and
     319\textit{constant} ($C$) terms
     320(Eq.~\ref{eq:caloresolution})~\citep{qr:resolutionterms}.
    288321\vspace{0.5cm}}
    289322\begin{tabular}[!h]{lccc}
    290323\hline
    291 %\multicolumn{2}{c}{Resolution Term}   & Value\\\hline
    292324        & $S$ (GeV$^{1/2}$) & $N$ (GeV) & $C$ \\\hline
    293  %\multicolumn{4}{l}{\textsc{ECAL}} \\
    294325  ECAL            & $0.05$   & $0.25$ & $0.0055$ \\
    295  %\multicolumn{4}{l}{\textsc{ECAL}, end caps} \\
    296326  ECAL, end caps  & $0.05$  & $0.25$ & $0.0055$ \\
    297  %\multicolumn{4}{l}{\textsc{FCAL}, electromagnetic part} \\
    298327  FCAL, e.m. part & $2.084$ & $0$    & $0.107$ \\
    299  %\multicolumn{4}{l}{\textsc{HCAL}} \\
    300328  HCAL            & $1.5$   & $0$    & $0.05$\\
    301  %\multicolumn{4}{l}{\textsc{HCAL}, end caps} \\
    302329  HCAL, end caps  & $1.5$   & $0$    & $0.05$\\
    303  %\multicolumn{4}{l}{\textsc{FCAL}, hadronic part} \\
    304330  FCAL, had. part & $2.7$   & $0$    & $0.13$\\
    305331\hline
    … …  
    310336
    311337
    312 Electrons and photons leave their energy in the electromagnetic parts of the calorimeters (\textsc{ECAL} and \textsc{FCAL}, e.m.), while charged and neutral final-state hadrons interact with the hadronic parts (\textsc{HCAL} and \textsc{FCAL}, had.).
    313 Some 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 by the generators although they may decay before the calorimeters. The energy smearing of such particles is therefore 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
     338Electrons and photons leave their energy in the electromagnetic parts of the
     339calorimeters (\textsc{ECAL} and \textsc{FCAL}, e.m.), while charged and neutral
     340final-state hadrons interact with the hadronic parts (\textsc{HCAL} and
     341\textsc{FCAL}, had.).
     342Some long-living particles, such as the $K^0_s$ and $\Lambda$'s, with lifetime
     343$c\tau$ smaller than $10~\textrm{mm}$ are considered as stable particles by the
     344generators although they may decay before the calorimeters. The energy smearing
     345of such particles is therefore performed using the expected fraction of the
     346energy, determined according to their decay products, that would be deposited
     347into the \textsc{ECAL} ($E_{\textsc{ECAL}}$) and into the \textsc{HCAL}
     348($E_{\textsc{HCAL}}$). Defining $F$ as the fraction of the energy leading to a
     349\textsc{HCAL} deposit, the two energy values are given by
    314350\begin{equation}
    315351\left\{
    … …  
    320356\right.
    321357\end{equation}
    322 where $0 \leq F \leq 1$. The electromagnetic part is handled similarly as for electrons and photons.
    323 The 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, the energy fraction is $F$ is assumed to be $0.7$~\citep{qr:emhadratios}.\\
    324 
    325 
    326 No sharing between neighbouring cells is implemented when particles enter a cell very close to its geometrical edge. Due to the finite segmentation, the smearing, as defined in Eq.~\ref{eq:caloresolution}, is applied directly on the accumulated electromagnetic and hadronic energies of each calorimetric cell. The calorimetric cells enter in the calculation of the missing transverse energy (\textsc{MET}), and are used as input for the jet reconstruction algorithms.
     358where $0 \leq F \leq 1$. The electromagnetic part is handled similarly as for
     359electrons and photons. The resulting calorimetry energy measurement given after
     360the application of the smearing is then $E = E_{\textsc{HCAL}} +
     361E_{\textsc{ECAL}}$. For $K_S^0$ and $\Lambda$ hadrons, the energy fraction is
     362$F$ is assumed to be $0.7$~\citep{qr:emhadratios}.\\
     363
     364
     365No sharing between neighbouring cells is implemented when particles enter a
     366cell very close to its geometrical edge. Due to the finite segmentation, the
     367smearing, as defined in Eq.~\ref{eq:caloresolution}, is applied directly on the
     368accumulated electromagnetic and hadronic energies of each calorimetric cell. The
     369calorimetric cells enter in the calculation of the missing transverse energy
     370(\textsc{MET}), and are used as input for the jet reconstruction algorithms.
    327371
    328372
    … …  
    331375\section{High-level object reconstruction}
    332376
    333 The output file created by \textit{Delphes}~\citep{qr:analysistree} stores the final collections of particles ($e^\pm$, $\mu^\pm$, $\gamma$) and objects (light jets, $b$-jets, $\tau$-jets, $E_T^\textrm{miss}$). In addition, some detector data are added, such as tracks, calorimetric cells and hits in the very forward detectors (\textsc{ZDC}, \textsc{RP220} and \textsc{FP420}, see Sec.~\ref{sec:vfd}). While electrons, muons and photons are easily identified, other quantities are more difficult to evaluate as they rely on sophisticated algorithms (e.g. jets or missing energy).
    334 
    335 For most of these objects, their four-momentum and related quantities are directly accessible in \textit{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).
     377The output file created by \textit{Delphes}~\citep{qr:analysistree} stores the
     378final collections of particles ($e^\pm$, $\mu^\pm$, $\gamma$) and objects (light
     379jets, $b$-jets, $\tau$-jets, $E_T^\textrm{miss}$). In addition, some detector
     380data are added, such as tracks, calorimetric cells and hits in the very forward
     381detectors (\textsc{ZDC}, \textsc{RP220} and \textsc{FP420}, see
     382Sec.~\ref{sec:vfd}). While electrons, muons and photons are easily identified,
     383other quantities are more difficult to evaluate as they rely on sophisticated
     384algorithms (e.g. jets or missing energy).
     385
     386For most of these objects, their four-momentum and related quantities are
     387directly accessible in \textit{Delphes} output ($E$, $\vec{p}$, $p_T$, $\eta$
     388and $\phi$). Additional properties are available for specific objects (like the
     389charge and the isolation status for $e^\pm$ and $\mu^\pm$, the result of
     390application of $b$-tag for jets and time-of-flight for some detector hits).
    336391
    337392\subsection{Photon and charged lepton}
    338 From here onwards, \textit{electrons} refer to both positrons ($e^+$) and electrons ($e^-$), and $\textit{charged leptons}$ refer to electrons and muons ($\mu^\pm$), leaving out the $\tau^\pm$ leptons as they decay before being detected.
    339 
    340 The electron, muon and photon collections contains only the true final-state particles identified via the generator-data.
    341 In addition, these particles must pass fiducial cuts taking into account the magnetic field effects and some additional reconstruction cuts.
