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   /Author (S. Ovyn, X. Rouby)
   /Title  (Delphes, a framework for fast simulation of a general purpose LHC detector)
   /Subject ()
   /Keywords (Delphes, Fast simulation, LHC, FROG, Hector, Smearing, FastJet)}
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\title{\textsc{Delphes}, a framework for fast simulation \\of a general purpose LHC detector}
\author{S. Ovyn and X. Rouby\thanks{Now in Physikalisches Institut, Albert-Ludwigs-Universit\"at Freiburg} \\
        Center for Particle Physics and Phenomenology (CP3)\\ Universit\'e catholique de Louvain \\ B-1348 Louvain-la-Neuve, Belgium \\ \\
        \textit{severine.ovyn@uclouvain.be, xavier.rouby@cern.ch} \\
}
\date{}

\begin{document}


\maketitle

Knowing whether theoretical predictions are visible and measurable in a high energy experiment is always delicate, due to the
complexity of the related detectors, data acquisition chain and software. We introduce here a new framework, \textsc{Delphes}, for fast simulation of
a general purpose experiment. The simulation includes a tracking system, embedded into a magnetic field, calorimetry and a muon
system, and possible very forward detectors arranged along the beamline.
The framework is interfaced to standard file formats (e.g. Les Houches Event File) and outputs observable analysis data objects, like missing transverse energy and collections of electrons or jets.
The simulation of detector response takes into account the detector resolution, and usual reconstruction algorithms for complex objects, like \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.
An overview of \textsc{Delphes} is given as well as a few use-cases for illustration.
\vspace{1cm}

\noindent
\textit{Keywords:} \textsc{Delphes}, fast simulation, LHC, smearing, trigger, \textsc{FastJet}, \textsc{Hector}, \textsc{Frog}
\vspace{1cm}

%\saythanks

\section{Introduction}
% Motiver l'utilisation d'un simulateur rapide
% - 1) rapide VS lent
% - 2) relativement bonne prédiction en premiÚre approximation
% - 3) permet de comparer

Experiments at high energy colliders are very complex systems, in several ways. First, in terms of the various detector subsystems, including tracking, central calorimetry, forward calorimetry, and muon chambers. These detectors differ with their principles, technologies, geometries and sensitivities. Then, due to the requirement of a highly effective online selection (i.e. a \textit{trigger}), subdivided into several levels for an optimal reduction factor, 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 schemes.

This complexity is handled by large collaborations of thousands of people, which restrict the availability of the data, software and documentation to their members. Real data analyses require a full detector simulation, including the various detector inefficiencies, the dead material, the imperfections and the geometrical details. Moreover, detector calibration and alignment are crucial. Such simulation is very complicated, technical and slow. On the other hand, phenomenological studies, looking for the observability of given signals, may require only fast but realistic estimates of the observables.

A new framework, called \textsc{Delphes}~\cite{bib:Delphes}, is introduced here, for the fast simulation of a general purpose collider experiment. 
Using the framework, observables can be estimated for specific signal and background channels, as well as their production and measurement rates, under a set of assumptions. 
Starting from the output of event generators, the simulation of the detector response takes into account the subdetector resolutions, by smearing the kinematical properties of the visible final particles. Tracks of charged particles and calorimetric towers are then created.

\textsc{Delphes} includes the most crucial experimental features, like (1) the geometry of both central or forward detectors; (2) lepton isolation; (3) reconstruction of photons, leptons, jets, $b$-jets, $\tau$-jets and missing transverse energy; (4) trigger emulation and (5) an event display (Fig.~\ref{fig:FlowChart}).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.9\columnwidth]{FlowDelphes}
\caption{Flow chart describing the principles behind \textsc{Delphes}. Event files coming from external Monte Carlo generators are read by a convertor stage. 
The kinematical variables of the final state particles are then smeared according to the subdetector resolutions. 
Tracks are reconstructed in a simulated dipolar magnetic field and calorimetric towers sample the energy deposits. Based on these, dedicated algorithms are applied for particle identification, isolation and reconstruction. 
The transport of very forward particle to the near-beam detectors is also simulated. 
Finally, an output file is written, including generator level and analysis object data. If requested, a fully parametrisable trigger can be emulated. Optionnally, the geometry and visualisation files for the 3D event display can also be produced.
All user parameters are set in the \textit{Smearing Card} and the \textit{Trigger Card}. }
\label{fig:FlowChart}
\end{center}
\end{figure}

Although 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.

%The simulation package proceeds in two stages. The first part is executed on the generated events. ``Particle-level" informations are read from input files and stored in a {\it \textsc{gen}} \textsc{root} tree. 

