Interfaces to Other Generators

In the previous section an approach to including external processes in PYTHIA was explained. While general enough, it may not always be the optimal choice. In particular, for $\mathrm{e}^+\mathrm{e}^-$ annihilation events one may envisage some standard cases where simpler approaches could be pursued. A few such standard interfaces are described in this section.

In $\mathrm{e}^+\mathrm{e}^-$ annihilation events, a convenient classification of electroweak physics is by the number of fermions in the final state. Two fermions from $\mathrm{Z}^0$ decay is LEP1 physics, four fermions can come e.g. from $\mathrm{W}^+ \mathrm{W}^-$ or $\mathrm{Z}^0 \mathrm{Z}^0$ events at LEP2, and at higher energies six fermions are produced by three-gauge-boson production or top-antitop. Often interference terms are non-negligible, requiring much more complex matrix-element expressions than are normally provided in PYTHIA. Dedicated electroweak generators often exist, however, and the task is therefore to interface them to the generic parton showering and hadronization machinery available in PYTHIA. In the LEP2 workshop [Kno96] one possible strategy was outlined to allow reasonably standardized interfaces between the electroweak and the QCD generators. The LU4FRM routine was provided for the key four-fermion case. This routine is now included here, in slightly modified form, together with two new siblings for two and six fermions. The former is trivial and included mainly for completeness, while the latter is rather more delicate.

In final states with two or three quark-antiquark pairs, the colour connection is not unique. For instance, a $\u\d\overline{\mathrm{u}}\overline{\mathrm{d}}$ final state could either stem from a $\mathrm{W}^+ \mathrm{W}^-$ or a $\mathrm{Z}^0 \mathrm{Z}^0$ intermediate state, or even from interference terms between the two. In order to shower and fragment the system, it is then necessary to pick one of the two alternatives, e.g. according to the relative matrix element weight of each alternative, with the interference term dropped. Some different such strategies are proposed as options below.

Note that here we discuss purely perturbative ambiguities. One can imagine colour reconnection at later stages of the process, e.g. if the intermediate state indeed is $\mathrm{W}^+ \mathrm{W}^-$, a soft-gluon exchange could still result in colour singlets $\u\overline{\mathrm{u}}$ and $\d\overline{\mathrm{d}}$. We are then no longer speaking of ambiguities related to the hard process itself but rather to the possibility of nonperturbative effects. This is an interesting topic in itself, addressed in section but not here.

The fermion-pair routines are not set up to handle QCD four-jet events, i.e. events of the types $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ and $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$ (with $\mathrm{q}' \overline{\mathrm{q}}'$ coming from a gluon branching). Such events are generated in normal parton showers, but not necessarily at the right rate (a problem that may be especially interesting for massive quarks like $\b$). Therefore one would like to start a QCD final-state parton shower from a given four-parton configuration. Already some time ago, a machinery was developed to handle this kind of occurrences [And98a]. This approach has now been adapted to PYTHIA, in a somewhat modified form, see section . The main change is that, in the original work, the colour flow was picked in a separate first step (not discussed in the publication, since it is part of the standard 4-parton configuration machinery of PYEEVT), which reduces the number of allowed $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ parton-shower histories. In the current implementation, more geared towards completely external generators, no colour flow assumptions are made, meaning a few more possible shower histories to pick between. Another change is that mass effects are better respected by the $z$ definition. The code contains one new user routine, PY4JET, two new auxiliary ones, PY4JTW and PY4JTS, and significant additions to the PYSHOW showering routine.

Purpose:

to allow a parton shower to develop and partons to hadronize from a two-fermion starting point. The initial list is supposed to be ordered such that the fermion precedes the antifermion. In addition, an arbitrary number of photons may be included, e.g. from initial-state radiation; these will not be affected by the operation and can be put anywhere. The scale for QCD (and QED) final-state radiation is automatically set to be the mass of the fermion-antifermion pair. (It is thus not suited for Bhabha scattering.)

IRAD :

final-state QED radiation.

= 0 :

no final-state photon radiation, only QCD showers.

= 1 :

photon radiation inside each final fermion pair, also leptons, in addition to the QCD one for quarks.

ITAU :

handling of $\tau$ lepton decay (where PYTHIA does not include spin effects, although some generators provide the helicity information that would allow a more sophisticated modelling).

= 0 :

$\tau$'s are considered stable (and can therefore be decayed afterwards).

= 1 :

$\tau$'s are allowed to decay.

ICOM :

place where information about the event (flavours, momenta etc.) is stored at input and output.

= 0 :

in the HEPEVT common block (meaning that information is automatically translated to PYJETS before treatment and back afterwards).

= 1 :

in the PYJETS common block. All fermions and photons can be given with status code K(I,1)=1, flavour code in K(I,2) and five-momentum (momentum, energy, mass) in P(I,J). The V vector and remaining components in the K one are best put to zero. Also remember to set the total number of entries N.

