User Hooks

Sometimes it may be convenient to step in during the generation process: to modify the built-in cross sections, to veto undesirable events or simply to collect statistics at various stages of the evolution. There is a base class UserHooks that gives you this access at a few selected places. This class in itself does nothing; the idea is that you should write your own derived class for your task. One simple derived class (SuppressSmallPT) comes with the program, mainly as illustration, and the main10.cc program provides a complete (toy) example how a derived class could be set up and used.

There are eight sets of routines, that give you different kinds of freedom. They are, in no particular order:
(i) Ones that give you access to the event record in between the process-level and parton-level steps, or in between the parton-level and hadron-level ones. You can study the event record and decide whether to veto this event.
(ii) Ones that allow you to set a scale at which the combined parton-level MPI+ISR+FSR downwards evolution in pT is temporarily interrupted, so the event can be studied and either vetoed or allowed to continue the evolution.
(iii) Ones that allow you to to study the event after the first few ISR/FSR emissions, or first few MPI, so the event can be vetoed or allowed to continue the evolution.
(iv) Ones that allow you to study the latest initial- or final-state emission and veto that emission, without vetoing the event as a whole.
(v) Ones that give you access to the properties of the trial hard process, so that you can modify the internal Pythia cross section, alternatively the phase space sampling, by your own correction factors.
(vi) Ones that allow you to reject the decay sequence of resonances at the process level.
(vii) Ones that let you set the scale of shower evolution, specifically for matching in resonance decays.
(viii) Ones that allow colour reconnection, notably in connection with resonance decays.
They are described further in the following numbered subsections.

All the possibilities above can be combined freely and also be combined with the standard flags. An event would then survive only if it survived each of the possible veto methods. There are no hidden interdependencies in this game, but of course some combinations may not be particularly meaningful. For instance, if you set PartonLevel:all = off then the doVetoPT(...) and doVetoPartonLevel(...) locations in the code are not even reached, so they would never be called.

The effect of the vetoes of types (i), (ii) and (iii) can be studied in the output of the Pythia::statistics() method. The "Selected" column represents the number of events that were found acceptable by the internal Pythia machinery, whereas the "Accepted" one are the events that also survived the user cuts. The cross section is based on the latter number, and so is reduced by the amount associated by the vetoed events. Also type (v) modifies the cross section, while types (iv), (vi) and (vii) do not.

A warning. When you program your own derived class, do remember that you must exactly match the arguments of the base-class methods you overload. If not, your methods will be considered as completely new ones, and compile without any warnings, but not be used inside Pythia. So, at the debug stage, do insert some suitable print statements to check that the new methods are called (and do what they should).

The basic components

For a derived UserHooks class to be called during the execution, a pointer to an object of this class should be handed in with the
Pythia::setUserHooksPtr( UserHooks*)
method. The first step therefore is to construct your own derived class, of course. This must contain a constructor and a destructor. The initPtr method comes "for free", and is set up without any intervention from you.

UserHooks::UserHooks()  
virtual UserHooks::~UserHooks()  
The constructor and destructor do not need to do anything.

void UserHooks::initPtr( Info* infoPtr, Settings* settingsPtr, ParticleData* particleDataPtr, Rndm* rndmPtr, BeamParticle* beamAPtr, BeamParticle* beamBPtr, BeamParticle* beamPomAPtr, BeamParticle* beamPomBPtr, CoupSM* coupSMPtr, PartonSystems* partonSystemsPtr, SigmaTotal* sigmaTotPtr)  
this (non-virtual) method is automatically called during the initialization stage to set several useful pointers, and to set up the workEvent below. The corresponding objects can later be used to extract some useful information.
Info: general event and run information, including some loop counters.
Settings: the settings used to determine the character of the run.
ParticleData: the particle data used in the event record (including workEvent below).
Rndm: the random number generator, that you could also use in your code.
BeamParticle: the beamAPtr and beamBPtr beam particles contain info on partons extracted from the two incoming beams, on the PDFs used, and more. In cases when diffraction is simulated, also special Pomeron beams beamPomAPtr and beamPomBPtr are introduced, for the Pomerons residing inside the respective proton.
CoupSM: Standard Model couplings.
PartonSystems: the list of partons that belong to each individual subcollision system.
SigmaTotal: total/elastic/diffractive cross section parametrizations.

