== 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

=== 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.

* {{{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 ===

The density (in GeV/A) of pile-up contamination (rho) per event is computed within the {{{FastJetFinder}}} module if the following parameters are defined:

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

The method for the area calculation can also be specified (active area, passive area, Voronoi …) via the parameter {{{AreaAlgorithm}}}. 

=== Pile-up subtraction ===

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

* 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 Delphes ROOT format:

{{{
./DelphesSTDHEP examples/root_converter.tcl MinBias.root MinBias.hep
./DelphesHepMC examples/root_converter.tcl MinBias.root MinBias.hepmc
}}}

Convert from Delphes ROOT format to binary

{{{
./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
}}}