Three formats of input files can currently be used as input in \textsc{Delphes}\footnote{\texttt{[code] }See the \texttt{HEPEVTConverter}, \texttt{LHEFConverter} and \texttt{STDHEPConverter} classes.}. In order to process events from many different generators, the standard Monte Carlo event structure \mbox{\textsc{s}td\textsc{hep}} can be used as an input. Besides, \textsc{Delphes} can also provide detector response for events read in ``Les Houches Event Format'' (\textsc{lhef}) and \textsc{root} files obtained using the \textbf{h2root} utility from the \textsc{root} framework~\cite{bib:Root}. 
%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. 

The output of \textsc{Delphes} 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). The program is driven by input cards. The detector card (\texttt{data/DataCardDet.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/trigger.dat}) lists the user algorithms for the simplified online preselection.\\


\section{Detector simulation}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=\columnwidth]{Detector_Delphes_1}
\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). 
It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections. 
The outer layer of the central system (red) consist of a muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector. 
The actual detector granularity and extension is defined in the user-configuration card. The detector is assumed to be strictly symmetric around the beam axis (black line). Additional forward detectors are not depicted.}
\label{fig:GenDet}
\end{center}
\end{figure}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.5\columnwidth]{Detector_Delphes_3}
\caption{Profile of the layout assumed in \textsc{Delphes}. The extension of the various subdetectors, as defined in Tab.~\ref{tab:defEta}, are clearly visible. 
Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
\label{fig:GenDet3}
\end{center}
\end{figure}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.6\columnwidth]{Detector_Delphes_2b}
\caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. Open 3D-view of the detector with solid volumes. Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
\label{fig:GenDet2}
\end{center}
\end{figure}


The overall layout of the general purpose detector simulated by \textsc{Delphes} is shown in figure \ref{fig:GenDet}. 
A central tracking system (\textsc{tracker}) is surrounded by an electromagnetic and a hadron calorimeters (\textsc{ecal} and \textsc{hcal}, resp.). Two forward calorimeters (\textsc{fcal}) ensure a larger geometric coverage for the measurement of the missing transverse energy. Finally, a muon system (\textsc{muon}) encloses the central detector volume
The fast simulation of the detector response takes into account geometrical acceptance of sub-detectors and their finite resolution, as defined in the smearing data card\footnote{\texttt{[code] }See the \texttt{RESOLution} class.}. 
If no such file is provided, predifined values are used. The coverage of the various subsystems used in the default configuration are summarised in table \ref{tab:defEta}.


\begin{table}[!h]
\begin{center}
\caption{Default extension in pseudorapidity $\eta$ of the different subdetectors.
The corresponding parameter name, in the smearing card, is given. \vspace{0.5cm}}
\begin{tabular}[!h]{lll}
\hline
\textsc{tracker} & {\verb CEN_max_tracker } & $0.0 \leq |\eta| \leq 2.5$\\
\textsc{ecal}, \textsc{hcal} & {\verb CEN_max_calo_cen } & $0.0 \leq |\eta| \leq 3.0$\\
\textsc{fcal} & {\verb CEN_max_calo_fwd } & $3.0 \leq |\eta| \leq5.0$\\
\textsc{muon} & {\verb CEN_max_mu } & $0.0 \leq |\eta| \leq 2.4$\\\hline
\end{tabular}
\label{tab:defEta}
\end{center}
\end{table}

\subsection{Tracks reconstruction}
Every stable charged particle with a transverse momentum above some threshold and lying inside the fiducial volume of the tracker provides a track. 
By default, a track is assumed to be reconstructed with $90\%$ probability\footnote{\texttt{[code]} The reconstruction efficiency is defined in the smearing datacard by the \texttt{TRACKING\_EFF} term.} if its transverse momentum $p_T$ is higher than $0.9~\textrm{GeV}$ and if its pseudorapidity $|\eta| \leq 2.5$. 


\subsection{Simulation of calorimeters}

The 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.
The response of each sub-calorimeter is parametrised as a function of the energy:
\begin{equation} 
\frac{\sigma}{E} = \frac{S}{\sqrt{E}} \oplus \frac{N}{E} \oplus C,
\label{eq:caloresolution}
\end{equation}
where $S$, $N$ and $C$ are the \textit{stochastic}, \textit{noise} and \textit{constant} terms, respectively.\\