Next you overload the desired methods listed in the sections below. These often come in pairs or triplets, where the first must return true for the last method to be called. This latter method typically hands you a reference to the event record, which you then can use to decide whether or not to veto. Often the event record can be quite lengthy and difficult to overview. The following methods and data member can then come in handy.

void UserHooks::omitResonanceDecays(const Event& process, bool finalOnly = false)  
is a protected method that you can make use of in your own methods to extract a simplified list of the hard process, where all resonance decay chains are omitted. Intended for the can/doVetoProcessLevel routines. Note that the normal process-level generation does include resonance decays. That is, if a top quark is produced in the hard process, then also decays such as t → b W+, W+ → u dbar will be generated and stored in process. The omitResonanceDecays routine will take the input process and copy it to workEvent (see below), minus the resonance decay chains. All particles produced in the hard process, such as the top, will be considered final-state ones, with positive status and no daughters, just as it is before resonances are allowed to decay.
(In the PartonLevel routines, these decay chains will initially not be copied from process to event. Instead the combined MPI, ISR and FSR evolution is done with the top above as final particle. Only afterwards will the resonance decay chains be copied over, with kinematics changes reflecting those of the top, and showers in the decays carried out.)
For the default finalOnly = false the beam particles and incoming partons are retained, so the event looks like a normal event record up to the point of resonance decays, with a normal history setup.
With finalOnly = true only the final-state partons are retained in the list. It therefore becomes similar in functionality to the subEvent method below, with the difference that subEvent counts the decay products of the resonances as the final state, whereas here the resonances themselves are the final state. Since the history has been removed in this option, mother1() and mother2() return 0, while daughter1() and daughter2() both return the index of the same parton in the original event record.

void UserHooks::subEvent(const Event& event, bool isHardest = true)  
is a protected method that you can make use of in your own methods to extract a brief list of the current partons of interest, with all irrelevant ones omitted. It is primarily intended to track the evolution at the parton level, notably the shower evolution of the hardest (i.e. first) interaction.
For the default isHardest = true only the outgoing partons from the hardest interaction (including the partons added to it by ISR and FSR) are extracted, as relevant e.g. for doVetoPT( iPos, event) with iPos = 0 - 4. With isHardest = false instead the outgoing partons of the latest "subprocess" are extracted, as relevant when iPos = 5, where it corresponds to the outgoing partons in the currently considered decay.
The method also works at the process level, but there simply extracts all final-state partons in the event, and thus offers no extra functionality.
The result is stored in workEvent below. Since the history has been removed, mother1() and mother2() return 0, while daughter1() and daughter2() both return the index of the same parton in the original event record (event; possibly process), so that you can trace the full history, if of interest.

Event UserHooks::workEvent  
This protected class member contains the outcome of the above omitResonanceDecays(...) and subEvent(...) methods. Alternatively you can use it for whatever temporary purposes you wish. You are free to use standard operations, e.g. to boost the event to its rest frame before analysis, or remove particles that should not be analyzed. The workEvent can also be sent on to a jet clustering algorithm.

(i) Interrupt between the main generation levels

virtual bool UserHooks::initAfterBeams()  
This routine is called by Pythia::init(), after the beams have been set up, but before any other initialisation. Therefore, at this stage, it is still possible to modify settings (apart from Beams:*) and particle data. This is mainly intended to be used in conjunction with Les Houches Event files, where headers are read in during beam initialisation, see the header functions in the Info class. In the base class this method returns true. By returning false, PYTHIA initialisation will be aborted.

virtual bool UserHooks::canVetoProcessLevel()  
In the base class this method returns false. If you redefine it to return true then the method doVetoProcessLevel(...) will be called immediately after a hard process (and associated resonance decays) has been selected and stored in the process event record.
At this stage, the process record typically contains the two beams in slots 1 and 2, the two incoming partons to the hard process in slots 3 and 4, the N (usually 1, 2 or 3) primary produced particles in slots 5 through 4 + N, and thereafter recursively the resonance decay chains, if any. Use the method omitResonanceDecays(...) if you want to skip these decay chains. There are exceptions to this structure, for soft QCD processes (where the partonic process may not yet have been selected at this stage), and when a second hard process has been requested (where two hard processes are bookkept). In general it is useful to begin the development work by listing a few process records, to clarify what the structure is for the cases of interest.