    342 
    343 Consequently, no fake candidates enter these collections. However, when needed, fake candidates can be added into the collections at the analysis level, when processing \textit{Delphes} output data. As effects like bremsstrahlung are not taken into account along the lepton propagation in the tracker, no clustering is needed for the electron reconstruction in \textit{Delphes}.
     393From here onwards, \textit{electrons} refer to both positrons ($e^+$) and
     394electrons ($e^-$), and $\textit{charged leptons}$ refer to electrons and muons
     395($\mu^\pm$), leaving out the $\tau^\pm$ leptons as they decay before being
     396detected.
     397
     398The electron, muon and photon collections contains only the true final-state
     399particles identified via the generator-data. In addition, these particles must
     400pass fiducial cuts taking into account the magnetic field effects and some
     401additional reconstruction cuts.
     402
     403Consequently, no fake candidates enter these collections. However, when needed,
     404fake candidates can be added into the collections at the analysis level, when
     405processing \textit{Delphes} output data. As effects like bremsstrahlung are not
     406taken into account along the lepton propagation in the tracker, no clustering is
     407needed for the electron reconstruction in \textit{Delphes}.
    344408
    345409\subsubsection*{Electrons and photons}
    346 Real electron ($e^\pm$) and photon candidates are associated to the final-state collections if they fall into the acceptance of the tracking system and have a transverse momentum above some threshold (default: $p_T > 10~\textrm{GeV}/c$).
    347 Assuming a good measurement of the track parameters in the real experiment, the electron energy can be reasonably recovered.
    348 \textit{Delphes} assumes a perfect algorithm for clustering and Brehmstrahlung recovery. Electron energy is smeared according to the resolution of the calorimetric cell where it points to, but independently from any other deposited energy is this cell.
     410Real electron ($e^\pm$) and photon candidates are associated to the final-state
     411collections if they fall into the acceptance of the tracking system and have a
     412transverse momentum above some threshold (default: $p_T > 10~\textrm{GeV}/c$).
     413Assuming a good measurement of the track parameters in the real experiment, the
     414electron energy can be reasonably recovered. \textit{Delphes} assumes a perfect
     415algorithm for clustering and Brehmstrahlung recovery. Electron energy is smeared
     416according to the resolution of the calorimetric cell where it points to, but
     417independently from any other deposited energy is this cell.
    349418Electrons and photons may create a candidate in the jet collection.
    350419
    351420\subsubsection*{Muons}
    352 Generator-level muons entering the muon detector acceptance (default: $-2.4 \leq \eta \leq 2.4$) and overpassing some threshold (default : $p_T > 10~\textrm{GeV}/c$) are considered as good candidates for analyses.
    353 The application of the detector resolution on the muon momentum depends on a Gaussian smearing of the $p_T$~\citep{qr:muonsmearing}.
    354 %\footnote{\texttt{[code]} See the \texttt{SmearMuon} method.}.
    355 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 \textit{Delphes} a better resolution than in a real detector.  At last, the particles which might leak out of the calorimeters into the muon systems (\textit{punch-through}) are not considered as muon candidates in \textit{Delphes}.
     421Generator-level muons entering the muon detector acceptance (default: $-2.4
     422\leq \eta \leq 2.4$) and overpassing some threshold (default : $p_T >
     42310~\textrm{GeV}/c$) are considered as good candidates for analyses.
     424The application of the detector resolution on the muon momentum depends on a
     425Gaussian smearing of the $p_T$~\citep{qr:muonsmearing}.
     426Neither $\eta$ nor $\phi$ variables are modified beyond the calorimeters: no
     427additional magnetic field is applied. Multiple scattering is neglected. This
     428implies that low energy muons have in \textit{Delphes} a better resolution than
     429in a real detector.  At last, the particles which might leak out of the
     430calorimeters into the muon systems (\textit{punch-through}) are not considered
     431as muon candidates in \textit{Delphes}.
    356432
    357433\subsubsection*{Charged lepton isolation}
    358434\label{sec:isolation}
    359435
    360 To improve the quality of the contents of the charged lepton collections, isolation criteria can be applied. This requires that electron or muon candidates are isolated in the detector from any other particle, within a small cone. In \textit{Delphes}, charged lepton isolation demands that there is no other charged particle with $p_T>2~\textrm{GeV}/c$ within a cone of $\Delta R = \sqrt{\Delta \eta^2 + \Delta \phi^2} <0.5$ centered on the cell associated to the charged lepton $\ell$, obviously taking the magnetic field into account.
     436To improve the quality of the contents of the charged lepton collections,
     437isolation criteria can be applied. This requires that electron or muon
     438candidates are isolated in the detector from any other particle, within a small
     439cone. In \textit{Delphes}, charged lepton isolation demands that there is no
     440other charged particle with $p_T>2~\textrm{GeV}/c$ within a cone of $\Delta R =
     441\sqrt{\Delta \eta^2 + \Delta \phi^2} <0.5$ centered on the cell associated to
     442the charged lepton $\ell$, obviously taking the magnetic field into account.
    361443
    362444The result (i.e.\ \textit{isolated} or \textit{not}) is added to the charged lepton measured properties.
    363445In addition, the sum $P_T$ of the transverse momenta of all tracks but the lepton one within the isolation cone is
    364446provided~\citep{qr:isolflag}:
    365 %\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.}
    366447$$ P_T = \sum_{i \neq \ell}^\textrm{tracks} p_T(i)$$
    367448
    368 No calorimetric isolation is applied, but the charged lepton collections contain also the ratio $\rho_\ell$ between (1) the sum of the transverse energies in all calorimetric cells in a $N \times N$ grid around the lepton, and (2) the lepton transverse momentum~\citep{qr:caloisolation}:
    369 %\footnote{\texttt{[code] }Calorimetric isolation parameters in the detector card are \texttt{ISOL\_Calo\_ET} and  \texttt{ISOL\_Calo\_Grid}.}:
    370 $$ \rho_\ell = \frac{\Sigma_i E_T(i)}{p_T(\ell)}~,~ i\textrm{ in }N \times N \textrm { grid centred on }\ell.$$
    371 
    372 
    373 % \subsubsection*{Forward neutrals}
    374 %
    375 % The 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 \textit{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 (def. $50$~GeV)~\citep{qr:fwdneutrals}.
    376 % %\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).
    377 
     449No calorimetric isolation is applied, but the charged lepton collections
     450contain also the ratio $\rho_\ell$ between (1) the sum of the transverse
     451energies in all calorimetric cells in a $N \times N$ grid around the lepton, and
     452(2) the lepton transverse momentum~\citep{qr:caloisolation}:
     453$$ \rho_\ell = \frac{\Sigma_i E_T(i)}{p_T(\ell)}~,~ i\textrm{ in }N \times N
     454\textrm { grid centred on }\ell.$$
    378455
    379456
    380457\subsection{Jet reconstruction}
    381458
    382 A realistic analysis requires a correct treatment of partons which have hadronised. Therefore, the most widely currently used jet algorithms have been integrated into the \textit{Delphes} framework using the FastJet tools\footnote{A more detailed description of the jet algorithms is given in the User Manual, in appendix.}.
