Timelike Showers

The PYTHIA algorithm for timelike final-state showers is based on the recent article [Sjo05], where a transverse-momentum-ordered evolution scheme is introduced. This algorithm is influenced by the previous mass-ordered algorithm in PYTHIA [Ben87] and by the dipole-emission formulation in Ariadne [Gus86]. From the mass-ordered algorithm it inherits a merging procedure for first-order gluon-emission matrix elements in essentially all two-body decays in the standard model and its minimal supersymmetric extension [Nor01].

The normal user is not expected to call TimeShower directly, but only have it called from Pythia. Some of the parameters below, in particular TimeShower:alphaSvalue, would be of interest for a tuning exercise, however.

Main variables

The amount of QCD radiation in the shower is determined by

parm name="TimeShower:alphaSvalue" default="0.1265" min="0.06" max="0.25"
The alpha_strong value at scale M_Z^2. The default value corresponds to the one tuned to LEP data (using a first-order running), so should be taken rather seriously [Rud04].

The actual value is then regulated by the running to the scale pT^2, at which the shower evaluates alpha_strong

mode name="TimeShower:alphaSorder" default="1" min="0" max="2"
Order at which alpha_strong runs,
option value="0": zeroth order, i.e. alpha_strong is kept fixed.
option value="1": first order, which is the normal value.
option value="2": second order. Since other parts of the code do not go to second order there is no strong reason to use this option, but there is also nothing wrong with it.

QED radiation is regulated by the alpha_electromagnetic value at the pT^2 scale of a branching.

mode name="TimeShower:alphaEMorder" default="1" min="-1" max="1"
The running of alpha_em.
option value="1": first-order running, constrained to agree with StandardModel:alphaEMmZ at the Z^0 mass.
option value="0": zeroth order, i.e. alpha_em is kept fixed at its value at vanishing momentum transfer.
option value="-1": zeroth order, i.e. alpha_em is kept fixed, but at StandardModel:alphaEMmZ, i.e. its value at the Z^0 mass.

The rate of radiation if divergent in the pT -> 0 limit. Here, however, perturbation theory is expected to break down. Therefore an effective pT_min cutoff parameter is introduced, below which no emissions are allowed. The cutoff may be different for QCD and QED radiation off quarks, and is mainly a technical parameter for QED radiation off leptons.

parm name="TimeShower:pTmin" default="0.5" min="0.1" max="2.0"
Parton shower cut-off pT for QCD emissions.

parm name="TimeShower:pTminChgQ" default="0.5" min="0.1" max="2.0"
Parton shower cut-off pT for photon coupling to coloured particle.

parm name="TimeShower:pTminChgL" default="0.0005" min="0.0001" max="2.0"
Parton shower cut-off pT for pure QED branchings. Assumed smaller than (or equal to) pTminChgQ.

Shower branchings gamma -> f fbar, where f is a quark or lepton, in part compete with the hard processes involving gamma^*/Z^0 production. In order to avoid overlap it makes sense to correlate the maximum gamma mass allowed in showers with the minumum gamma^*/Z^0 mass allowed in hard processes. In addition, the shower contribution only contains the pure gamma^* contribution, i.e. not the Z^0 part, so the mass spectrum above 50 GeV or so would not be well described.

parm name="TimeShower:mMaxGamma" default="10.0" min="0.001" max="50.0"
Maximum invariant mass allowed for the created fermion pair in a gamma -> f fbar branching in the shower.

Radiation off octet onium states

In the current implementation, charmonium and bottomonium production can proceed either through colour singlet or colour octet mechanisms, both of them implemented in terms of 2 -> 2 hard processes such as g g -> (onium) g. In the former case the state does not radiate and the onium therefore is produced in isolation, up to normal underlying-event activity. In the latter case the situation is not so clear, but it is sensible to assume that a shower can evolve. (Assuming, of course, that the transverse momentum of the onium state is sufficiently high that radiation is of relevance.)