virtual bool UserHooks::doVetoProcessLevel(Event& process)  
can optionally be called, as described above. You can study the process event record of the hard process. Based on that you can decide whether to veto the event, true, or let it continue to evolve, false. If you veto, then this event is not counted among the accepted ones, and does not contribute to the estimated cross section. The Pytha::next() method will begin a completely new event, so the vetoed event will not appear in the output of Pythia::next().
Warning: Normally you should not modify the process event record. However, for some matrix-element-matching procedures it may become unavoidable. If so, be very careful, since there are many pitfalls. Only to give one example: if you modify the incoming partons then also the information stored in the beam particles may need to be modified.
Note: the above veto is different from setting the flag PartonLevel:all = off. Also in the latter case the event generation will stop after the process level, but an event generated up to this point is considered perfectly acceptable. It can be studied and it contributes to the cross section. That is, PartonLevel:all = off is intended for simple studies of hard processes, where one can save a lot of time by not generating the rest of the story. By contrast, the doVetoProcessLevel() method allows you to throw away uninteresting events at an early stage to save time, but those events that do survive the veto are allowed to develop into complete final states (unless flags have been set otherwise).

virtual bool UserHooks::canVetoPartonLevel()  
In the base class this method returns false. If you redefine it to return true then the method doVetoPartonLevel(...) will be called immediately after the parton level has been generated and stored in the event event record. Thus showers, multiparton interactions and beam remnants have been set up, but hadronization and decays have not yet been performed. This is already a fairly complete event, possibly with quite a complex parton-level history. Therefore it is usually only meaningful to study the hardest interaction, e.g. using subEvent(...) introduced above, or fairly generic properties, such as the parton-level jet structure.

virtual bool UserHooks::doVetoPartonLevel(const Event& event)  
can optionally be called, as described above. You can study, but not modify, the event event record of the partonic process. Based on that you can decide whether to veto the event, true, or let it continue to evolve, false. If you veto, then this event is not counted among the accepted ones, and does not contribute to the estimated cross section. The Pytha::next() method will begin a completely new event, so the vetoed event will not appear in the output of Pythia::next().
Note: the above veto is different from setting the flag HadronLevel:all = off. Also in the latter case the event generation will stop after the parton level, but an event generated up to this point is considered perfectly acceptable. It can be studied and it contributes to the cross section. That is, HadronLevel:all = off is intended for simple studies of complete partonic states, where one can save time by not generating the complete hadronic final state. By contrast, the doVetoPartonLevel() method allows you to throw away uninteresting events to save time that way, but those events that do survive the veto are allowed to develop into complete final states (unless flags have been set otherwise).

virtual bool UserHooks::canVetoPartonLevelEarly()  
is very similar to canVetoPartonLevel() above, except that the chance to veto appears somewhat earlier in the generation chain, after showers and multiparton interactions, but before the beam remnants and resonance decays have been added. It is therefore somewhat more convenient for many matrix element strategies, where the primordial kT added along with the beam remnants should not be included.

virtual bool UserHooks::doVetoPartonLevelEarly(const Event& event)  
is very similar to doVetoPartonLevel(...) above, but the veto can be done earlier, as described for canVetoPartonLevelEarly().

(ii) Interrupt during the parton-level evolution, at a pT scale

During the parton-level evolution, multiparton interactions (MPI), initial-state radiation (ISR) and final-state radiation (FSR) are normally evolved downwards in one interleaved evolution sequence of decreasing pT values. For some applications, e.g matrix-element-matching approaches, it may be convenient to stop the evolution temporarily when the "hard" emissions have been considered, but before continuing with the more time-consuming soft activity. Based on these hard partons one can make a decision whether the event at all falls in the intended event class, e.g. has the "right" number of parton-level jets. If yes then, as for the methods above, the evolution will continue all the way up to a complete event. Also as above, if no, then the event will not be considered in the final cross section.