    383 Six different jet reconstruction schemes are available~\citep{bib:FASTJET,qr:jetalgo}.
    384 %\footnote{\texttt{[code] }The choice is done by allocating the \texttt{JET\_jetalgo } input parameter in the detector card.}.
    385 % The first three belong to the cone algorithm class while the last three are using a sequential recombination scheme.
    386 For all of them, the calorimetric cells are used as inputs. Jet algorithms differ in their sensitivity to soft particles or collinear splittings, and in their computing speed performances.
     459A realistic analysis requires a correct treatment of partons which have
     460hadronised. Therefore, the most widely currently used jet algorithms have been
     461integrated into the \textit{Delphes} framework using the FastJet
     462tools\footnote{A more detailed description of the jet algorithms is given in the
     463User Manual, in appendix.}. Six different jet reconstruction schemes are
     464available~\citep{bib:FASTJET,qr:jetalgo}. For all of them, the calorimetric
     465cells are used as inputs. Jet algorithms differ in their sensitivity to soft
     466particles or collinear splittings, and in their computing speed performances.
    387467 
    388468\subsubsection*{Cone algorithms}
    … …  
    390470\begin{enumerate}
    391471 
    392 \item {\it CDF Jet Clusters}~\citep{bib:jetclu}: Cone algorithm forming jets by combining cells lying within a circle (default radius $\Delta R=0.7$) in the $(\eta$, $\phi)$ space. Jets are seeded by all cells with
    393  transverse energy $E_T$ above a given threshold (default: $E_T > 1~\textrm{GeV}$)~\citep{qr:jetparams}.
    394  
    395 \item {\it CDF MidPoint}~\citep{bib:midpoint}: Cone algorithm with additional ``midpoints'' (energy barycentres) in the list of seeds.
    396  
    397 \item {\it Seedless Infrared Safe Cone}~\citep{bib:SIScone}: The \textsc{SISC}one algorithm is simultaneously insensitive to additional soft particles and collinear splittings.
     472\item {\it CDF Jet Clusters}~\citep{bib:jetclu}: Cone algorithm forming jets by
     473combining cells lying within a circle (default radius $\Delta R=0.7$) in the
     474$(\eta$, $\phi)$ space. Jets are seeded by all cells with transverse energy
     475$E_T$ above a given threshold (default: $E_T >
     4761~\textrm{GeV}$)~\citep{qr:jetparams}.
     477 
     478\item {\it CDF MidPoint}~\citep{bib:midpoint}: Cone algorithm with additional
     479``midpoints'' (energy barycentres) in the list of seeds.
     480 
     481\item {\it Seedless Infrared Safe Cone}~\citep{bib:SIScone}: The
     482\textsc{SISC}one algorithm is simultaneously insensitive to additional soft
     483particles and collinear splittings.
    398484\end{enumerate}
    399485
    400486\subsubsection*{Recombination algorithms}
    401487
    402 The next three jet algorithms rely on recombination schemes where calorimeter cell pairs are successively merged:
    403 
    404 % Two such variables are defined: the distance $d_{ij}$ between each pair of cells $(i,j)$, and a variable $d_{iB}$ (\textit{beam distance}) depending on the transverse momentum of the cell $i$.
    405 
    406 % The jet reconstruction algorithm browses the calorimetric cell 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 cells $i$ and $j$ are merged into a single cell 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 cell is declared as a final jet and is removed from the input list. This procedure is repeated until no cells 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 calorimetric cell $i$ and $\Delta R_{ij}= \sqrt{(y_i-y_j)^2+(\phi_i-\phi_j)^2}$ as the jet-radius parameter:
     488The next three jet algorithms rely on recombination schemes where calorimeter
     489cell pairs are successively merged:
    407490 
    408491\begin{enumerate}[start=4]
    409  
    410492\item {\it Longitudinally invariant $k_t$ jet}~\citep{bib:ktjet},
    411 % \begin{equation}
    412 % \begin{array}{l}
    413 %   d_{ij} = \min(k_{ti}^2,k_{tj}^2)\Delta R_{ij}^2/R^2 \\
    414 %   d_{iB}=k_{ti}^2 \\
    415 % \end{array}
    416 % \end{equation}
    417  
    418493\item {\it Cambridge/Aachen jet}~\citep{bib:aachen},
    419 % \begin{equation}
    420 % \begin{array}{l}
    421 % d_{ij} = \Delta R_{ij}^2/R^2\\
    422 % d_{iB}=1 \\
    423 % \end{array}
    424 % \end{equation}
    425  
    426 \item {\it Anti $k_t$ jet}~\citep{bib:antikt}, where hard jets are exactly circular in the $(y,\phi)$ plane.
    427 % \begin{equation}
    428 % \begin{array}{l}
    429 % d_{ij} =  \min(1/k_{ti}^2,1/k_{tj}^2)\Delta R_{ij}^2/R^2 \\
    430 % d_{iB}=1/k_{ti}^2 \\
    431 % \end{array}
    432 % \end{equation}
     494\item {\it Anti $k_t$ jet}~\citep{bib:antikt}, where hard jets are exactly
     495circular in the $(y,\phi)$ plane.
    433496\end{enumerate}
    434497
    435 The recombination algorithms are safe with respect to soft radiations (\textit{infrared}) and collinear splittings. Their implementations are similar except for the definition of the \textit{distances} used during the merging procedure.
    436 
    437 By default, reconstruction uses the CDF cone algorithm.
    438 Jets are stored if their transverse energy is higher than $20~\textrm{GeV}$~\citep{qr:ptcutjet}.
     498The recombination algorithms are safe with respect to soft radiations
     499(\textit{infrared}) and collinear splittings. Their implementations are similar
     500except for the definition of the \textit{distances} used during the merging
     501procedure.
     502
     503By default, reconstruction uses the CDF cone algorithm. Jets are stored if their
     504transverse energy is higher than $20~\textrm{GeV}$~\citep{qr:ptcutjet}.
    439505 
    440506
    441507\subsubsection*{Energy flow}
    442508
    443 In jets, several particle can leave their energy into a given calorimetric cell, 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 cells with multiple hits. When the \textit{energy flow} is switched on in \textit{Delphes}
    444 %\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.}
    445 , the energy of tracks pointing to calorimetric cells is subtracted and smeared separately, before running the chosen jet reconstruction algorithm. This option allows a better jet $E$ reconstruction~\citep{qr:energyflow}.