The particle 4-momentum $p^\mu$ are smeared with a parametrisation directly derived from the detector techinal designs\footnote{\texttt{[code] }The response of the detector is applied to the electromagnetic and the hadronic particles through the \texttt{SmearElectron} and \texttt{SmearHadron} functions.}.
In the default parametrisation, the calorimeter is assumed to cover the pseudorapidity range $|\eta|<3$ and consists in an electromagnetic and an hadronic part. Coverage between pseudorapidities of $3.0$ and $5.0$ is provided by forward calorimeters, with different response to electromagnetic objects ($e^\pm, \gamma$) or hadrons. 
Muons and neutrinos are assumed no to interact with the calorimeters\footnote{In the current \textsc{Delphes} version, particles other than electrons ($e^\pm$), photons ($\gamma$), muons ($\mu^\pm$) and neutrinos ($\nu_e$, $\nu_\mu$ and $\nu_\tau$) are simulated as hadrons for their interactions with the calorimeters. The simulation of stable particles beyond the Standard Model should subsequently be handled with care.}.
The default values of the stochastic, noisy and constant terms are given in Table~\ref{tab:defResol}.\\

\begin{table}[!h]
\begin{center}
\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}).
The corresponding parameter name, in the smearing card, is given. \vspace{0.5cm}}
\begin{tabular}[!h]{lclc}
\hline
\multicolumn{2}{c}{Resolution Term}   & Card flag & Value\\\hline
 \multicolumn{4}{l}{\textsc{ecal}} \\
        & $S$ & {\verb ELG_Scen }  & $0.05$ \\
        & $N$ & {\verb ELG_Ncen }  & $0.25$ \\
        & $C$ & {\verb ELG_Ccen }  & $0.0055$ \\
 \multicolumn{4}{l}{\textsc{fcal}, electromagnetic part} \\
        & $S$ & {\verb ELG_Sfwd }  & $2.084$ \\
        & $N$ & {\verb ELG_Nfwd }  & $0$ \\
        & $C$ & {\verb ELG_Cfwd }  & $0.107$ \\
 \multicolumn{4}{l}{\textsc{hcal}} \\
        & $S$ & {\verb HAD_Shcal } & $1.5$ \\
        & $N$ & {\verb HAD_Nhcal } & $0$\\
        & $C$ & {\verb HAD_Chcal } & $0.05$\\
 \multicolumn{4}{l}{\textsc{fcal}, hadronic part} \\
        & $S$ & {\verb HAD_Shf }   & $2.7$\\
        & $N$ & {\verb HAD_Nhf }   & $0$. \\
        & $C$ & {\verb HAD_Chf }   & $0.13$\\
\hline
\end{tabular}
\label{tab:defResol}
\end{center}
\end{table}

The 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}. 
Some long-living particles, such as the $K^0_s$, possessing 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 
\begin{equation}
\left\{
\begin{array}{l}
E_{\textsc{hcal}} = E \times F \\
E_{\textsc{ecal}} = E \times (1-F) \\
\end{array}
\right.
\end{equation}
where $0 \leq F \leq 1$. The electromagnetic part is handled as the electrons. The resulting final energy 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 worth $0.7$.\\

\subsection{Calorimetric towers}

The smallest unit for geometrical sampling of the calorimeters is a \textit{tower}; it segments the $(\eta,\phi)$ plane for the energy measurement.
All undecayed particles, except muons and neutrinos produce a calorimetric tower, either in \textsc{ecal}, in \textsc{hcal} or \textsc{fcal}. 
As the detector is assumed to be symmetric in $\phi$ and with respect to the $\eta=0$ plane, the smearing card stores the number of calorimetric towers with $\phi=0$ and $\eta>0$ (default: $40$ towers). For a given $\eta$, the size of the $\phi$ segmentation is also specified. 

The calorimetric towers directly enter in the calculation of the missing transverse energy, and as input for the jet reconstruction algorithms.
No longitudinal segmentation is available in the simulated calorimeters. 
No sharing between neighbouring towers is implemented when particles enter a tower very close to its geometrical edge.

\textcolor{red}{Mettre une figure avec une grille en $(\eta,\phi)$ pour illustrer la segmentation (un peu comme une feuille quadrillée).}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.8\columnwidth]{calosegmentation}
\caption{Default segmentation of the calorimeters in the $(\eta,\phi)$ plane. Only the central detectors (\textsc{ecal}, \textsc{hcal} and \textsc{fcal}) are considered.}
\label{fig:calosegmentation}
\end{center}
\end{figure}