Recall that the new or modified partons resulting from a MPI, ISR or FSR step are always appended to the end of the then-current event record. Previously existing partons are not touched, except for the status, mother and daughter values, which are updated to reflect the modified history. It is therefore straightforward to find the partons associated with the most recent occurrence.
An MPI results in four new partons being appended, two incoming and two outgoing ones.
An ISR results in the whole affected system being copied down, with one of the two incoming partons being replaced by a new one, and one more outgoing parton.
An FSR results in three new partons, two that come from the branching and one that takes the recoil.
The story becomes more messy when rescattering is allowed as part of the MPI machinery. Then there will not only be a new system, as outlined above, but additionally some existing systems will undergo cascade effects, and be copied down with changed kinematics.

In this subsection we outline the possibility to interrupt at a given pT scale, in the next to interrupt after a given number of emissions.

virtual bool UserHooks::canVetoPT()  
In the base class this method returns false. If you redefine it to return true then the method doVetoPT(...) will interrupt the downward evolution at scaleVetoPT().

virtual double UserHooks::scaleVetoPT()  
In the base class this method returns 0. You should redefine it to return the pT scale at which you want to study the event.

virtual bool UserHooks::doVetoPT(int iPos, const Event& event)  
can optionally be called, as described above. You can study, but not modify, the event event record of the partonic process. Based on that you can decide whether to veto the event, true, or let it continue to evolve, false. If you veto, then this event is not counted among the accepted ones, and does not contribute to the estimated cross section. The Pytha::next() method will begin a completely new event, so the vetoed event will not appear in the output of Pythia::next().
argument iPos : is the position/status when the routine is called, information that can help you decide your course of action:
argumentoption 0 : when no MPI, ISR or FSR occurred above the veto scale;
argumentoption 1 : when inside the interleaved MPI + ISR + FSR evolution, after an MPI process;
argumentoption 2 : when inside the interleaved MPI + ISR + FSR evolution, after an ISR emission;
argumentoption 3 : when inside the interleaved MPI + ISR + FSR evolution, after an FSR emission;
argumentoption 4 : for the optional case where FSR is deferred from the interleaved evolution and only considered separately afterward (then alternative 3 would never occur);
argumentoption 5 : is for subsequent resonance decays, and is called once for each decaying resonance in a chain such as t → b W, W → u dbar.
argument event : the event record contains a list of all partons generated so far, also including intermediate ones not part of the "current final state", and also those from further multiparton interactions. This may not be desirable for comparisons with matrix-element calculations. You may want to make use of the subEvent(...) method below to obtain a simplified event record workEvent.

(iii) Interrupt during the parton-level evolution, after a step

These options are closely related to the ones above in section (ii), so we do not repeat the introduction, nor the possibilities to study the event record, also by using subEvent(...) and workEvent. What is different is that the methods in this section give access to the event as it looks like after each of the first few steps in the downwards evolution, irrespective of the pT scales of these branchings. Furthermore, it is here assumed that the focus normally is on the hardest subprocess, so that ISR/FSR emissions associated with additional MPI's are not considered. For MPI studies, however, a separate simpler alternative is offered to consider the event after a given number of interactions.

virtual bool UserHooks::canVetoStep()  
In the base class this method returns false. If you redefine it to return true then the method doVetoStep(...) will interrupt the downward ISR and FSR evolution the first numberVetoStep() times.

virtual int UserHooks::numberVetoStep()  
Returns the number of steps n each of ISR and FSR, for the hardest interaction, that you want to be able to study. That is, the method will be called after the first n ISR emissions, irrespective of the number of FSR ones at the time, and after the first n FSR emissions, irrespective of the number of ISR ones. The number of steps defaults to the first one only, but you are free to pick another value. Note that double diffraction is handled as two separate Pomeron-proton collisions, and thus has two sequences of emissions.