     509In jets, several particle can leave their energy into a given calorimetric cell,
     510which broadens the jet energy resolution. However, the energy of charged
     511particles associated to jets can be deduced from their reconstructed track, thus
     512providing a way to identify some of the components of cells with multiple hits.
     513When the \textit{energy flow} is switched on in \textit{Delphes}, the energy of
     514tracks pointing to calorimetric cells is subtracted and smeared separately,
     515before running the chosen jet reconstruction algorithm. This option allows a
     516better jet $E$ reconstruction~\citep{qr:energyflow}.
    446517 
    447518\subsection{$b$-tagging}
    448519\label{btagging}
    449520
    450 A jet is tagged as $b$-jets if its direction lies in the acceptance of the tracker and if it is associated to a parent $b$-quark. 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~\citep{qr:btag}.
    451 %\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.}.
    452 The (mis)tagging relies on the true parton identity of the most energetic parton within a cone around the $(\eta,\phi)$ region, with a radius equal to the one used to reconstruct the jet (default: $\Delta R$ of $0.7$). In current version of \textit{Delphes}, the displacement of secondary vertices is not simulated.
     521A jet is tagged as $b$-jets if its direction lies in the acceptance of the
     522tracker and if it is associated to a parent $b$-quark. By default, a $b$-tagging
     523efficiency of $40\%$ is assumed if the jet has a parent $b$ quark. For $c$-jets
     524and light jets (i.e.\ originating in $u$, $d$, $s$ quarks or in gluons), a fake
     525$b$-tagging efficiency of $10 \%$ and $1 \%$ respectively is
     526assumed~\citep{qr:btag}. The (mis)tagging relies on the identity of
     527the most energetic parton within a cone around the jet axis, with a
     528radius equal to the one used to reconstruct the jet (default: $\Delta R$ of
     529$0.7$). In current version of \textit{Delphes}, the displacement of secondary
     530vertices is not simulated.
    453531
    454532\subsection{\texorpdfstring{$\tau$}{\texttau} identification}
    455533
    456 Jets originating from $\tau$-decays are identified using a procedure consistent with the one applied in a full detector simulation~\citep{bib:cmsjetresolution}.
    457 The 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}). Secondly, the particles arisen from the $\tau$ lepton produce narrow jets in the calorimeter (this is defined as the jet \textit{collimation}).
     534Jets originating from $\tau$-decays are identified using a procedure consistent
     535with the one applied in a full detector simulation~\citep{bib:cmsjetresolution}.
     536The tagging relies on two properties of the $\tau$ lepton. First, $77\%$ of the
     537$\tau$ hadronic decays contain only one charged hadron associated to a few
     538neutrals (Tab.~\ref{tab:taudecay}). Secondly, the particles arisen from the
     539$\tau$ lepton produce narrow jets in the calorimeter (this is defined as the jet
     540\textit{collimation}).
    458541
    459542
    460543\begin{table}[!h]
    461544\begin{center}
    462 \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.
     545\caption{ Branching ratios for $\tau^-$ lepton~\citep{bib:pdg}. $h^\pm$ and
     546$h^0$ refer to charged and neutral hadrons, respectively. $n \geq 0$ and $m \geq
     5470$ are integers.
    463548\vspace{0.5cm}  }
    464549\begin{tabular}[!h]{lll}
    … …  
    491576\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 calorimetric cells $E_T^\textrm{cell}$ 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~\citep{qr:taujets}.
    492577\vspace{0.5cm}  }
    493 % \begin{tabular}[!h]{lll}
    494 % \hline
    495 % Parameter  & Card flag & Value\\\hline
    496 % \multicolumn{3}{l}{\textbf{Electromagnetic collimation}} \\
    497 % $R^\textrm{em}$     & \texttt{TAU\_energy\_scone } & $0.15$\\
    498 % min $E_{T}^\textrm{tower}$     & {\verb JET_M_seed }  & $1.0$~GeV\\
    499 % $C_{\tau}$         & \texttt{TAU\_energy\_frac} & $0.95$\\
    500 % \multicolumn{3}{l}{\textbf{Tracking isolation}} \\
    501 % $R^\textrm{tracks}$ & \texttt{TAU\_track\_scone} & $0.4$\\
    502 % min $p_T^\textrm{tracks}$      & \texttt{PTAU\_track\_pt } & $2$ GeV$/c$\\
    503 % \multicolumn{3}{l}{\textbf{$\tau$-jet candidate}} \\
    504 % $\min p_T$ & \texttt{TAUJET\_pt} & $10$ GeV$/c$\\
    505 % \hline
    506 % \end{tabular}
    507578\begin{tabular}[!h]{lll}
    508579\hline
    … …  
    525596\subsubsection*{Electromagnetic collimation}
    526597
    527 To use the narrowness of the $\tau$-jet, the \textit{electromagnetic collimation} $C_{\tau}$ is defined as the sum of the energy of cells in a small cone of radius $R^\textrm{em}$ around the jet axis, divided by the energy of the reconstructed jet.
    528 To be taken into account, a calorimeter cell should have a transverse energy $E_T^\textrm{cell}$ above a given threshold.
    529 A 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}).
     598To use the narrowness of the $\tau$-jet, the \textit{electromagnetic
     599collimation} $C_{\tau}$ is defined as the sum of the energy of cells in a small
     600cone of radius $R^\textrm{em}$ around the jet axis, divided by the energy of the
     601reconstructed jet. To be taken into account, a calorimeter cell should have a
     602transverse energy $E_T^\textrm{cell}$ above a given threshold. A large fraction
     603of the jet energy is expected in this small cone. This fraction, or
     604\textit{collimation factor}, is represented in Fig.~\ref{fig:tau2} for the
     605default values (see Tab.~\ref{tab:tauRef}).
    530606
    531607\begin{figure}[!ht]
    … …  
    543619\subsubsection*{Tracking isolation}
    544620
    545 The 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).
    546 This 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}.
     621The tracking isolation for the $\tau$ identification requires that the number
     622of tracks associated to particles with significant transverse momenta is one and
     623only one in a cone of radius $R^\textrm{tracks}$ ($3-$prong $\tau$-jets are
     624dropped). This cone should be entirely incorporated into the tracker to be taken
     625into account. Default values of these parameters are given in
     626Tab.~\ref{tab:tauRef}.
    547627
    548628
    … …  
    560640
    561641\subsubsection*{Purity}
    562 Once 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 $66\%$.
     642Once both electromagnetic collimation and tracking isolation are applied, a
     643threshold on the $p_T$ of the $\tau$-jet candidate is requested to purify the
     644collection. This procedure selects $\tau$ leptons decaying hadronically with a
     645typical efficiency of $66\%$.