\subsection{Very forward detectors simulation}

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. 
Zero Degree Calorimeters (\textsc{zdc}) are located at zero angle, i.e. are aligned with the beamline axis at the interaction point, and placed at the distance where the paths of incoming and outgoing beams separate (Fig.~\ref{fig:fdets}). These allow the measurement of stable neutral particles ($\gamma$ and $n$) coming from the interaction point, with large pseudorapirities (e.g. $|\eta_{\textrm{n,}\gamma}| > 8.3$ in \textsc{cms}).
Forward taggers (called here \textsc{rp220} and \textsc{fp420} as at the \textsc{lhc}) are meant for the measurement of particles following very closely the beam path. To be able to reach these detectors, such particles must have a charge identical to the beam particles, and a momentum very close to the nominal value for the beam. These taggers are near-beam detectors located a few millimeters from the true beam trajectory and this distance defines their acceptance (Table~\ref{tab:fdetacceptance}).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.8\columnwidth]{fdets}
\caption{Default location of the very forward detectors, including \textsc{zdc}, \textsc{rp220} and \textsc{fp420} in the \textsc{lhc} beamline. 
Incoming (red) and outgoing (black) beams on one side of the interaction point ($s=0~\textrm{m}$). 
The Zero Degree Calorimeter is located in perfect alignment with the beamline axis at the interaction point, at $140~\textrm{m}$, where the beam paths are separated. The forward taggers are near-beam detectors located at $220~\textrm{m}$ and $420~\textrm{m}$.}
\label{fig:fdets}
\end{center}
\end{figure}

\begin{table}[!h]
\begin{center}
\caption{Default parameters for the forward detectors: distance from the interaction point and detector acceptance. The \textsc{lhc} beamline is assumed around the fifth interaction point. For the \textsc{zdc}, the acceptance depends only on the pseudorapidity $\eta$ of the particle, which should be neutral and stable. 
The tagger acceptance is fully determined by the distance in the transverse plane of the detector to the real beam position~\cite{bib:Hector}. It is expressed in terms of the particle energy.
\vspace{0.5cm}}
\begin{tabular}[!h]{llcl}
\hline
Detector & Distance & Acceptance & \\ \hline
\textsc{zdc}   & $140$ m & $|\eta|> 8.3$       & for $n$ and $\gamma$\\
\textsc{rp220} & $220$ m & $E \in [6100 ; 6880]$ (GeV) & at $2~\textrm{mm}$\\
\textsc{fp420} & $420$ m & $E \in [6880 ; 6980]$ (GeV) & at $4~\textrm{mm}$\\
\hline
\end{tabular}
\label{tab:fdetacceptance}
\end{center}
\end{table}


While neutral particles propagate along a straight line to the \textsc{zdc}, a dedicated simulation of the transport of charged particles is needed for \textsc{rp220} and \textsc{fp420}. This fast simulation uses the \textsc{Hector} software~\cite{bib:Hector}, which includes the chromaticity effects and the geometrical aperture of the beamline elements.

Some subdetectors have the ability to measure the time of flight of the particle. 
This corresponds to the delay after which the particle is observed in the detector, after the bunch crossing. The time of flight measurement of \textsc{zdc} and \textsc{fp420} detector is implemented here. For the \textsc{zdc}, the formula is simply
\begin{equation}
 t = t_0 + \frac{1}{v} \times \Big( \frac{s-z}{\cos \theta}\Big),
\end{equation}
where $t$ is the time of flight, $t_0$ is the true time coordinate of the vertex from which the particle originates, $v$ the particle velocity, $s$ is the \textsc{zdc} distance to the interaction point, $z$ is the longitudinal coordinate of the vertex from which the particle comes from, $\theta$ is the particle emission angle. This assumes that the neutral particle observed in the \textsc{zdc} is highly relativistic, i.e. travelling at the speed of light $c$. We also assume that $\cos \theta = 1$, i.e. $\theta \approx 0$ or equivalently $\eta$ is large. As an example, $\eta = 5$ leads to $\theta = 0.013$ and $1 - \cos \theta < 10^{-4}$.
The formula then reduces to
\begin{equation}
 t = \frac{1}{c} \times (s-z)
\end{equation}
Only neutrons and photons are currently assumed to be able to reach the \textsc{zdc}. All other particles are neglected in the \textsc{zdc}.
To fix the ideas, if the \textsc{zdc} is located at $s=140~\textrm{m}$, neglecting $z$ and $\theta$, and assuming that $v=c$, one gets  $t=0.47~\mu\textrm{s}$.

\section{High-level object reconstruction}

Analysis object data contain the final collections of particles ($e^\pm$, $\mu^\pm$, $\gamma$) or objects (light jets, $b$-jets, $\tau$-jets, $E_T^\textrm{miss}$) and are stored\footnote{\texttt{[code] }All these processed data are located under the \texttt{Analysis} tree.} in the output file created by \textsc{Delphes}. 
In addition, some detector data are added: tracks, calorometric towers and hits in \textsc{zdc}, \textsc{rp220} and \textsc{fp420}. 
While electrons, muons and photons are easily identified, some other objects are more difficult to measure, like jets or missing energy due to invisible particles.
 