virtual bool UserHooks::doVetoStep(int iPos, int nISR, int nFSR, const Event& event)  
can optionally be called, as described above. You can study, but not modify, the event event record of the partonic process. Based on that you can decide whether to veto the event, true, or let it continue to evolve, false. If you veto, then this event is not counted among the accepted ones, and does not contribute to the estimated cross section. The Pytha::next() method will begin a completely new event, so the vetoed event will not appear in the output of Pythia::next().
argument iPos : is the position/status when the routine is called, information that can help you decide your course of action. Agrees with options 2 - 5 of the doVetoPT(...) routine above, while options 0 and 1 are not relevant here.
argument nISR : is the number of ISR emissions in the hardest process so far. For resonance decays, iPos = 5, it is 0.
argument nFSR : is the number of FSR emissions in the hardest process so far. For resonance decays, iPos = 5, it is the number of emissions in the currently studied system.
argument event : the event record contains a list of all partons generated so far, also including intermediate ones not part of the "current final state", and also those from further multiparton interactions. This may not be desirable for comparisons with matrix-element calculations. You may want to make use of the subEvent(...) method above to obtain a simplified event record.

virtual bool UserHooks::canVetoMPIStep()  
In the base class this method returns false. If you redefine it to return true then the method doVetoMPIStep(...) will interrupt the downward MPI evolution the first numberVetoMPIStep() times.

virtual int UserHooks::numberVetoMPIStep()  
Returns the number of steps in the MPI evolution that you want to be able to study, right after each new step has been taken and the subcollision has been added to the event record. The number of steps defaults to the first one only, but you are free to pick another value. Note that the hardest interaction of an events counts as the first multiparton interaction. For most hard processes it thus at the first step offers nothing not available with the VetoProcessLevel functionality above. For the minimum-bias and diffractive systems the hardest interaction is not selected at the process level, however, so there a check after the first multiparton interaction offers new functionality. Note that double diffraction is handled as two separate Pomeron-proton collisions, and thus has two sequences of interactions. Also, if you have set up a second hard process then a check is made after these first two, and the first interaction coming from the MPI machinery would have sequence number 3.

virtual bool UserHooks::doVetoMPIStep(int nMPI, const Event& event)  
can optionally be called, as described above. You can study, but not modify, the event event record of the partonic process. Based on that you can decide whether to veto the event, true, or let it continue to evolve, false. If you veto, then this event is not counted among the accepted ones, and does not contribute to the estimated cross section. The Pytha::next() method will begin a completely new event, so the vetoed event will not appear in the output of Pythia::next().
argument nMPI : is the number of MPI subprocesses has occurred so far.
argument event : the event record contains a list of all partons generated so far, also including intermediate ones not part of the "current final state", e.g. leftovers from the ISR and FSR evolution of previously generated systems. The most recently added one has not had time to radiate, of course.

(iv) Veto emissions

The methods in this group are intended to allow the veto of an emission in ISR, FSR or MPI, without affecting the evolution in any other way. If an emission is vetoed, the event record is "rolled back" to the way it was before the emission occurred, and the evolution in pT is continued downwards from the rejected value. The decision can be based on full knowledge of the kinematics of the shower branching or MPI.

To identify where shower emissions originated, the ISR/FSR veto routines are passed the system from which the radiation occurred, according to the Parton Systems class (see Advanced Usage). Note, however, that inside the veto routines only the event record has been updated; all other information, including the Parton Systems, reflects the event before the shower branching or MPI has taken place.

virtual bool UserHooks::canVetoISREmission()  
In the base class this method returns false. If you redefine it to return true then the method doVetoISREmission(...) will interrupt the initial-state shower immediately after each emission and allow that emission to be vetoed.

virtual bool UserHooks::doVetoISREmission( int sizeOld, const Event& event, int iSys)  
can optionally be called, as described above. You can study, but not modify, the event event record of the partonic process. Based on that you can decide whether to veto the emission, true, or not, false. If you veto, then the latest emission is removed from the event record. In either case the evolution of the shower will continue from the point where it was left off.
argument sizeOld : is the size of the event record before the latest emission was added to it. It will also become the new size if the emission is vetoed.
argument event : the event record contains a list of all partons generated so far. Of special interest are the ones associated with the most recent emission, which are stored in entries from sizeOld through event.size() - 1 inclusive. If you veto the emission these entries will be removed, and the history info in the remaining partons will be restored to a state as if the emission had never occurred.
argument iSys : the system where the radiation occurs, according to Parton Systems.

virtual bool UserHooks::canVetoFSREmission()  
In the base class this method returns false. If you redefine it to return true then the method doVetoFSREmission(...) will interrupt the final-state shower immediately after each emission and allow that emission to be vetoed.

