Matching and Merging

• A formal order-by-order perturbative calculation, in each order higher including graphs both with one particle more in the final state and with one loop more in the intermediate state. This is accurate to the order of the calculation, and limited to a first- or second-order corrections.
• Multiple hard real emission corrections, but neglecting the virtual corrections that should accompany the corrections. Thereby it is possible to allow for topologies with a larger and varying number of partons, at the prize of not being accurate to any particular order.
• The parton shower provides an approximation to higher orders, both real and virtual contributions for the emission of arbitrarily many particles.

The common traits of all combination methods are that matrix elements are used to describe the production of hard and well separated particles, and parton showers for the production of soft or collinear particles. What differs between the various approaches that have been proposed are which matrix elements are being used, how doublecounting is avoided, and how the transition from the hard to the soft regime is handled. These combination methods are typically referred to as "matching" or "merging" algorithms. There is some confusion about the distinction between the two terms. We will use "matching" to describe the combination of one (NLO) calculation with the parton shower, and "merging" when several calculations are combined with each other (and the shower). PYTHIA offers implementations of several different matching and merging algorithms, which hopefully suit most needs.

• For many/most resonance decays the first branching in the shower is merged with first-order matrix elements [] Nor01. This means that the emission rate is accurate to NLO, similarly to the POWHEG strategy (see below), but built into the timelike showers. The angular orientation of the event after the first emission is only handled by the parton shower kinematics, however. Needless to say, this formalism is precisely what is tested by Z^0 decays at LEP1, and it is known to do a pretty good job there.
• Also the spacelike showers contain a correction to first-order matrix elements, but only for the one-body-final-state processes q qbar → gamma^*/Z^0/W^+-/h^0/H^0/A0/Z'0/W'+-/R0 [Miu99] and g g → h^0/H^0/A0, and only to leading order. That is, it is equivalent to the POWHEG formalism for the real emission, but the prefactor "cross section normalization" is LO rather than NLO. Therefore this framework is less relevant, and has been superseded the following ones.
• The POWHEG strategy [Nas04] provides a cross section accurate to NLO. The hardest emission is constructed with unit probability, based on the ratio of the real-emission matrix element to the Born-level cross section, and with a Sudakov factor derived from this ratio, i.e. the philosophy introduced in [Ben87].
  While POWHEG is a generic strategy, the POWHEG BOX [Ali10] is an explicit framework, within which several processes are available. The code required for merging the PYTHIA showers with POWHEG input can be found in include/Pythia8Plugins/PowHegHooks.h, and is further described on a separate page. A user example is found in examples/main153.cc.
• The other traditional approach for NLO calculations is the MC@NLO one [Fri02]. In it the shower emission probability, without its Sudakov factor, is subtracted from the real-emission matrix element to regularize divergences. It therefore requires a analytic knowledge of the way the shower populates phase space. The aMC@NLO package [Fre11] offers an implementation for PYTHIA 8, developed by Paolo Torrielli and Stefano Frixione. The global-recoil option of the PYTHIA final-state shower has been constructed to be used for the above-mentioned subtraction.
• Multi-jet merging in the CKKW-L approach [Lon01] is directly available. Its implementation, relevant parameters and test programs are documented on a separate page.
• Multi-jet matching in the MLM approach [Man02, Man07] is also available, either based on the ALPGEN or on the Madgraph variant, and with input events either from ALPGEN or from Madgraph. For details see separate page.
• Unitarised matrix element + parton shower merging (UMEPS) is directly available. Its implementation, relevant parameters and test programs are documented on a separate page.
• Next-to-leading order multi-jet merging (in the NL3 and UNLOPS approaches) is directly available. Its implementation, relevant parameters and test programs are documented on a separate page.
• Next-to-leading order jet matching in the FxFx approach is also available. For details see the jet matching page.

For quick-and-dirty studies, note that the field is open-ended, however: any external program can feed in Les Houches events that PYTHIA subsequently processes. In this case, the maximum pT of the shower evolution is set by the Les Houches scale, on the one hand, and by the values of the SpaceShower:pTmaxMatch, TimeShower:pTmaxMatch and other parton-shower settings, on the other. It is typically not possible to achieve perfect matching this simplistic way, given that the PYTHIA pT evolution variables are not likely to agree with the variables used for cuts in the external program. Often one can get close enough with simple means but, for an improved matching, User Hooks may be inserted to control the steps taken on the way, e.g. to veto those parton shower branchings that would doublecount emissions included in the matrix elements.

main164.cc: A generic interface for matching and merging

All settings can be transferred to main164.cc through an input file. The input file is part of the command line input of main164.cc, i.e. you can execute main164 with the command

./main164 myInputFile.cmnd

to read the input myInputFile.cmnd. Since main164.cc is currently a "front-end" for different types of matching/merging, we will briefly discuss the inputs for this sample program in the following.

Inputs

Beams:frameType = 4
Beams:LHEF = file.lhe

or with HDF5 event files by setting

Beams:frameType = 5
Beams:LHEF = file.hdf5

It is possible to include all parton multiplicities in one sample. If e.g. UMEPS merging for W-boson + up to two additional partons is to be performed, either one LHE file containing W+zero, W+one and W+two parton events or three separate LHE files can be generated.

All input settings are handed to main164.cc in the form of an input file. We have included the input settings files

         main164mlm.cmnd, which illustrates the MLM jet matching interface,

         main164fxfx.cmnd, which illustrates the FxFx NLO jet matching interface,

         main164ckkwl.cmnd, which illustrates the CKKW-L multi-jet merging interface,

         main164mess.cmnd, which illustrates the VINCIA MESS multi-jet merging interface,

         main164umeps.cmnd, which illustrates the UMEPS multi-jet merging interface, and

         main164unlops.cmnd, which illustrates the UNLOPS multi-jet NLO merging interface.

Other settings (e.g. using main164.cc as simple LO+PS or as MC@NLO interface) are of course possible. In the following, we will briefly explain how input for the five choices above are generated and handled.

MC@NLO matching with main164.cc

POWHEG matching with main164.cc

MLM jet matching with main164.cc

FxFx (NLO) jet matching with main164.cc

CKKW-L merging with main164.cc

Sector merging (MESS) in VINCIA with main164.cc

UMEPS merging with main164.cc

UNLOPS (NLO) merging with main164.cc