    563646
    564647\subsection{Missing transverse energy}
    565 In 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 $\overrightarrow{p_T}^\textrm{miss}$.
    566 \begin{equation}
    567 \overrightarrow{p_T} = \left(
    568 \begin{array}{c}
    569 p_x\\
    570 p_y\\
    571 \end{array}
    572 \right)
    573 ~ \textrm{and} ~
    574 \left\{
    575 \begin{array}{l}
    576  p_x^\textrm{miss} = - p_x^\textrm{obs} \\
    577  p_y^\textrm{miss} = - p_y^\textrm{obs} \\
    578 \end{array}
    579 \right.
    580 \end{equation}
    581 The \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.
    582 In a real experiment, calorimeters measure energy and not momentum. Any problem affecting the detector (dead channels, misalignment, noisy cells, cracks) worsens directly the measured missing transverse energy $\overrightarrow {E_T}^\textrm{miss}$. In \textit{Delphes}, \textsc{MET} is based on the calorimetric cells only. Muons and neutrinos are therefore not taken into account for its evaluation:
     648In an ideal detector, momentum conservation imposes the transverse momentum of
     649the observed final state $\overrightarrow{p_T}^\textrm{obs}$ to be equal and
     650in opposite direction to the $\overrightarrow{p_T}$ vector sum of the
     651invisible particles, written $\overrightarrow{p_T}^\textrm{miss}$.
     652The \textit{true} missing transverse energy, i.e.\ at generator-level, is
     653calculated as the opposite of the vector sum of the transverse momenta of all
     654visible particles -- or equivalently, to the vector sum of invisible particle
     655transverse momenta.
     656In a real experiment, calorimeters measure energy and not momentum. Any problem
     657affecting the detector (dead channels, misalignment, noisy cells, cracks)
     658worsens directly the measured missing transverse energy $\overrightarrow
     659{E_T}^\textrm{miss}$. In \textit{Delphes}, \textsc{MET} is based on the
     660calorimetric cells only. Muons and neutrinos are therefore not taken into
     661account for its evaluation:
    583662\begin{equation}
    584663\overrightarrow{E_T}^\textrm{miss} = - \sum^\textrm{cells}_i \overrightarrow{E_T}(i)
    585664\end{equation}
    586 However, as muon candidates, tracks and calorimetric cells are available in the output file, the missing transverse energy can always be reprocessed a posteriori with more specialised algorithms.
     665However, as muon candidates, tracks and calorimetric cells are available in the
     666output file, the missing transverse energy can always be reprocessed a
     667posteriori with more specialised algorithms.
    587668
    588669\section{Trigger emulation}
    589670
    590 % New physics in collider experiment are often characterised in phenomenology by low cross-section values, compared to the Standard Model (\textsc{SM}) processes.
    591 %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 $2 \times 10^{-3}~\textrm{nb}$ ($pp \rightarrow WH$, $m_H=115~\textrm{GeV}/c^2$).
    592 
    593 %High statistics are required for data analyses, consequently imposing high luminosity, i.e.\ a high collision rate.
    594 % As 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.
    595 % This data selection is supposed to reject only well-known \textsc{SM} events\footnote{In real experiments, some bandwidth is allocated to minimum-bias and/or zero-bias (``random'') triggers that stores a small fraction of  random events without any selection criteria.}.
    596 % Dedicated 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.
    597 
    598 Most of the usual trigger algorithms select events containing leptons, jets, and \textsc{MET} with an energy scale above some threshold.
    599 This is often expressed in terms of a cut on the transverse momentum of one or several objects of the measured event.
    600 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 $p_T^e > 50~\textrm{GeV}/c$.
    601 
    602 A trigger emulation is included in \textit{Delphes}, using a fully parametrisable \textit{trigger table} \citep{qr:triggercard}. When enabled, this trigger is applied on analysis-object data.
    603 In a real experiment, the online selection is often divided into several steps (or \textit{levels}).
    604 % This splits the overall reduction factor into a product of smaller factors, corresponding to the different trigger levels.
    605 % This is related to the architecture of the experiment data acquisition chain, with limited electronic buffers requiring a quick decision for the first trigger level.
    606 First-level triggers are fast and simple but based only on partial data as not all detector front-ends are readable within the decision latency.
    607 Higher level triggers are more complex, of finer-but-not-final quality and based on full detector data.
    608 
    609 Real triggers are thus intrinsically based on reconstructed data with a worse resolution than final analysis data.
    610 On the contrary, same data are used in \textit{Delphes} for trigger emulation and for final analyses.
     671Most of the usual trigger algorithms select events containing leptons, jets, and
     672\textsc{MET} with an energy scale above some threshold. This is often expressed
     673in terms of a cut on the transverse momentum of one or several objects of the
     674measured event. Logical combinations of several conditions are also possible.
     675For instance, a trigger path could select events containing at least one jet and
     676one electron such as $p_T^\textrm{jet} > 100~\textrm{GeV}/c$ and $p_T^e >
     67750~\textrm{GeV}/c$.
     678
     679A trigger emulation is included in \textit{Delphes}, using a fully
     680parametrisable \textit{trigger table} \citep{qr:triggercard}. When enabled, this
     681trigger is applied on analysis-object data. In a real experiment, the online
     682selection is often divided into several steps (or \textit{levels}).
     683corresponding to the different trigger levels.
     684First-level triggers are fast and simple but based only on partial data as not
     685all detector front-ends are readable within the decision latency.
     686Higher level triggers are more complex, of finer-but-not-final quality and
     687based on full detector data.
     688
     689Real triggers are thus intrinsically based on reconstructed data with a worse
     690resolution than final analysis information. On the contrary, the same
     691information is used in \textit{Delphes} for the trigger emulation and for final
     692analyses.
    611693
    612694\section{\label{sec:vfd}Very forward detector simulation}
    613695
    614 Most of the recent experiments in beam colliders have additional instrumentation along the beamline. These extend the $\eta$ coverage to higher values, for the detection of very forward final-state particles. In \textit{Delphes}, Zero Degree Calorimeters, roman pots and forward taggers have been implemented (Fig.~\ref{fig:fdets}), similarly to the plans for CMS and ATLAS collaborations~\citep{bib:cmsjetresolution, bib:ATLASresolution}.
     696Most of the recent experiments in beam colliders have additional
     697instrumentation along the beamline. These extend the $\eta$ coverage to higher
     698values, for the detection of very forward final-state particles. In
     699\textit{Delphes}, Zero Degree Calorimeters, roman pots and forward taggers have
     700been implemented (Fig.~\ref{fig:fdets}), similarly as for CMS and
     701ATLAS collaborations~\citep{bib:cmsjetresolution, bib:ATLASresolution}.
    615702
    616703\begin{figure}[!ht]
    … …  
    618705%\includegraphics[width=\columnwidth]{fdets}
    619706\includegraphics[width=\columnwidth]{fig4}
    620 \caption{Default location of the very forward detectors, including \textsc{ZDC}, \textsc{RP220} and \textsc{FP420} in the \textsc{LHC} beamline.
