Alpgen-specific parameters

Madgraph-specific parameters

A preliminary implementation of the FxFx prescription for combining multiple NLO calculations [Fre12] is available. We would like to stress that this implementation is still undergoing validation. FxFx merging with aMC@NLO shares most parameters with the leading-order (MadGraph-style) MLM prescriptions and can be activated by using the three additional settings below.

JetMatching:doFxFx On Off   (default = off)
If turned on, then FxFx merging with aMC@NLO inputs is performed. Note that this requires event samples that are specifically generated for this task.

mode  JetMatching:nPartonsNow   (default = -1)
The number of partons in Born-like events for the current input LHEF. If the current sample e.g. contains pp → e+e- + 2 partons Born-like configurations, and pp → e+e- + 3 partons Real-emission-type events, then JetMatching:nPartonsNow = 2 applies.

JetMatching:qCutME

(default = 10.0)

The cut applied to regulate multi-jet matrix elements. Note that this cut can differ from the matching scale.

Alpgen-style parton-jet matching and merging

First, either the CellJet or SlowJet jet algorithm is chosen. Both of these algorithms have an R and an etaMax parameter. In addition, CellJet has an eTmin and SlowJet has a pTmin parameter. These are the primary three parameters of the merging procedure, and in practice are set dependent on the cuts applied to the matrix element (ME) generation. We stress that the merging procedure is not tied to the geometry of a specific physical detector, but only to the match between the original partons and the resulting jets, using standard jet algorithms in the phase space region where partons have been generated.

ME samples with different jet multiplicities are run through the event generator, and the generation interrupted after parton showers have been applied, but before resonance decays and beam remnants have been processed. Note in particular that top quarks will not yet be decayed, which may lead to slight differences with the PYTHIA 6 interface included with the ALPGEN package. In what follows, the hardness measure of jets/partons is taken to be eT when CellJet is used and pT when SlowJet is used. The hard system (ignoring all MPI systems) is then analysed:

• The particles in the original matrix element process are sorted into light partons, heavy partons and other particles. For backwards compatibility, a light parton is defined as the set (d, u, s, c, b, g) with zero mass. A heavy parton is defined as the set (c, b, t) with non-zero mass.
• All particles not originating from the heavy partons or other particles are passed to the jet algorithm and clustered.
• Clustered jets are matched to the light partons in the original ME process. There are two different methods which can be used:
  • Method 1: The following is done for each parton, in order of decreasing hardness. The delta R between the parton and all jets is calculated and the smallest value taken. If this is less than the jet R parameter, possibly multiplied by a constant, the jet and parton are considered to match, and the jet is removed from further consideration. Note that for CellJet the delta R measure is in (eta, phi), while for SlowJet, it is in (y, phi).
  • Method 2: This method is only possible when using the SlowJet algorithm. Before the clustering is performed, extremely soft "ghost" particles are added to the event at the (y, phi) coordinates of the original matrix element partons. If such a particle is clustered into a jet, the parton and jet are considered to match. The idea of "ghost" particles was originally introduced by FastJet as a way to measure jet areas [Cac06] and should not affect clustering with an infrared-safe jet algorithm.
• If there is a light ME parton remaining which has not been matched to a jet, then the event is vetoed. If all ME partons have been matched to a jet, but there are still some extra jets remaining, then two options are possible:
  • Exclusive mode: the event is vetoed. This is typically used when there are ME samples with higher jet multiplicities, which would fill in the extra jets.
  • Inclusive mode: the event is retained if the extra jets are softer than the softest matched jet. This is typically used when there is no ME sample with higher jet multiplicity, so the parton shower should be allowed to give extra jets.
• All particles originating from the heavy partons are passed to the jet algorithm and clustered.
• The clustered jets are again matched to the original partons, but there is no requirement for a match to be present; all matched jets are immediately discarded. The matching procedure is much the same as for light partons, but with two differences when delta R matching is used. First, a different R parameter than that used by the jet algorithm may optionally be given. Second, all jets that are within the given radius of the parton are matched, not just the one with the smallest delta R measure. If there are still extra jets remaining then in exclusive mode the event is immediately vetoed, while in inclusive mode the event is retained if the extra jets are softer than the softest light matched jet.

Some different options are provided, specified further above in the parameters section. These are set so that, by default, the algorithm closely follows the official MLM interface provided in the ALPGEN package.

All vetoing of events is done through the usual ";?>User Hooks machinery, and is therefore already taken into account in the cross section. In the output from ";?>Pythia::stat(), the difference between the "Selected" and "Accepted" columns gives the number of events that have not survived the vetoing procedure. It is still the responsibility of the user to add together the results from runs with different jet multiplicities. In the simplest case, when ALPGEN input is used and the hard process parameters are used to guide the merging procedure, it is enough to set the JetMatching:nJetMax parameter.

Madgraph-style parton-jet Merging and Matching

This section describes the Madgraph-style parton-jet matching algorithm for PYTHIA8.

First, the k_T jet algorithm is applied using the PYTHIA8 SlowJet implementation. The useStandardR = false is used, ie. the (delta R)^2 separation is defined as 2 (cosh(delta y) - cos(delta phi)) rather than the more common (delta y)^2 + delta phi)^2. The R, etaMax, and a pTmin parameters are specified. By default, R = 1 and pTmin = qCut . It is not recommended to change these. These should match the algorithm parameters used in the Madgraph Matrix Element (ME) generation.