virtual bool UserHooks::doVetoFSREmission( int sizeOld, const Event& event, int iSys, bool inResonance = false)  
can optionally be called, as described above. You can study, but not modify, the event event record of the partonic process. Based on that you can decide whether to veto the emission, true, or not, false. If you veto, then the latest emission is removed from the event record. In either case the evolution of the shower will continue from the point where it was left off.
argument sizeOld : is the size of the event record before the latest emission was added to it. It will also become the new size if the emission is vetoed.
argument event : the event record contains a list of all partons generated so far. Of special interest are the ones associated with the most recent emission, which are stored in entries from sizeOld through event.size() - 1 inclusive. If you veto the emission these entries will be removed, and the history info in the remaining partons will be restored to a state as if the emission had never occurred.
argument iSys : the system where the radiation occurs, according to Parton Systems.
argument inResonance : true if the emission takes place in a resonance decay, subsequent to the hard process.

virtual bool UserHooks::canVetoMPIEmission()  
In the base class this method returns false. If you redefine it to return true then the method doVetoMPIEmission(...) will interrupt the MPI machinery immediately after each multiparton interaction and allow it to be vetoed.

virtual bool UserHooks::doVetoMPIEmission( int sizeOld, const Event& event)  
can optionally be called, as described above. You can study, but not modify, the event event record of the partonic process. Based on that you can decide whether to veto the MPI, true, or not, false. If you veto, then the latest MPI is removed from the event record. In either case the interleaved evolution will continue from the point where it was left off.
argument sizeOld : is the size of the event record before the latest MPI was added to it. It will also become the new size if the MPI is vetoed.
argument event : the event record contains a list of all partons generated so far. Of special interest are the ones associated with the most recent MPI, which are stored in entries from sizeOld through event.size() - 1 inclusive. If you veto the MPI these entries will be removed.

(v) Modify cross-sections or phase space sampling

This section addresses two related but different topics. In both cases the sampling of events in phase space is modified, so that some regions are more populated while others are depleted. In the first case, this is assumed to be because the physical cross section should be modified relative to the built-in Pythia form. Therefore not only the relative population of phase space is changed, but also the integrated cross section of the process. In the second case the repopulation is only to be viewed as a technical trick to sample some phase-space regions better, so as to reduce the statistical error. There each event instead obtains a compensating weight, the inverse of the differential cross section reweighting factor, in such a way that the integrated cross section is unchanged. Below these two cases are considered separately, but note that they share many points.

virtual bool UserHooks::canModifySigma()  
In the base class this method returns false. If you redefine it to return true then the method multiplySigmaBy(...) will allow you to modify the cross section weight assigned to the current event.

virtual double UserHooks::multiplySigmaBy( const SigmaProcess* sigmaProcessPtr, const PhaseSpace* phaseSpacePtr, bool inEvent)  
when called this method should provide the factor by which you want to see the cross section weight of the current event modified. If you return unity then the normal cross section is obtained. Note that, unlike the methods above, these modifications do not lead to a difference between the number of "selected" events and the number of "accepted" ones, since the modifications occur already before the "selected" level. The integrated cross section of a process is modified, of course. Note that the cross section is only modifiable for normal hard processes. It does not affect the cross section in further multiparton interactions, nor in elastic/diffractive/minimum-bias events.
argument sigmaProcessPtr, phaseSpacePtr : : what makes this routine somewhat tricky to write is that the hard-process event has not yet been constructed, so one is restricted to use the information available in the phase-space and cross-section objects currently being accessed. Which of their methods are applicable depends on the process, in particular the number of final-state particles. The multiplySigmaBy code in UserHooks.cc contains explicit instructions about which methods provide meaningful information, and so offers a convenient starting point.
argument inEvent : : this flag is true when the method is called from within the event-generation machinery and false when it is called at the initialization stage of the run, when the cross section is explored to find a maximum for later Monte Carlo usage. Cross-section modifications should be independent of this flag, for consistency, but if multiplySigmaBy(...) is used to collect statistics on the original kinematics distributions before cuts, then it is important to be able to exclude the initialization stage from comparisons.