    621 Incoming (beam 1, red) and outgoing (beam 2, black) beams on one side of the fifth interaction point (\textsc{IP5}, $s=0~\textrm{m}$ on the plot).
    622 The 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 \textit{Hector}~\citep{bib:hector}. All very forward detectors are located symmetrically around the interaction point. }
     707\caption{Default location of the very forward detectors, including
     708\textsc{ZDC}, \textsc{RP220} and \textsc{FP420} in the \textsc{LHC} beamline.
     709Incoming (beam 1, red) and outgoing (beam 2, black) beams on one side of the
     710fifth interaction point (\textsc{IP5}, $s=0~\textrm{m}$ on the plot).
     711The Zero Degree Calorimeter is located in perfect alignment with the beamline
     712axis at the interaction point, at $140~\textrm{m}$, where the beam paths are
     713well separated. The forward taggers are near-beam detectors located at
     714$220~\textrm{m}$ and $420~\textrm{m}$. Beamline simulation with
     715\textit{Hector}~\citep{bib:hector}. All very forward detectors are located
     716symmetrically around the interaction point. }
    623717\label{fig:fdets}
    624718\end{center}
    625719\end{figure}
    626720
    627 %\begin{table*}[t]  % the star (*) allows to arrange the table over the two columns
    628721\begin{table}[t]
    629722\begin{center}
    630 \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.
    631 % The tagger acceptance is fully determined by the distance in the transverse plane of the detector to the real beam position~\citep{bib:hector}.
     723\caption{Default parameters for the forward detectors: distance from the
     724interaction point and detector acceptance. The \textsc{LHC} beamline is assumed
     725around the fifth \textsc{LHC} interaction point (\textsc{IP}). For the
     726\textsc{ZDC}, the acceptance depends only on the pseudorapidity $\eta$ of the
     727particle, which should be neutral and stable.
    632728It is expressed in terms of the particle energy ($E$).
    633729All detectors are located on both sides of the interaction point.
    … …  
    635731\begin{tabular}{llcl}
    636732\hline
    637 %Detector & Distance from \textsc{IP}& Acceptance & \\ \hline
    638733Detector & Distance & Acceptance & \\ \hline
    639734\textsc{ZDC}   & $\pm 140$ m & $|\eta|> 8.3$       & for $n$ and $\gamma$\\
    … …  
    649744\subsection{Zero Degree Calorimeters}
    650745
    651 In direct sight of the interaction point, on both sides of the central detector, the Zero Degree Calorimeters (\textsc{ZDC}s) are located at zero angle, i.e.\ are aligned with the beamline axis at the interaction point. They are placed beyond the point where the paths of incoming and outgoing beams separate. 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}).
    652 
    653 The trajectory of the neutrals observed in the \textsc{ZDC}s is a straight line, while charged particles are deflected away from their acceptance window by the powerful magnets located in front of them. The fact that additional charged particles may enter the \textsc{ZDC} acceptance is neglected in the current versions of \textit{Delphes}.
     746In direct sight of the interaction point, on both sides of the central
     747detector, the Zero Degree Calorimeters (\textsc{ZDC}s) are located at zero
     748angle, i.e.\ are aligned with the beamline axis at the interaction point. They
     749are placed beyond the point where the paths of incoming and outgoing beams
     750separate. These allow the measurement of stable neutral particles ($\gamma$ and
     751$n$) coming from the interaction point, with large pseudorapidities (e.g.\
     752$|\eta_{\textrm{n,}\gamma}| > 8.3$ in \textsc{ATLAS} and \textsc{CMS}).
     753
     754The trajectory of the neutrals observed in the \textsc{ZDC}s is a straight
     755line, while charged particles are deflected away from their acceptance window by
     756the powerful magnets located in front of them. The fact that additional charged
     757particles may enter the \textsc{ZDC} acceptance is neglected in the current
     758versions of \textit{Delphes}.
    654759
    655760The \textsc{ZDC}s have the ability to measure the time-of-flight of the particle.
    656 This corresponds to the delay $t$ after which the particle is observed in the detector, with respect to the bunch crossing reference time at the interaction point ($t_0$):
     761This corresponds to the delay $t$ after which the particle is observed in the
     762detector, with respect to the bunch crossing reference time at the interaction
     763point ($t_0$):
    657764\begin{equation}
    658765 t = t_0 + \frac{1}{v} \times \Big( \frac{s-z}{\cos \theta}\Big) \approx \frac{1}{c} \times (s-z),
    659766\end{equation}
    660 where $t_0$ is thus 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, $\theta$ is the particle emission angle. It is assumed that the neutral particle observed in the \textsc{ZDC} is highly relativistic and very forward.
    661 % 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 $1 - \cos \theta < 10^{-4}$.
    662 % The formula then reduces to
    663 % \begin{equation}
    664 %  t = \frac{1}{c} \times (s-z).
    665 % \end{equation}
    666 % For example, a photon takes $0.47~\mu\textrm{s}$ to reach a \textsc{ZDC} located at $s=140~\textrm{m}$, neglecting $z$ and $\theta$.
    667 For the time-of-flight measurement, a Gaussian smearing can be applied according to the detector resolution (Tab.~\ref{tab:defResolZdc})~\citep{qr:resolutionterms}.
    668 %In the current version of \textit{Delphes}, only neutrons, antineutrons and photons are assumed to be able to reach the \textsc{ZDC}s, all other particles being neglected.
    669 
    670 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 corresponding section resolutions (Tab.~\ref{tab:defResolZdc}). The \textsc{ZDC} hits do not enter in the calorimeter cell list used for reconstruction of jets and missing transverse energy.
     767where $t_0$ is thus the true time coordinate of the vertex from which the
     768particle originates, $v$ the particle velocity, $s$ is the \textsc{ZDC} distance
     769to the interaction point, $z$ is the longitudinal coordinate of the vertex,
     770$\theta$ is the particle emission angle. It is assumed that the neutral particle
     771observed in the \textsc{ZDC} is highly relativistic and very forward.
     772For the time-of-flight measurement, a Gaussian smearing can be applied according
     773to the detector resolution
     774(Tab.~\ref{tab:defResolZdc})~\citep{qr:resolutionterms}.
     775
     776
     777The \textsc{ZDC}s are composed of an electromagnetic and a hadronic sections,
     778for the measurement of photons and neutrons, respectively. The energy of the
     779observed neutral is smeared according to Eq.~\ref{eq:caloresolution} and the
     780corresponding section resolutions (Tab.~\ref{tab:defResolZdc}). The \textsc{ZDC}
     781hits do not enter in the calorimeter cell list used for reconstruction of jets
     782and missing transverse energy.
    671783
    672784\begin{table}[!h]
    673785\begin{center}
    674 \caption{Default values for the resolution of the zero degree calorimeters. Resolution on energy measurement is parametrised by the \textit{stochastic} ($S$), \textit{noise} ($N$) and \textit{constant} ($C$) terms (Eq.~\ref{eq:caloresolution})~\citep{qr:resolutionterms}. The time-of-flight is smeared according to a Gaussian function.