\subsection{Photon and charged lepton reconstruction}
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.
\subsubsection*{Electrons and photons}
Photon and electron ($e^\pm$) candidates are reconstructed if they fall into the acceptance of the tracking system and have a transverse momentum above a threshold (default $p_T > 10~\textrm{GeV}$). A calorimetric tower will be seen in the detector, an electrons leave in addition a track. Consequently, electrons and photons creates as usual a candidate in the jet collection.

\subsubsection*{Muons}

Generator level muons entering the detector acceptance are considered as candidates for the analysis level.
The acceptance is defined in terms of a transverse momentum threshold to overpass (default : $p_T > 0~\textrm{GeV}$) and of the pseudorapidity coverage of the muon system of the detector (default: $-2.4 \leq \eta \leq 2.4$).
The application of the detector resolution on the muon momentum depends on a Gaussian smearing of the $p_T$ variable\footnote{\texttt{[code]} See the \texttt{SmearMuon} method.}. Neither $\eta$ nor $\phi$ variables are modified. Multiple scattering is thus neglected, while low energy muons have a worst resolution in a real detector.

\subsubsection*{Charged lepton isolation}

To improve the quality of the contents of the charged lepton collections, additional criteria are applied to impose some isolation. This requires that the electron or muon candidate is isolated in the detector from any other particle, within a small cone. In \textsc{Delphes}, charged lepton isolation demands that there is no other charged particle with $p_T>2~\textrm{GeV}$ within a cone of $\Delta R<0.5$ around the lepton.\\ 







\subsection{Jet reconstruction}

A realistic analysis requires a correct treatment of final state particles which hadronise. Therefore, the most widely currently used jet algorithms have been integrated into the \textsc{Delphes} framework using the \textsc{FastJet} tools~\cite{bib:FastJet}. 
Six different jet reconstruction schemes are available\footnote{\texttt{[code] }The choice is done by allocating the \texttt{JET\_jetalgo } input parameter in the smearing card.}. The first three belong to the cone algorithm class while the last three are using a sequential recombinaison scheme. For all of them, the towers are used as input of the jet clustering. Jet algorithms also differ with their sensitivity to soft particles or collinear splittings, and with their computing speed performance.
 
\begin{itemize}
 
\item \textbf{Cone algorithms:}
 
\begin{enumerate}
 
\item {\it CDF JetClu}: Algorithm forming jets by associating together towers lying within a circle (default radius $R=0.7$) in the $(\eta$, $\phi)$ space. 
The so-called \textsc{jetclu} cone jet algorithm that was used by \textsc{cdf} in Run II is used. 
All towers with a transverse energy $E_T$ higher than a given threshold (default: $E_T > 1~\textrm{GeV}$) are used to seed the jet candidates. 
The existing \textsc{FastJet} code as been modified to allow easy modification or the tower pattern in $\eta$, $\phi$ space. 
In the following versions of \textsc{Delphes}, a new dedicated plugin will be created on this purpose\footnote{\texttt{[code] }\texttt{JET\_coneradius} and \texttt{JET\_seed} variables in the smearing card.}.
 
\item {\it CDF MidPoint}: Algorithm developped for the \textsc{cdf} Run II to reduce infrared and collinear sensitivity compared to purely seed-based cone by adding `midpoints' (energy barycenters) in the list of cone seeds.
 
\item {\it SISCone}: Seedless Infrared Safe Cone~\cite{bib:SIScone}: Cone algorithm simultaneously insensitive to additional soft particles and collinear splittings, and fast enough to be used in experimental analysis.
 
\end{enumerate}
 
\item {\bf Recombination algorithms:}
 
The three following infrared and collinear safe algorithms rely on recombination schemes where neighbouring calotower pairs are successively merged. The definitions of the jet algorithms are identical except for the distance used during the merging procedure. The jet reconstruction stars by finding the minimum value $d_{min}$ of all the distances $d_{ij}$ between each pair of towers and all `beam distance' $d_{iB}$. If the minimum distance is a $d_{ij}$ the towers are merged into a single tower, summing their four-momenta using the E-scheme recombination. If the minimum value is a $d_{iB}$, the object is declared as a final jet and is removed from the input list. This procedure is repeated until no input towers are left. More information on these jet can be found here.
 
\begin{enumerate}[start=4]
 
\item {\it Longitudinally invariant $k_t$ jet}:
\begin{equation}
d_{ij} = min(k_{ti}^2,k_{tj}^2)\Delta R_{ij}^2/R^2,
\end{equation}
with $\Delta R_{ij}^2= (y_i-y_j)^2+(\phi_i)-\phi_j)^2$, $k_{ti}$, $y_{i}$ and $\phi_i$ are the transverse momentum, rapidity and azimuth of calotower i and $R$ is the jet-radius parameter defined in the datacard. The beam distance is defined as $d_{iB}=k_{ti}^2$.
 