One derived class is supplied as an example how this facility can be used to reweight cross sections in the same spirit as is done with QCD cross sections for the minimum-bias/underlying-event description:

class  SuppressSmallPT : public UserHooks  
suppress small-pT production for 2 → 2 processes only, while leaving other processes unaffected. The basic suppression factor is pT^4 / ((k*pT0)^2 + pT^2)^2, where pT refers to the current hard subprocess and pT0 is the same energy-dependent dampening scale as used for multiparton interactions. This class contains canModifySigma() and multiplySigmaBy() methods that overload the base class ones.

SuppressSmallPT::SuppressSmallPT( double pT0timesMPI = 1., int numberAlphaS = 0, bool useSameAlphaSasMPI = true)  
The optional arguments of the constructor provides further variability.
argument pT0timesMPI : corresponds to the additional factor k in the above formula. It is by default equal to 1 but can be used to explore deviations from the expected value.
argument numberAlphaS : if this number n is bigger than the default 0, the corresponding number of alpha_strong factors is also reweighted from the normal renormalization scale to a modified one, i.e. a further suppression factor ( alpha_s((k*pT0)^2 + Q^2_ren) / alpha_s(Q^2_ren) )^n is introduced.
argument useSameAlphaSasMPI : regulates which kind of new alpha_strong value is evaluated for the numerator in the above expression. It is by default the same as set for multiparton interactions (i.e. same starting value at M_Z and same order of running), but if false instead the one for hard subprocesses. The denominator alpha_s(Q^2_ren) is always the value used for the "original", unweighted cross section.

The second main case of the current section involves three methods, as follows.

virtual bool UserHooks::canBiasSelection()  
In the base class this method returns false. If you redefine it to return true then the method biasSelectionBy(...) will allow you to modify the phase space sampling, with a compensating event weight, such that the cross section is unchanged. You cannot combine this kind of reweighting with the selection of a second hard process.

virtual double UserHooks::biasSelectionBy( const SigmaProcess* sigmaProcessPtr, const PhaseSpace* phaseSpacePtr, bool inEvent)  
when called this method should provide the factor by which you want to see the phase space sampling of the current event modified. Events are assigned a weight being the inverse of this, such that the integrated cross section of a process is unchanged. Note that the selection is only modifiable for normal hard processes. It does not affect the selection in further multiparton interactions, nor in elastic/diffractive/minimum-bias events.
argument sigmaProcessPtr, phaseSpacePtr : : what makes this routine somewhat tricky to write is that the hard-process event has not yet been constructed, so one is restricted to use the information available in the phase-space and cross-section objects currently being accessed. Which of their methods are applicable depends on the process, in particular the number of final-state particles. The biasSelectionBy code in UserHooks.cc contains explicit instructions about which methods provide meaningful information, and so offers a convenient starting point.
argument inEvent : : this flag is true when the method is called from within the event-generation machinery and false when it is called at the initialization stage of the run, when the cross section is explored to find a maximum for later Monte Carlo usage. Cross-section modifications should be independent of this flag, for consistency, but if biasSelectionBy(...) is used to collect statistics on the original kinematics distributions before cuts, then it is important to be able to exclude the initialization stage from comparisons.

virtual double UserHooks::biasedSelectionWeight()  
Returns the weight you should assign to the event, to use e.g. when you histogram results. It is the exact inverse of the weight you used to modify the phase-space sampling, a weight that must be stored in the selBias member variable, such that this routine can return 1/selBias. The weight is also returned by the Info::weight() method, which may be more convenient to use.

(vi) Reject the decay sequence of resonances

Resonance decays are performed already at the process level, as an integrated second step of the hard process itself. One reason is that the matrix element of many processes encode nontrivial decay angular distributions. Another is to have equivalence with Les Houches input, where resonance decays typically are provided from the onset. The methods in this section allow you to veto that decay sequence and try a new one. Unlike the veto of the whole process-level step, in point (i), the first step of the hard process is retained, i.e. where the resonances are produced. For this reason the cross section is not affected here but, depending on context, you may want to introduce your own counters to check how often a new set of decay modes and kinematics is selected, and correct accordingly.