Purpose:

to allow a parton shower to develop and partons to hadronize from a four-fermion starting point. The initial list of fermions is supposed to be ordered in the sequence fermion (1) - antifermion (2) - fermion (3) - antifermion (4). The flavour pairs should be arranged so that, if possible, the first two could come from a $\mathrm{W}^+$ and the second two from a $\mathrm{W}^-$; else each pair should have flavours consistent with a $\mathrm{Z}^0$. In addition, an arbitrary number of photons may be included, e.g. from initial-state radiation; these will not be affected by the operation and can be put anywhere. Since the colour flow need not be unique, three real and one integer numbers are providing further input. Once the colour pairing is determined, the scale for final-state QCD (and QED) radiation is automatically set to be the mass of the fermion-antifermion pair. (This is the relevant choice for normal fermion pair production from resonance decay, but is not suited e.g. for $\gamma\gamma$ processes dominated by small-$t$ propagators.) The pairing is also meaningful for QED radiation, in the sense that a four-lepton final state is subdivided into two radiating subsystems in the same way. Only if the event consists of one lepton pair and one quark pair is the information superfluous.

ATOTSQ :

total squared amplitude for the event, irrespective of colour flow.

A1SQ :

squared amplitude for the configuration with fermions $1 + 2$ and $3 + 4$ as the two colour singlets.

A2SQ :

squared amplitude for the configuration with fermions $1 + 4$ and $3 + 2$ as the two colour singlets.

ISTRAT :

the choice of strategy to select either of the two possible colour configurations. Here 0 is supposed to represent a reasonable compromise, while 1 and 2 are selected so as to give the largest reasonable spread one could imagine.

= 0 :

pick configurations according to relative probabilities A1SQ : A2SQ.

= 1 :

assign the interference contribution to maximize the $1 + 2$ and $3 + 4$ pairing of fermions.

= 2 :

assign the interference contribution to maximize the $1 + 4$ and $3 + 2$ pairing of fermions.

IRAD :

final-state QED radiation.

= 0 :

no final-state photon radiation, only QCD showers.

= 1 :

photon radiation inside each final fermion pair, also leptons, in addition to the QCD one for quarks.

ITAU :

handling of $\tau$ lepton decay (where PYTHIA does not include spin effects, although some generators provide the helicity information that would allow a more sophisticated modelling).

= 0 :

$\tau$'s are considered stable (and can therefore be decayed afterwards).

= 1 :

$\tau$'s are allowed to decay.

ICOM :

place where information about the event (flavours, momenta etc.) is stored at input and output.

= 0 :

in the HEPEVT common block (meaning that information is automatically translated to PYJETS before treatment and back afterwards).

= 1 :

in the PYJETS common block. All fermions and photons can be given with status code K(I,1)=1, flavour code in K(I,2) and five-momentum (momentum, energy, mass) in P(I,J). The V vector and remaining components in the K one are best put to zero. Also remember to set the total number of entries N.

Comment :

Also colour reconnection phenomena can be studied with the PY4FRM routine. MSTP(115) can be used to switch between the scenarios, with default being no reconnection. Other reconnection parameters also work as normally, including that MSTI(32) can be used to find out whether a reconnection occured or not. In order for the reconnection machinery to work, the event record is automatically complemented with information on the $\mathrm{W}^+ \mathrm{W}^-$ or $\mathrm{Z}^0 \mathrm{Z}^0$ pair that produced the four fermions, based on the rules described above.
We remind that the four first parameters of the PY4FRM call are supposed to parameterize an ambiguity on the perturbative level of the process, which has to be resolved before parton showers are performed. The colour reconnection discussed here is (in most scenarios) occuring on the nonperturbative level, after the parton showers.

Purpose:

to allow a parton shower to develop and partons to hadronize from a six-fermion starting point. The initial list of fermions is supposed to be ordered in the sequence fermion (1) - antifermion (2) - fermion (3) - antifermion (4) - fermion (5) - antifermion (6). The flavour pairs should be arranged so that, if possible, the first two could come from a $\mathrm{Z}^0$, the middle two from a $\mathrm{W}^+$ and the last two from a $\mathrm{W}^-$; else each pair should have flavours consistent with a $\mathrm{Z}^0$. Specifically, this means that in a $\t\overline{\mathrm{t}}$ event, the $\t$ decay products would be found in 1 ($\b$) and 3 and 4 (from the $\mathrm{W}^+$ decay) and the $\overline{\mathrm{t}}$ ones in 2 ( $\overline{\mathrm{b}}$) and 5 and 6 (from the $\mathrm{W}^-$ decay). In addition, an arbitrary number of photons may be included, e.g. from initial-state radiation; these will not be affected by the operation and can be put anywhere. Since the colour flow need not be unique, further input is needed to specify this. The number of possible interference contributions being much larger than for the four-fermion case, we have not tried to implement different strategies. Instead six probabilities may be input for the different pairings, that you e.g. could pick as the six possible squared amplitudes, or according to some more complicated scheme for how to handle the interference terms. The treatment of final-state cascades must be quite different for top events and the rest. For a normal three-boson event, each fermion pair would form one radiating system, with scale set equal to the fermion-antifermion invariant mass. (This is the relevant choice for normal fermion pair production from resonance decay, but is not suited e.g. for $\gamma\gamma$ processes dominated by small-$t$ propagators.) In the top case, on the other hand, the $\b$ ( $\overline{\mathrm{b}}$) would be radiating with a recoil taken by the $\mathrm{W}^+$ ($\mathrm{W}^-$) in such a way that the $\t$ ( $\overline{\mathrm{t}}$) mass is preserved, while the $\mathrm{W}$ dipoles would radiate as normal. Therefore you need also supply a probability for the event to be a top one, again e.g. based on some squared amplitude.