ME samples with different jet multiplicities are run through the event generator, and the generation is interrupted after parton showers have been applied, but before resonance decays and beam remnants have been processed. In what follows, the hardness measure of jets/partons is taken to be k_T relative to qCut. The hard system (ignoring all MPI systems) is analyzed:

• The hard partons in the original matrix element process, provided by the LHEF, are sorted into light partons, heavy partons and other particles. A heavy parton is defined by the JetMatching:nQmatch or by the maxjetflavor value in the LHEF. nQmatch refers to the absolute value of the quark PDG identity code.
• All partons arising from the parton shower are sorted based on their motherhood. A showered parton arising from a heavy parton or "other" parton classified in the previous step is not passed to the jet algorithm. All other partons are clustered into light jets.
• It is checked whether there are "too few" or "too many" light jets. If the number of light jets is less than the number of light partons defined by nQmatch, the event is vetoed. If the number is larger, the event is vetoed only in exclusive mode (defined below).
• In exclusive mode, the number of jets matches the number of light partons. In inclusive mode, the jets are re-clustered until the number of jets equals the number of light partons. Next, each light hard parton is clustered, one at a time, with the jets until a match is found. A match is defined as a squared cluster scale that equals:
  • |clFact| * qCut for inclusive mode,
  • |clFact| * max(qCut,min(p_T(parton))) for exclusive mode, clFact ≥ 0, or
  • |clFact| * min(k_T(parton)) for exclusive mode, clFact < 0.
  If no match is found, the event is vetoed. When a parton matches a jet, the jet is removed from the collection, and the process continues. The process terminates when all partons are matched to a jet, or a parton is unmatched.
• All particles originating from the heavy partons are not used.

Some different options are provided, specified further above. These are set so that, by default, the algorithm closely follows the FORTRAN interface ME2Pythia provided in the Madgraph package.

All vetoing of events is done through the usual ";?>User Hooks machinery, and is therefore already taken into account in the cross section. In the output from ";?>Pythia::stat(), the difference between the "Selected" and "Accepted" columns gives the number of events that have not survived the vetoing procedure. It is still the responsibility of the user to add together the results from runs with different jet multiplicities. In the simplest case, when the hard process parameters are used to guide the merging procedure, events will be matched in the exclusive mode.

Madgraph-style jet matching with no internal vetoes (assuming an external veto implementation)

This section describes the facilities that allow expert users to use their own veto code to perform a Madgraph-style jet matching. This can e.g. be useful to assess jet matching uncertainties without having to process the same input events multiple times.

As a first step, any vetoes in the Pythia Jet Matching need to be disabled by using JetMatching:doVeto = off. In this mode, Pythia only stores all the information that is necessary to check (and apply) the shower-kT or kT-MLM vetoes externally by hand. This information can be accessed by calling the functions

Event JetMatchingMadgraph::getWorkEventJet()  
Return the event after parton showering, without resonance decay products and particles that should not be included in the jet matching, as necessary to implement the vetoes in the kT-MLM scheme.

Event JetMatchingMadgraph::getProcessSubset()  
Return the event record containing the hard process, without resonance decay products and particles that should not be included in the jet matching, as necessary to implement the vetoes in the shower-kT and kT-MLM schemes. In the former, this event is needed to find the lowest pT in the ME inputs. In the latter, the event record is used to count the number of hard-process partons, minimal hard process pT, and to perform the matching of hard-process particles to shower jets.

bool JetMatchingMadgraph::getExclusive()  
Return flag to identify if exclusive or inclusive vetoes should be applied to this event.

double JetMatchingMadgraph::getPTfirst()  
Return the transverse momentum (w.r.t. the beam) of the first parton shower emission, as needed for the shower-kT scheme.

vector <double> JetMatchingMadgraph::getDJR()  
Return a vector of jet clustering scales produced by running the jet algorithm used for jet matching on the event record without resonance decay products and particles that should not be included in the matching. In this vector, clustering scales for combining few jets appear before scales from combining many jets. This function is useful for the kT-MLM scheme, or to have quick access to this information for histogramming and sanity checks.

We do not currently supply example code for this very advanced functionality. Interested expert users should feel free to contact the Pythia authors for further explanations.

A note on combining UserHooks

One must then combine multiple UserHooks classes, such that the functionality of both is present. A prerequisite is that the different UserHooks classes should be declared with virtual inheritance, e.g.

 
  class JetMatching : virtual public UserHooks 

The two first classes in CombineMatchingInput.h combine ALPGEN input with the two different matching schemes, e.g. for the first

 
class JetMatchingAlpgenInputAlpgen : public AlpgenHooks, 
  public JetMatchingAlpgen { 
public: 
  // Constructor and destructor. 
  JetMatchingAlpgenInputAlpgen(Pythia& pythia) : AlpgenHooks(pythia), 
    JetMatchingAlpgen() { } 
  ~JetMatchingAlpgenInputAlpgen() {} 
  // Initialisation. 
  virtual bool initAfterBeams() { 
    if (!AlpgenHooks::initAfterBeams()) return false; 
    if (!JetMatchingAlpgen::initAfterBeams()) return false; 
    return true; 
  } 
  // Process level vetos. 
  virtual bool canVetoProcessLevel() { 
    return JetMatchingAlpgen::canVetoProcessLevel(); 
  } 
  .... 
};