\item {\it Cambridge/Aachen jet}:
 
\begin{equation}
d_{ij} = \Delta R_{ij}^2/R^2,~d_{iB}=1.
\end{equation}
 
\item {\it Anti $k_t$ jet}: hard jets are exactly circular on Behaves like
 
\begin{equation}
d_{ij} =  min(1/k_{ti}^2,1/k_{tj}^2)\Delta R_{ij}^2/R^2,~d_{iB}=1/k_{ti}^2
\end{equation}
 \end{enumerate}
\end{itemize}
 
The reconstructed jets are conserved in the jet list if their transverse energy is bigger than {\verb PTCUT_jet }.
By default, jets are reconstructed using a cone algorithm with $R=0.7$ and use the calorimetric towers. The reconstructed jets are required to have a transverse momentum above $20~\textrm{GeV}$ and $|\eta|<3.0$. 

 
\subsection{$b$-tagging}

A jet is tagged as $b$-jets if its direction lies in the acceptance of the tracker and if it is associated to a parent $b$-quark. A $b$-tagging efficiency of $40\%$ is assumed if the jet has a parent $b$ quark. For $c$-jets and light/gluon jets, a fake $b$-tagging efficiency of $10 \%$ and $1 \%$ respectively is assumed\footnote{\texttt{[code] }Corresponding to the \texttt{TAGGING\_B}, \texttt{MISTAGGING\_C} and \texttt{MISTAGGING\_L} constants, for (respectively) the efficiency of tagging of a $b$-jet, the efficiency of mistagging a c-jet as a $b$-jet, and the efficiency of mistatting a light jet (u,d,s,g) as a $b$-jet.} 
%(Fig.~\ref{fig:btag})
. 
The (mis)tagging relies on the true particle \textsc{id} of the most energetic particle within a cone around the observed $(\eta,\phi)$ region, with a radius $R = \sqrt{\Delta \eta^2 + \Delta \phi^2}$ of $0.7$.

%\begin{figure}[!h]
%\begin{center}
%\includegraphics[width=0.6\columnwidth]{btag}
%\caption{Default efficiency of $b$-tag for jets coming from $b$ quarks, $c$ quarks and from other particles (jets from gluons or $u$, $d$ and $s$ quarks).}
%\label{fig:btag}
%\end{center}
%\end{figure}


\subsection{$\tau$ identification}

Jets originating from $\tau$-decays are identified using an identification procedure consistent with the one applied in a full detector simulation~\cite{bib:cmstaus}. 


\begin{wrapfigure}{l}{0.3\columnwidth}
\includegraphics[width=0.3\columnwidth]{Tau}
\caption{Illustration of the identification of $\tau$ jets.}
\label{h_WW_ss_cut1}
\end{wrapfigure}

The tagging rely on two properties of the $\tau$ lepton. First, in roughly $75 \%$ of the time, the hadronic $\tau$-decay products contain only one charged hadron and a number of $\pi^0$. Secondly, the particles arisen from the $\tau$ lepton produce narrow jets in the calorimeter. 

\subsubsection*{Electromagnetic collimation}

To use the narrowness of the $\tau$-jet, the \textit{electromagnetic collimation} ($C_{\tau}^{em}$) is defined as the sum of the energy in a cone with $\Delta R = ${\verb TAU_energy_scone } around the jet axis divided by the energy of the reconstructed jet. The energy in the small cone is calculated using the towers objects. To be taken into account a calorimeter tower should have a transverse energy above a given threshold {\verb JET_M_seed }. A large fraction of the jet energy, denominated here with {\verb TAU_energy_frac } is expected in this small cone. The quantity is represented in figure \ref{fig:tau1} for the default values (see table \ref{tab:tauRef}).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.8\columnwidth]{figures/Tau2}
\caption{\textcolor{red}{Distribution of the $\tau \bar \tau$ events} with respect to the electromagnetic collimation factor $C_\tau$. }
\label{fig:tau1}
\end{center}
\end{figure}

\subsubsection*{$\tau$ selection using tracks}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.8\columnwidth]{figures/Tau1}
\caption{\textcolor{red}{Distribution of the...}}
\label{h_WW_ss_cut1}
\end{center}
\end{figure}