     786\caption{Default values for the resolution of the zero degree calorimeters.
     787Resolution on energy measurement is parametrised by the \textit{stochastic}
     788($S$), \textit{noise} ($N$) and \textit{constant} ($C$) terms
     789(Eq.~\ref{eq:caloresolution})~\citep{qr:resolutionterms}. The time-of-flight is
     790smeared according to a Gaussian function.
    675791\vspace{0.5cm}}
    676 % \begin{tabular}[!h]{lllc}
    677 % \hline
    678 % \multicolumn{2}{c}{Resolution Term}   & Card flag & Value\\\hline
    679 %  \multicolumn{4}{l}{\textsc{ZDC}, electromagnetic part} \\
    680 %         & $S$ (GeV$^{1/2}$)& \texttt{ELG\_Szdc}  & $0.7$ \\
    681 %         & $N$ (GeV)& \texttt{ELG\_Nzdc}  & $0.0$ \\
    682 %         & $C$ & \texttt{ELG\_Czdc}  & $0.08$ \\
    683 %  \multicolumn{4}{l}{\textsc{ZDC}, hadronic part} \\
    684 %         & $S$ (GeV$^{1/2}$)& \texttt{HAD\_Szdc}   & $1.38$\\
    685 %         & $N$ (GeV)& \texttt{HAD\_Nzdc}   & $0$ \\
    686 %         & $C$ & \texttt{HAD\_Czdc}   & $0.13$\\
    687 %  \multicolumn{4}{l}{\textsc{ZDC}, timing resolution} \\
    688 %         & $\sigma_t$ (s) & \texttt{ZDC\_T\_resolution} & $0$ \\
    689 % \hline
    690 % \end{tabular}
    691792\begin{tabular}[!h]{llcc}
    692793\hline
    … …  
    703804\end{table}
    704805
    705 % \subsubsection*{Forward neutrals}
    706 
    707 The reconstructed ZDC 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: $|\eta|>8.3$).
    708 %In current versions of \textit{Delphes}, only photons and neutrons are considered.
    709 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 (def. $50$~GeV)~\citep{qr:fwdneutrals}.
    710 %\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).
     806The reconstructed ZDC hits correspond to neutral particles with a lifetime long
     807enough to reach these detectors (default: $c \tau \geq 140~\textrm{m}$) and very
     808large pseudorapidities (default: $|\eta|>8.3$).
     809Photons and neutrons are identified if their energy overpasses a given threshold
     810(def. $E_\gamma \leq 20$~GeV and $E_n \leq 50$~GeV)~\citep{qr:fwdneutrals}.
     811
    711812
    712813
    713814\subsection{Forward taggers}
    714815
    715 Forward 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. Such devices, also used at \textsc{HERA} and Tevatron, are located very far away from the interaction point (further than $150$~m in the \textsc{LHC} case).
    716 
    717 To be able to reach these detectors, particles must have a charge identical to the beam particles, and a momentum very close to the nominal value of 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}).
    718 For instance, roman pots at $220~\textrm{m}$ from the  \textsc{IP} and $2~\textrm{mm}$ from the beam will detect all forward protons with an energy between $120$ and $900~\textrm{GeV}$~\citep{bib:hector}.
    719 In practice, in the \textsc{LHC}, only positively charged muons ($\mu^+$) and protons can reach the forward taggers as other particles with a single positive charge coming from the interaction points will decay before their possible tagging. In \textit{Delphes}, extra hits coming from the beam-gas events or secondary particles hitting the beampipe in front of the detectors are not taken into account.
    720 
    721 While neutral particles propagate along a straight line to the \textsc{ZDC}, a dedicated simulation of the transport of charged particles is needed for \textsc{RP220} and \textsc{FP420}. This fast simulation uses the \textit{Hector} software~\citep{bib:hector}, which includes the chromaticity effects and the geometrical aperture of the beamline elements of any arbitrary collider.
    722 
    723 Forward taggers are able to measure the hit positions ($x,y$) and angles ($\theta_x,\theta_y$) in the transverse plane at the location of the detector ($s$ meters away from the \textsc{IP}), as well as the time-of-flight\footnote{It is worth noting that for both \textsc{CMS} and \textsc{ATLAS} experiments, the taggers located at $220$~m are not able to measure the time-of-flight, contrary to \textsc{FP420} detectors.} ($t$). Out of these the particle energy ($E$) and the momentum transfer it underwent during the interaction ($q^2$) can be reconstructed at the analysis level (it is not implemented in the current versions of \textit{Delphes}. The time-of-flight measurement can be smeared with a Gaussian distribution (default value
    724 %\footnote{\texttt{[code] } The resolution is defined by the \texttt{RP220\_T\_resolution} and \texttt{RP420\_T\_resolution} parameters in the detector card.}
     816Forward taggers (called here \textsc{RP220}, for ``roman pots at
     817$220~\textrm{m}$'' and \textsc{FP420} for ``forward proton taggers at
     818$420~\textrm{m}$'', as at the \textsc{LHC}) are meant for the measurement of
     819particles following very closely the beam path. Such devices, also used at
     820\textsc{HERA} and Tevatron, are located very far away from the interaction point
     821(further than $150$~m in the \textsc{LHC} case).
     822
     823To be able to reach these detectors, particles must have a charge identical to
     824the beam particles, and a momentum very close to the nominal value of the beam.
     825These taggers are near-beam detectors located a few millimetres from the true
     826beam trajectory and this distance defines their acceptance
     827(Tab.~\ref{tab:fdetacceptance}). For instance, roman pots at $220~\textrm{m}$
     828from the  \textsc{IP} and $2~\textrm{mm}$ from the beam will detect all forward
     829protons with an energy between $120$ and $900~\textrm{GeV}$~\citep{bib:hector}.
     830In practice, in the \textsc{LHC}, only positively charged muons ($\mu^+$) and
     831protons can reach the forward taggers as other particles with a single positive
     832charge coming from the interaction points will decay before their possible
     833tagging. In \textit{Delphes}, extra hits coming from the beam-gas events or
     834secondary particles hitting the beampipe in front of the detectors are not taken
     835into account.
     836
     837While neutral particles propagate along a straight line to the \textsc{ZDC}, a
     838dedicated simulation of the transport of charged particles is needed for
     839\textsc{RP220} and \textsc{FP420}. This fast simulation uses the \textit{Hector}
     840software~\citep{bib:hector}, which includes the chromaticity effects and the
     841geometrical aperture of the beamline elements of any arbitrary collider.
