== 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}}}, {{{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 Poisson statistics with a mean {{{MeanPileUp}}}.

* {{{ZVertexSpread}}}:

Pile-up events randomly populate the z-axis. The position of each pile-up event is generated from a gaussian distribution with a standard deviation ZVertexSpread.

* {{{ZVertexResolution}}}

For |z|< ZVertexResolution the hard interaction vertex cannot be distinguished from pile-up vertices. For such pile-up events both charged and neutrals are then merged in the event (no charged particle subtraction).
For |z|> ZVertexResolution the hard interaction vertex can be distinguished from pile-up vertices. For such pile-up events only neutrals are merged in the event (total charged particle subtraction), which assumes perfect vertex resolution and efficiency.

=== Pile-up contamination ===

For estimating 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.  
 

=== 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
}}}

Run Delphes on your sample X with pile-up:

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