Timelike Showers

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

parm  TimeShower:pTmaxFudge   (default = 1.0; minimum = 0.5; maximum = 2.0)
While the above rules would imply that pT_max = pT_factorization, pTmaxFudge introduced a multiplicative factor f such that instead pT_max = f * pT_factorization. Only applies to the hardest interaction in an event. It is strongly suggested that f = 1, but variations around this default can be useful to test this assumption.

The amount of QCD radiation in the shower is determined by

parm  TimeShower:alphaSvalue   (default = 0.137; minimum = 0.06; maximum = 0.25)
The alpha_strong value at scale M_Z^2. The default value corresponds to a crude tuning to LEP data, to be improved.

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

mode  TimeShower:alphaSorder   (default = 1; minimum = 0; maximum = 2)
Order at which alpha_strong runs,
option 0 : zeroth order, i.e. alpha_strong is kept fixed.
option 1 : first order, which is the normal value.
option 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  TimeShower:alphaEMorder   (default = 1; minimum = -1; maximum = 1)
The running of alpha_em.
option 1 : first-order running, constrained to agree with StandardModel:alphaEMmZ at the Z^0 mass.
option 0 : zeroth order, i.e. alpha_em is kept fixed at its value at vanishing momentum transfer.
option -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  TimeShower:pTmin   (default = 0.5; minimum = 0.1; maximum = 2.0)
Parton shower cut-off pT for QCD emissions.

parm  TimeShower:pTminChgQ   (default = 0.5; minimum = 0.1; maximum = 2.0)
Parton shower cut-off pT for photon coupling to coloured particle.

parm  TimeShower:pTminChgL   (default = 0.0005; minimum = 0.0001; maximum = 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  TimeShower:mMaxGamma   (default = 10.0; minimum = 0.001; maximum = 50.0)
Maximum invariant mass allowed for the created fermion pair in a gamma -> f fbar branching in the shower.

Interleaved evolution

There is no corresponding requirement for final-state radiation (FSR) to be interleaved. Such an FSR emission does not compete directly for beam energy (but see below), and also can be viewed as occuring after the other two components in some kind of time sense. Interleaving is allowed, however, since it can be argued that a high-pT FSR occurs on shorter time scales than a low-pT MI, say. Backwards evolution of ISR is also an example that physical time is not the only possible ordering principle, but that one can work with conditional probabilities: given the partonic picture at a specific pT resolution scale, what possibilities are open for a modified picture at a slightly lower pT scale, either by MI, ISR or FSR? Complete interleaving of the three components also offers advantages if one aims at matching to higher-order matrix elements above some given scale.

flag  TimeShower:interleave   (default = on)
If on, final-state emissions are interleaved in the same decreasing-pT chain as multiple interactions and initial-state emissions. If off, final-state emissions are only addressed after the multiple interactions and initial-state radiation have been considered.

As an aside, it should be noted that such interleaving does not affect showering in resonance decays, such as a Z^0. These decays are only introduced after the production process has been considered in full, and the subsequent FSR is carried out inside the resonance, with preserved resonance mass.

One aspect of FSR for a hard process in hadron collisions is that often colour diples are formed between a scattered parton and a beam remnant, or rather the hole left behind by an incoming partons. If such holes are allowed as dipole ends and take the recoil when the scattered parton undergoes a branching then this translates into the need to take some amount of remnant energy also in the case of FSR, i.e. the roles of ISR and FSR are not completely decoupled. The energy taken away is bokkept by increasing the x value assigned to the incoming scattering parton, and a reweighting factor x_new f(x_new, pT^2) / x_old f(x_old, pT^2) in the emission probability ensures that not unphysically large x_new values are reached. Usually such x changes are small, and they can be viewed as a higher-order effect beyond the accuracy of the leading-log initial-state showers.

This choice is not unique, however. As an alternative, if nothing else useful for cross-checks, one could imagine that the FSR is completely decoupled from the ISR and beam remnants.

flag  TimeShower:allowBeamRecoil   (default = on)
If on, the final-state shower is allowed to borrow energy from the beam remnants as described above, thereby changing the mass of the scattering subsystem. If off, the partons in the scattering subsystem are constrained to borrow energy from each other, such that the total four-momentum of the system is preserved. This flag has no effect on resonance decays, where the shower always preserves the resonance mass, cf. the comment above about showers for resonances never being interleaved.

Radiation off octet onium states

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  TimeShower:octetOniumFraction   (default = 1.; minimum = 0.; maximum = 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.

parm  TimeShower:octetOniumColFac   (default = 2.; minimum = 0.; maximum = 4.)
The colour factor used used in the splitting kernel for those octet onium states that are allowed to radiate, normalized to the q -> q g splitting kernel. Thus the default corresponds to twice the radiation off a quark. The physically preferred range would be between 1 and 9/4.

Further variables

flag  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  TimeShower:nGluonToQuark   (default = 5; minimum = 0; maximum = 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  TimeShower:QEDshowerByQ   (default = on)
Allow quarks to radiate photons, i.e. branchings q -> q gamma; on/off = true/false.

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

flag  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  TimeShower:nGammaToQuark   (default = 5; minimum = 0; maximum = 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  TimeShower:nGammaToLepton   (default = 3; minimum = 0; maximum = 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  TimeShower:MEcorrections   (default = on)
Use of matrix element corrections where available; on/off = true/false.

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