The main method below is applied after all decays. For the production of a t tbar pair this typically means after four decays, namely those of the t, the tbar, the W+ and the W-. If Les Houches events are processed, the rollback is to the level of the originally read events. For top, that might mean either to the tops, or to the W bosons, or no rollback at all, depending on how the process generation was set up.

virtual bool UserHooks::canVetoResonanceDecays()  
In the base class this method returns false. If you redefine it to return true then the method doVetoResonanceDecays(...) will be called immediately after the resonance decays have been selected and stored in the process event record, as described above for canVetoProcessLevel().

virtual bool UserHooks::doVetoResonanceDecays(Event& process)  
can optionally be called, as described above. You can study the process event record of the hard process. Based on that you can decide whether to reject the sequence of resonance decays that was not already fixed by the production step of the hard process (which can vary depending on how a process has been set up, see above). If you veto, then a new resonance decay sequence is selected, but the production step remains unchanged. The cross section remains unaffected by this veto, for better or worse.
Warning: Normally you should not modify the process event record. However, as an extreme measure, parts or the complete decay chain could be overwritten. If so, be very careful.

(vii) Modify scale in shower evolution

The choice of maximum shower scale in resonance decays is normally not a big issue, since the shower here is expected to cover the full phase space. In some special cases a matching scheme is intended, where hard radiation is covered by matrix elements, and only softer by showers. The below two methods support such an approach. Note that the two methods are not used in the TimeShower class itself, but when showers are called from the PartonLevel generation. Thus user calls directly to TimeShower are not affected.

virtual bool UserHooks::canSetResonanceScale()  
In the base class this method returns false. If you redefine it to return true then the method scaleResonance(...) will set the initial scale of downwards shower evolution.

virtual double UserHooks::scaleResonance( int iRes, const Event& event)  
can optionally be called, as described above. You should return the maximum scale, in GeV, from which the shower evolution will begin. The base class method returns 0, i.e. gives no shower evolution at all. You can study, but not modify, the event event record of the partonic process to check which resonance is decaying, and into what.
argument iRes : is the location in the event record of the resonance that decayed to the particles that now will shower.
argument event : the event record contains a list of all partons generated so far, specifically the decaying resonance and its immediate decay products.

(viii) Allow colour reconnection

PYTHIA contains only a limites set of possibilities for colour reconnection, and none of them are geared specifically towards rapidly decaying resonances. Notably, with the default PartonLevel:earlyResDec = off, resonances will only decay after colour reconnection has already been considered. Thus a coloured parton like the top may be reconnected but, apart from this external connection with the rest of the event, the top decay products undergo no colour reconnection. For PartonLevel:earlyResDec = on the resonance will decay earlier, and thus the decay products may undergo reconnections, but not necessarily by models that are specifically geared towards this kind of events. For tryout purposes, a user hook can be called directly after the resonance decays, and there modify the colour flow. This holds whether the resonance decay is handled early or late, but is especially appropriate for the latter default possibility. While intended specifically for resonance decays, alternatively it is possible to switch off the built-in colour reconnection and here implement your own reconnection model for the whole event.

virtual bool UserHooks::canReconnectResonanceSystems()  
In the base class this method returns false. If you redefine it to return true then the method doReconnectResonanceSystems(...) will be called immediately after the resonance decays and their associated final-state showers have been added to the event record.

virtual bool UserHooks::doReconnectResonanceSystems(int oldSizeEvent, Event& event)  
can optionally be called, as described above, to reconnect colours in the event. The method should normally return true, but false if the colour-reconnected event is unphysical and to be rejected. (If this is likely to happen, having a safety copy to restore to is a good idea, so that false can be avoided to the largest extent possible.)
argument oldSizeEvent : the size of the event record before resonance decay products and their associated final-state showers have been added to the event. Can thus be used to easily separate the resonance-decay partons from those in the rest of the event.
argument event : the event record contains a list of all particles generated so far. You are allowed to freely modify this record, but with freedom comes responsibility. Firstly, it is only meaningful to modify the colour indices of final-state (at the time) partons; all other event properties had better be left undisturbed. Secondly, it is up to you to ensure that the new colour topology is meaningful, e.g. that no gluon has obtained the same colour as anticolour index and thereby forms a singlet on its own.