     842
     843Forward taggers are able to measure the hit positions ($x,y$) and angles
     844($\theta_x,\theta_y$) in the transverse plane at the location of the detector
     845($s$ meters away from the \textsc{IP}), as well as the
     846time-of-flight\footnote{It is worth noting that for both \textsc{CMS} and
     847\textsc{ATLAS} experiments, the taggers located at $220$~m are not able to
     848measure the time-of-flight, contrary to \textsc{FP420} detectors.} ($t$). Out of
     849these the particle energy ($E$) and the momentum transfer it underwent during
     850the interaction ($q^2$) can be reconstructed at the analysis level (it is not
     851implemented in the current versions of \textit{Delphes}. The time-of-flight
     852measurement can be smeared with a Gaussian distribution (default value
    725853$\sigma_t = 0~\textrm{s}$)~\citep{qr:protontaggers}.
    726854
    … …  
    730858
    731859\textit{Delphes} performs a fast simulation of a collider experiment.
    732 Its 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.
    733 The quality and validity of the output are assessed by comparing the resolutions on the reconstructed data to the expectations of both \textsc{CMS}~\citep{bib:cmsjetresolution} and \textsc{ATLAS}~\citep{bib:ATLASresolution} detectors.
    734 
    735 Electrons and muons are by construction equal to the experiment designs, as the Gaussian smearing of their kinematics properties is defined according to the detector specifications.
    736 Similarly, the $b$-tagging efficiency (for real $b$-jets) and misidentification rates (for fake $b$-jets) are taken directly from the expected values of the experiment.
    737 Unlike these simple objects, jets and missing transverse energy should be carefully cross-checked.
     860Its performances in terms of computing time and data size are directly
     861proportional to the number of simulated events and on the considered physics
     862process. As an example, $10,000$ $pp \rightarrow t \bar t X$ events are
     863processed in $110~\textrm{s}$ on a regular laptop and use less than
     864$250~\textrm{MB}$ of disk space.
     865The quality and validity of the output are assessed by comparing the
     866resolutions on the reconstructed data to the expectations of both
     867\textsc{CMS}~\citep{bib:cmsjetresolution} and
     868\textsc{ATLAS}~\citep{bib:ATLASresolution} detectors.
     869
     870Electrons and muons are by construction equal to the experiment designs, as the
     871Gaussian smearing of their kinematics properties is defined according to the
     872detector specifications. Similarly, the $b$-tagging efficiency (for real
     873$b$-jets) and misidentification rates (for fake $b$-jets) are taken directly
     874from the expected values of the experiment. Unlike these simple objects, jets
     875and missing transverse energy should be carefully cross-checked.
    738876
    739877\subsection{Jet resolution}
    740878 
    741 The majority of interesting processes at the \textsc{LHC} contain jets in the final state. The jet resolution obtained using \textit{Delphes} is therefore a crucial point for its validation, both for \textsc{CMS}- and \textsc{ATLAS}-like detectors.
    742 This validation is based on $pp \rightarrow gg$ events produced with MadGraph/MadEvent and hadronised using \textit{Pythia}~\citep{bib:mgme,bib:pythia}.
    743 
    744 For a \textsc{CMS}-like detector, a similar procedure as the one explained in published results is applied here.
    745 The events were arranged in $14$ bins of gluon transverse momentum $\hat{p}_T$. In each $\hat{p}_T$ bin, every jet in \textit{Delphes} is matched to the closest jet of generator-level particles, using the spatial separation between the two jet axes
     879The majority of interesting processes at the \textsc{LHC} contain jets in the
     880final state. The jet resolution obtained using \textit{Delphes} is therefore a
     881crucial point for its validation, both for \textsc{CMS}- and \textsc{ATLAS}-like
     882detectors. This validation is based on $pp \rightarrow gg$ events produced with
     883MadGraph/MadEvent and hadronised
     884using \textit{Pythia}~\citep{bib:mgme,bib:pythia}.
     885
     886For a \textsc{CMS}-like detector, a similar procedure as the one explained in
     887published results is applied here. The events were arranged in $14$ bins of
     888gluon transverse momentum $\hat{p}_T$. In each $\hat{p}_T$ bin, every jet in
     889\textit{Delphes} is matched to the closest jet of generator-level particles,
     890using the spatial separation between the two jet axes
    746891\begin{equation}
    747 \Delta R = \sqrt{ \big(\eta^\textrm{rec} - \eta^\textrm{MC} \big)^2 +  \big(\phi^\textrm{rec} - \phi^\textrm{MC} \big)^2}<0.25.
     892\Delta R = \sqrt{ \big(\eta^\textrm{rec} - \eta^\textrm{MC} \big)^2 +
     893\big(\phi^\textrm{rec} - \phi^\textrm{MC} \big)^2}<0.25.
    748894\end{equation}
    749 The 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 (i.e.\ including muons).
    750 Jets produced by \textit{Delphes} and satisfying the matching criterion are called hereafter \textit{reconstructed jets}.
    751 All jets are computed with the clustering algorithm (JetCLU) with a cone radius $R$ of $0.7$.
    752 
    753 The 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.
    754 The $E_T^\textrm{rec}/E_T^\textrm{MC}$ histogram is fitted with a Gaussian distribution in the interval \mbox{$\pm 2$~\textsc{RMS}} centred around the mean value.
    755 The resolution in each $\hat{p}_T$ bin is obtained by the fit mean $\langle x \rangle$ and variance $\sigma^2(x)$:
     895The jets made of generator-level particles, here referred as \textit{MC jets},
     896are obtained by applying the algorithm to all particles considered as stable
     897after hadronisation (i.e.\ including muons). Jets produced by \textit{Delphes}
     898and satisfying the matching criterion are called hereafter \textit{reconstructed
     899jets}. All jets are computed with the clustering algorithm (JetCLU) with a cone
     900radius $R$ of $0.7$.
     901
     902The ratio of the transverse energies of every reconstructed jet
     903$E_T^\textrm{rec}$ to its corresponding \textsc{MC} jet $E_T^\textrm{MC}$ is
     904calculated in each $\hat{p}_T$ bin. The $E_T^\textrm{rec}/E_T^\textrm{MC}$
     905histogram is fitted with a Gaussian distribution in the interval \mbox{$\pm
     9062$~\textsc{RMS}} centred around the mean value. The resolution in each
     907$\hat{p}_T$ bin is obtained by the fit mean $\langle x \rangle$ and variance
     908$\sigma^2(x)$:
    756909\begin{equation}
    757 %\frac{\sigma(R_{jet})}{\langle R_{jet} \rangle }=
    758 \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}}~
     910\frac{\sigma \Big (\frac{E_T^\textrm{rec}}{E_T^\textrm{MC}} \Big)_\textrm{fit}}{
     911\Big \langle \frac{E_T^\textrm{rec}}{E_T^\textrm{MC}} \Big
     912\rangle_\textrm{fit}}~
    759913\Big( \hat{p}_T(i) \Big)\textrm{, for all }i.
    760914\end{equation}
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