The tracking isolation for the $\tau$ identification requires that the number of tracks associated to a particle with $p_T >$ {\verb TAU_track_pt } is one and only one in a cone with $\Delta R =$ {\verb TAU_track_scone }. This cone should be entirely included in the tracker to be taken into account. This procedure selects taus decaying hadronically with a typical efficiency of $60\%$. Moreover, the minimal $p_T$ of the $\tau$-jet is required to be {\verb TAUJET_pt } (default value: $10~\textrm{GeV}$).\\

\begin{table}[!h]
\begin{center}
\begin{tabular}[!h]{llc}
\hline
Tau definition  & Card flag & Value\\\hline
$\Delta R^{for~em}$     & {\verb TAU_energy_scone } & 0.15\\
min $E_{T}^{tower}$     & {\verb JET_M_seed }  & 1.0~GeV\\
$C_{\tau}^{em}$         & {\verb TAU_energy_frac } & 0.95.\\
$\Delta R^{for~tracks}$ & {\verb TAU_track_scone } & 0.4\\
min $p_T^{tracks}$      & {\verb PTAU_track_pt } & 2 GeV\\\hline
\end{tabular}
\label{tab:tauRef}
\end{center}
\end{table}

\subsection{Transverse missing energy}
In an ideal detector, the transverse missing energy is simply computed as the missing term which would balance the transverse momentum in the observed event. Its value is then computed as the opposite of the sum of the momentum of all observed particles. In a real experiment, any problem affecting the detector (dead channels, misalignment, noisy towers, cracks) is directly worsening the measured missing transverse energy. In this document, the missing transverse energy (\textcolor{red}{symbol???}) is based on the calorimetric towers and only muons and neutrinos are not taken into account for its evaluation.

\section{Trigger emulation}

New physics in collider experiment are often characterised by the phenomenology by low cross-section values. High statistics are required for their studies, which in turn imposes high luminosity collisions.

On the other hand, due to the very high collision rate in recent collider ($40~\textrm{MHz}$ at the \textsc{lhc}) and the large total cross-section ($\mathcal{O}(110~\textrm{mb})$ at the \textsc{lhc}), the need for an online event selection is crucial in order to reject most of the event and keep

\section{Validation}    

\section{Visualisation}


As an illustration, an associated photoproduction of a $W$ boson and a $t$ quark is shown in Fig.~\ref{fig:wt}. This corresponds to a $pp \rightarrow Wt \ +  \ p  \ + \ X$ process, where the $Wt$ couple is induced by an incoming photon emitted by one interacting proton. This leading proton survives from the photon emission and subsequently from the $pp$ interaction, and is present in the final state. The experimental signature is a lack of hadronic activity in one forward hemisphere, where the surviving proton escapes. The $t$ quark decays into a $W$ and a $b$. Both $W$ bosons decay into leptons ($W \rightarrow \mu \nu_\mu$ and $W \rightarrow \tau \nu_\tau$).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=\columnwidth]{Events_Delphes_1}
\caption{Example of $pp(\gamma p \rightarrow Wt)pY$ event. One $W$ boson decays into a $\mu \ \nu_\mu$ pair and the second one into a $\tau \ \nu_\tau$ pair. The surviving proton leaves a forward hemisphere with no hadronic activity. The isolated muon is shown as the blue vector. The $\tau$-jet is the cone around the green vector, while the reconstructed missing energy is shown in gray. One jet is visible in one forward region, along the beamline axis, opposite to the direction of the escaping proton.}
\label{fig:wt}
\end{center}
\end{figure}


\section{Conclusion and perspectives}


\newpage

\appendix

\section{User manual}

The available code is a tar file which comes with everything you need to run the \textsc{Delphes} package. Nevertheless in order to visualise the events with the \textsc{Frog} program, you need to install libraries as explained in {\it href="http://projects.hepforge.org/frog/}

\subsection{Getting started}

In order to run \textsc{Delphes} on your system, first download is sources and compile it:\\
\begin{quote}
\begin{verbatim}
me@mylaptop:~$ wget http://www.fynu.ucl.ac.be/users/s.ovyn/files/Delphes_V_*.*.tar 
me@mylaptop:~$ tar -xvf Delphes_V_*.*. tar  
me@mylaptop:~$ cd Delphes_V_*.* 
me@mylaptop:~$ ./genMakefile.tcl > Makefile 
me@mylaptop:~$ make 
\end{verbatim}
\end{quote}    


\subsection{Running \textsc{Delphes} on your events}

\subsubsection{Setting the run configuration}

The program is driven by two datacards (default cards are data/DataCardDet.dat and data/trigger.dat) which allow a large spectrum of running conditions. 
{\b The run card }\\

Contains all needed information to run \textsc{Delphes}
\begin{itemize}
  
\item The following parameters are available: detector parameters, including calorimeter and tracking coverage and resolution, transverse energy thresholds allowed for reconstructed objects, jet algorithm to use as well as jet parameters. 
  