There could be two parts to such a shower. Firstly a gluon (or even a quark, though less likely) produced in a hard 2 -> 2 process can undergo showering into many gluons, whereof one branches into the heavy-quark pair. Secondly, once the pair has been produced, each quark can radiate further gluons. This latter kind of emission could easily break up a semibound quark pair, but might also create a new semibound state where before an unbound pair existed, and to some approximation these two effects should balance in the onium production rate. The showering "off an onium state" as implemented here therefore should not be viewed as an accurate description of the emission history step by step, but rather as an effective approach to ensure that the octet onium produced "in the hard process" is embedded in a realistic amount of jet activity. Of course both the isolated singlet and embedded octet are likely to be extremes, but hopefully the mix of the two will strike a reasonable balance. However, it is possible that some part of the octet production occurs in channels where it should not be accompanied by (hard) radiation. Therefore reducing the fraction of octet onium states allowed to radiate is a valid variation to explore uncertainties.

If an octet onium state is chosen to radiate, the simulation of branchings is based on the assumption that the full radiation is provided by an incoherent sum of radiation off the quark and off the antiquark of the onium state. Thus the splitting kernel is taken to be the normal q -> q g one, multiplied by a factor of two. Obviously this is a simplification of a more complex picture, averaging over factors pulling in different directions. Firstly, radiation off a gluon ought to be enhanced by a factor 9/4 relative to a quark rather than the 2 now used, but this is a minor difference. Secondly, our use of the q -> q g branching kernel is roughly equivalent to always following the harder gluon in a g -> g g branching. This could give us a bias towards producing too hard onia. A soft gluon would have little phase space to branch into a heavy-quark pair however, so the bias may not be as big as it would seem at first glance. Thirdly, once the gluon has branched into a quark pair, each quark carries roughly only half of the onium energy. The maximum energy per emitted gluon should then be roughly half the onium energy rather than the full, as it is now. Thereby the energy of radiated gluons is exaggerated, i.e. onia become too soft. So the second and the third points tend to cancel each other.

Finally, note that the lower cutoff scale of the shower evolution depends on the onium mass rather than on the quark mass, as it should be. Gluons below the octet-onium scale should only be part of the octet-to-singlet transition.

parm name="TimeShower:octetOniumFraction" default="1." min="0." max="1."
Allow colour-octet charmonium and bottomonium states to radiate gluons. 0 means that no octet-onium states radiate, 1 that all do, with possibility to interpolate between these two extremes.

Further variables

There are several possibilities you can use to switch on or off selected branching types in the shower, or in other respects simplify the shower. These should normally not be touched. Their main function is for cross-checks.

flag name="TimeShower:QCDshower" default="on"
Allow a QCD shower, i.e. branchings q -> q g, g -> g g and g -> q qbar; on/off = true/false.

mode name="TimeShower:nGluonToQuark" default="5" min="0" max="5"
Number of allowed quark flavours in g -> q qbar branchings (phase space permitting). A change to 4 would exclude g -> b bbar, etc.

flag name="TimeShower:QEDshowerByQ" default="on"
Allow quarks to radiate photons, i.e. branchings q -> q gamma; on/off = true/false.

flag name="TimeShower:QEDshowerByL" default="on"
Allow leptons to radiate photons, i.e. branchings l -> l gamma; on/off = true/false.

flag name="TimeShower:QEDshowerByGamma" default="on"
Allow photons to branch into lepton or quark pairs, i.e. branchings gamma -> l+ l- and gamma -> q qbar; on/off = true/false.

mode name="TimeShower:nGammaToQuark" default="5" min="0" max="5"
Number of allowed quark flavours in gamma -> q qbar branchings (phase space permitting). A change to 4 would exclude g -> b bbar, etc.

mode name="TimeShower:nGammaToLepton" default="3" min="0" max="3"
Number of allowed lepton flavours in gamma -> l+ l- branchings (phase space permitting). A change to 2 would exclude gamma -> tau+ tau-, and a change to 1 also gamma -> mu+ mu-.

flag name="TimeShower:MEcorrections" default="on"
Use of matrix element corrections where available; on/off = true/false.

flag name="TimeShower:phiPolAsym" default="on"
Azimuthal asymmetry induced by gluon polarization; on/off = true/false.