== Pile-up implementation in Delphes ==

Multiple particle interactions per bunch-crossing are now implemented in Delphes. The procedure is divided in two main parts: 

* mixing pile-up events with the main interaction
* pile-up subtraction with the fast jet area method

An example card that uses the following is {{{examples/delphes_card_CMS_PileUp.tcl}}}

=== Mixing pile-up ===

The mixing procedure is done via the {{{PileUpMerger}}} module. The user can specify 4 parameters: {{{PileUpFile}}}, {{{MeanPileUp}}}, {{{PileUpDistribution}}}, {{{ZVertexWidth}}}, {{{ZVertexResolution}}}.

* {{{PileUpFile}}}: 

the event sample containing pile-up events in binary format. This format allows for faster random event access compared to root trees. Basic information about the event is contained (particle 4-momenta, vertex position, and Particle ID)

This sample has to be generated in advance with an event generator (typically Pythia6/8 or HERWIG) and then converted into binary format (see example below).

* {{{MeanPileUp}}}:

the average amount of pile-up events per bunch-crossing. For each hard scattering, N pile-up events will be randomly chosen from the {{{PileUpFile}}}, where N is a random number following a distribution defined by the parameter {{{PileUpDistribution}}} with a mean {{{MeanPileUp}}}.

* {{{PileUpDistribution}}}

defines the distribution of the number of pile-up events. 0 for Poisson, 1 for Uniform. 

* {{{ZVertexSpread}}}:

Pile-up and hard scattering events are randomly distributed in time and z position according to some parametrization specified by the user (in meters and second units). It can be either continuous or binned:

{{{
set VertexDistributionFormula {exp(-(t^2/(2*(0.05/2.99792458E8*exp(-(z^2/(2*(0.05)^2))))^2)))}
}}}

{{{
set VertexDistributionFormula { (abs(t) <= 1.0e-09) * (abs(z) <= 0.15) * (1.00) + \
                                                 (abs(t) >  1.0e-09) * (abs(z) <= 0.15) * (0.00) + \
                                                 (abs(t) <= 1.0e-09) * (abs(z) > 0.15)  * (0.00) + \
                                                 (abs(t) >  1.0e-09) * (abs(z) > 0.15)  * (0.00)}

}}}
 

=== Time propagation and measurement ===

The time particle candidate of each particle candidate is then propagated up to the calorimeters. 
For calorimeter towers and jets, which are composite objects, the final time is simply the average time weighted by sqrt(E) of each individual component.

By default the time information is now stored in each output collection object. However, in order to account for an actual timing measurement,
the module !TimeSmearing should be called. This module simply smears (by a gaussian) the final time according to some resolution specificed by the user, controlled by the parameter

{{{
set TimeResolution 1.0e-10
}}}

A simple example of time propagation for muons is provided in the card {{{examples/delphes_card_CMS_PileUp_Timing.tcl }}}

=== Pile-up contamination ===

For estimating neutral pile-up contribution we use the well known fastjet area method, see for instance [http://arxiv.org/abs/0802.1188 arXiv:0802.1188], [http://arxiv.org/abs/0707.1378 arXiv:0707.1378].

First, the user must specify whether to calculate the area while clustering the jets within the {{{FastJetFinder}}} module. Several methods for the area calculation can be specified (active area, passive area, Voronoi …) via the parameter {{{AreaAlgorithm}}}. By default this parameter is set to 0 (no area calculation):

{{{
# area algorithm: 0 Do not compute area, 1 Active area explicit ghosts, 2 One ghost passive area, 3 Passive area, 4 Voronoi, 5 Active area
set AreaAlgorithm 5
}}} 

Then the median density (in GeV/A) of pile-up contamination (rho) per event can the be computed within the {{{FastJetFinder}}} module:

{{{
set ComputeRho true
set RhoOutputArray rho
}}}

Note that it is common to use one jet algorithm for the rho density calculation (e.g kt with 0.6 cone) and one for the analysis (anti-kt with 0.5). In such a case, in order to be able to perform the pile-up subtraction (see below), one needs to compute the area also for the jets relevant for the analysis.

It is now possible to specify several eta ranges for the computation of the pile-up density, leading to a more accurate estimate. For instance:

{{{
add RhoEtaRange 0.0 2.5
add RhoEtaRange 2.5 5.0
}}}


=== Charged Pile-up subtraction ===

The charged pile-up subtraction is done via the !TrackPileUpSubtractor module. 
It simply removes from the specified input collections tracks that are distant enough from the primary vertex.
The distance is controlled by the parameter !ZVertexResolution:

* {{{ZVertexResolution}}}

For |z|< ZVertexResolution the hard interaction vertex cannot be distinguished from pile-up vertices.
For |z|> ZVertexResolution the hard interaction vertex can be distinguished from pile-up vertices.


{{{

module TrackPileUpSubtractor TrackPileUpSubtractor {

  add InputArray Calorimeter/eflowTracks eflowTracks
  add InputArray ElectronEnergySmearing/electrons electrons
  add InputArray MuonMomentumSmearing/muons muons

  set ZVertexResolution 0.0001
}

}}}

=== Neutral Pile-up subtraction ===

Since charged particles have already been subtracted to some extent, pile-up contamination only affects the jet energy resolution and the lepton/photon isolation.

* Jet pile-up subtraction is done via the {{{JetPileUpSubtractor}}} module that takes as input the jet collection and rho:

{{{
set JetInputArray FastJetFinder/jets
set RhoInputArray rho
}}}

* Isolation subtraction is done inside the {{{Isolation}}} module itself just by adding the line in the delphes card:

{{{
set RhoInputArray rho
}}}






== Running Delphes with Pile-Up ==

Convert your minimum bias sample into binary format:

{{{
./stdhep2pileup MinBias.pileup MinBias.hep
./hepmc2pileup MinBias.pileup MinBias.hepmc
./root2pileup MinBias.pileup MinBias.root
}}}

or, alternatively, download (and unzip) here: [http://cp3.irmp.ucl.ac.be/downloads/MinBias.pileup.gz MinBias.pileup.gz]

Run Delphes on your sample X with pile-up:

{{{
./DelphesSTDHEP examples/delphes_card_CMS_PileUp.tcl X_PileUp.root X.hep
./DelphesSTDHEP examples/delphes_card_ATLAS_PileUp.tcl X_PileUp.root X.hep
}}}