\item Four flags, {\verb FLAG_bfield }, {\verb FLAG_vfd }, {\verb FLAG_trigger } and {\verb FLAG_frog } should be assigned to decide if the magnetic field propagation, the very forward detectors acceptance, the trigger selection and the preparation for \textsc{Frog} display respectively are running by \textsc{Delphes}.
  
\item An example (the default detector card) can be found in {\verb files/DataCardDet.dat }
\end{itemize}

{\b The trigger card }\\
Contains the definition of all trigger bits
\begin{itemize}
  
\item Cuts can be applied on the transverse momentum of electrons, muons, jets, tau-jets, photons and transverse missing energy.
\item Be careful that the following structured should be used: 
  \begin{enumerate}
  \item One trigger bit per line, the first entry in the line is the name of the trigger bit 
  \item If the trigger bit uses the presence of multiple identical objects, their transverse momentum thresholds must be defined in decreasing order 
  \item The different object requirements must be separated by a {\verb && } flag
  \item Example of a trigger bit line:\\
    \begin{quote}
\begin{verbatim}        
DoubleElec  >> ELEC1_PT: '20' && ELEC2_PT: '10'    
\end{verbatim}
    \end{quote}
  \end{enumerate}
\item An example (the default trigger card) can be found <a href="files/trigger.dat" title="Home">here</a></li>
\end{itemize}

\subsubsection{Running the code}
Create the above cards (data/mydetector.dat and data/mytrigger.dat)
Create a text file containing the list of input files that will be used by \textsc{Delphes} (with extension *.lhe, *.root or *.hep)
To run the code, type the following
\begin{quote}
\begin{verbatim}
me@mylaptop:~$ ./Delphes inputlist.list OutputRootFileName.root data/mydetector.dat data/mytrigger.dat
\end{verbatim}
\end{quote}


\subsection{Running an analysis on your \textsc{Delphes} events}

Two examples of codes running on the output root file of \textsc{Delphes} are coming with the package
\begin{enumerate}
\item The {\verb Examples/Analysis_Ex.cpp } code shows how to access the available reconstructed objects and the trigger information The two following arguments are required: a text file containing the input \textsc{Delphes} root files to run, and the name of the output root file. To run the code:
  \begin{quote}
\begin{verbatim}
./Analysis_Ex input_file.list output_file.root
\end{verbatim}
  \end{quote}
  
\item The {\verb Examples/Trigger_Only.cpp } code permits to run the trigger selection separately from the general detector simulation on output \textsc{Delphes} root files. An input \textsc{Delphes} root file is mandatory as argument. The new tree containing the trigger information will be added in these file. The trigger datacard is also necessary. To run the code:
  \begin{quote}
\begin{verbatim}
./Trigger_Only input_file.root data/trigger.dat
\end{verbatim}
  \end{quote}
  
\end{enumerate}

\subsection{Running the \textsc{Frog} event display}

\begin{itemize}
\item If the { \verb FLAG_frog } was switched on, two files were created during the run of \textsc{Delphes}: {\verb DelphesToFrog.vis } and {\verb DelphesToFrog.geom }. They contain all the needed information to run frog.
\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 }.
\item Go back into the main directory and type {\verb ./Utilities/FROG/frog }.
\end{itemize}

\begin{thebibliography}{99}
  
\bibitem{bib:Delphes} \textsc{Delphes}, hepforge:
\bibitem{bib:FastJet} \textsc{Fast-Jet},
\bibitem{bib:SIScone} A practical Seedless Infrared-Safe Cone jet algorithm, G.P. Salam, G. Soyez, JHEP0705:086,2007.
\bibitem{bib:Hector} \textsc{Hector},
\bibitem{bib:Frog} \textsc{Frog},
\bibitem{bib:CMSresolution} CMS IN 2007/053
\bibitem{bib:Root} \textsc{Root} - An Object Oriented Data Analysis Framework, R. Brun and F. Rademakers, Nucl. Inst. \& Meth. in Phys. Res. A 389 (1997) 81-86, \url{http://root.cern.ch} 
\bibitem{bib:cmstaus} Tau reconstruction in CMS
\end{thebibliography}

In the list of input files, all files should have the same type 

 in other words, the effect related to the particle showers that would happen in the calorimeters are not taken into account.

\end{document}