P12, P13, P21, P23, P31, P32 :

relative probabilities for the six possible pairings of fermions with antifermions. The first (second) digit tells which antifermion the first (second) fermion is paired with, with the third pairing given by elimination. Thus e.g. P23 means the first fermion is paired with the second antifermion, the second fermion with the third antifermion and the third fermion with the first antifermion. Pairings are only possible between quarks and leptons separately. The sum of probabilities for allowed pairings is automatically normalized to unity.

PTOP :

the probability that the configuration is a top one; a number between 0 and 1. In this case, it is important that the order described above is respected, with the $\b$ and $\overline{\mathrm{b}}$ coming first. No colour ambiguity exists if the top interpretation is selected, so then the P12 - P32 numbers are not used.

IRAD :

final-state QED radiation.

= 0 :

no final-state photon radiation, only QCD showers.

= 1 :

photon radiation inside each final fermion pair, also leptons, in addition to the QCD one for quarks.

ITAU :

handling of $\tau$ lepton decay (where PYTHIA does not include spin effects, although some generators provide the helicity information that would allow a more sophisticated modelling).

= 0 :

$\tau$'s are considered stable (and can therefore be decayed afterwards).

= 1 :

$\tau$'s are allowed to decay.

ICOM :

place where information about the event (flavours, momenta etc.) is stored at input and output.

= 0 :

in the HEPEVT common block (meaning that information is automatically translated to PYJETS before treatment and back afterwards).

= 1 :

in the PYJETS common block. All fermions and photons can be given with status code K(I,1)=1, flavour code in K(I,2) and five-momentum (momentum, energy, mass) in P(I,J). The V vector and remaining components in the K one are best put to zero. Also remember to set the total number of entries N.

Purpose:

to allow a parton shower to develop and partons to hadronize from a $\mathrm{q}\overline{\mathrm{q}}\mathrm{g}\mathrm{g}$ or $\mathrm{q}\overline{\mathrm{q}}\mathrm{q}' \overline{\mathrm{q}}'$ original configuration. The partons should be ordered exactly as indicated above, with the primary $\mathrm{q}\overline{\mathrm{q}}$ pair first and thereafter the two gluons or the secondary $\mathrm{q}' \overline{\mathrm{q}}'$ pair. (Strictly speaking, the definition of primary and secondary fermion pair is ambiguous. In practice, however, differences in topological variables like the pair mass should make it feasible to have some sensible criterion on an event by event basis.) Within each pair, fermion should precede antifermion. In addition, an arbitrary number of photons may be included, e.g. from initial-state radiation; these will not be affected by the operation and can be put anywhere. The program will select a possible parton shower history from the given parton configuration, and then continue the shower from there on. The history selected is displayed in lines NOLD+1 to NOLD+6, where NOLD is the N value before the routine is called. Here the masses and energies of intermediate partons are clearly displayed. The lines NOLD+7 and NOLD+8 contain the equivalent on-mass-shell parton pair from which the shower is started.

PMAX :

the maximum mass scale (in GeV) from which the shower is started in those branches that are not already fixed by the matrix-element history. If PMAX is set zero (actually below PARJ(82), the shower cutoff scale), the shower starting scale is instead set to be equal to the smallest mass of the virtual partons in the reconstructed shower history. A fixed PMAX can thus be used to obtain a reasonably exclusive set of four-jet events (to that PMAX scale), with little five-jet contamination, while the PMAX=0 option gives a more inclusive interpretation, with five- or more-jet events possible. Note that the shower is based on evolution in mass, meaning the cut is really one of mass, not of $p_{\perp}$, and that it may therefore be advantageous to set up the matrix elements cuts accordingly if one wishes to mix different event classes. This is not a requirement, however.

IRAD :

final-state QED radiation.

= 0 :

no final-state photon radiation, only QCD showers.

= 1 :

photon radiation inside each final fermion pair, also leptons, in addition to the QCD one for quarks.

ICOM :

place where information about the event (flavours, momenta etc.) is stored at input and output.

= 0 :

in the HEPEVT common block (meaning that information is automatically translated to PYJETS before treatment and back afterwards).

= 1 :

in the PYJETS common block. All fermions and photons can be given with status code K(I,1)=1, flavour code in K(I,2) and five-momentum (momentum, energy, mass) in P(I,J). The V vector and remaining components in the K one are best put to zero. Also remember to set the total number of entries N.