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

The amount of QCD radiation in the shower is determined by

TimeShower:alphaSvalue

(default = 0.1383; 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.

TimeShower:alphaSorder

(default = 1; minimum = 0; maximum = 2)

Order at which alpha_strong runs,
0 : zeroth order, i.e. alpha_strong is kept fixed.
1 : first order, which is the normal 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.

TimeShower:alphaEMorder

(default = 1; minimum = -1; maximum = 1)

The running of alpha_em.
1 : first-order running, constrained to agree with StandardModel:alphaEMmZ at the Z^0 mass.
0 : zeroth order, i.e. alpha_em is kept fixed at its value at vanishing momentum transfer.
-1 : zeroth order, i.e. alpha_em is kept fixed, but at StandardModel:alphaEMmZ, i.e. its value at the Z^0 mass.

The natural scale for couplings, and PDFs for dipoles stretching out to the beam remnants, is pT^2. To explore uncertainties it is possibly to vary around this value, however, in analogy with what can be done for ";?>hard processes.

TimeShower:renormMultFac

(default = 1.; minimum = 0.1; maximum = 10.)

The default pT^2 renormalization scale is multiplied by this prefactor. For QCD this is equivalent to a change of Lambda^2 in the opposite direction, i.e. to a change of alpha_strong(M_Z^2) (except that flavour thresholds remain at fixed scales).

TimeShower:factorMultFac

(default = 1.; minimum = 0.1; maximum = 10.)

The default pT^2 factorization scale is multiplied by this prefactor.

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.

TimeShower:pTmin

(default = 0.4; minimum = 0.1; maximum = 2.0)

Parton shower cut-off pT for QCD emissions.

TimeShower:pTminChgQ

(default = 0.4; minimum = 0.1; maximum = 2.0)

Parton shower cut-off pT for photon coupling to coloured particle.

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.

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 MPI, 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 MPI, 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.

TimeShower:interleave On Off   (default = on)
If on, final-state emissions are interleaved in the same decreasing-pT chain as multiparton interactions and initial-state emissions. If off, final-state emissions are only addressed after the multiparton 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.

TimeShower:allowBeamRecoil On Off   (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.

TimeShower:dampenBeamRecoil On Off   (default = on)
When beam recoil is allowed there is still some ambiguity how far into the beam end of the dipole that emission should be allowed. It is dampened in the beam region, but probably not enough. When on an additional suppression factor 4 pT2_hard / (4 pT2_hard + m2) is multiplied on to the emission probability. Here pT_hard is the transverse momentum of the radiating parton and m the off-shell mass it acquires by the branching, m2 = pT2/(z(1-z)). Note that m2 = 4 pT2_hard is the kinematical limit for a scattering at 90 degrees without beam recoil.

Global recoil

Technically, the radiation pattern is most conveniently represented in the rest frame of the final state of the hard subprocess. Then, for each parton at a time, the rest of the final state can be viewed as a single effective parton. This "parton" has a fixed invariant mass during the emission process, and takes the recoil without any changed direction of motion. The momenta of the individual new recoilers are then obtained by a simple common boost of the original ones.

This alternative approach will miss out on the colour coherence phenomena. Specifically, with the whole subcollision mass as "dipole" mass, the phase space for subsequent emissions is larger than for the normal dipole algorithm. The phase space difference grows as more and more gluons are created, and thus leads to a way too steep multiplication of soft gluons. Therefore the main application is for the first one or few emissions of the shower, where a potential overestimate of the emission rate is to be corrected for anyway, by matching to the relevant matrix elements. Thereafter, subsequent emissions should be handled as before, i.e. with dipoles spanned between nearby partons. Furthermore, only the first (hardest) subcollision is handled with global recoils, since subsequent MPI's would not be subject to matrix element corrections anyway.

In order for the mid-shower switch from global to local recoils to work, colours are traced and bookkept just as for normal showers; it is only that this information is not used in those steps where a global recoil is requested. (Thus, e.g., a gluon is still bookkept as one colour and one anticolour dipole end, with half the charge each, but with global recoil those two ends radiate identically.)

TimeShower:globalRecoil On Off   (default = off)
Alternative approach as above, where all final-state particles share the recoil of an emission.
If off, then use the standard dipole-recoil approach.
If on, use the alternative global recoil, but only for the first interaction, and only while the number of particles in the final state is at most TimeShower:nMaxGlobalRecoil before the branching.

TimeShower:nMaxGlobalRecoil

(default = 2; minimum = 1)

Represents the maximum number of particles in the final state for which the next final-state emission can be performed with the global recoil strategy. This number counts all particles, whether they are allowed to radiate or not, e.g. also Z^0. Also partons created by initial-state radiation emissions counts towards this sum, as part of the interleaved evolution. Without interleaved evolution this option would not make sense, since then a varying and large number of partons could already have been created by the initial-state radiation before the first final-state one, and then there is not likely to be any matrix elements available for matching.

The global-recoil machinery does not work well with rescattering in the MPI machinery, since then the recoiling system is not uniquely defined. MultipartonInteractions:allowRescatter = off by default, so this is not a main issue. If both options are switched on, rescattering will only be allowed to kick in after the global recoil has ceased to be active, i.e. once the nMaxGlobalRecoil limit has been exceeded. This should not be a major conflict, since rescattering is mainly of interest at later stages of the downwards pT evolution.

Further, it is strongly recommended to set TimeShower:MEcorrections = off (not default!), i.e. not to correct the emission probability to the internal matrix elements. The internal ME options do not cover any cases relevant for a multibody recoiler anyway, so no guarantees are given what prescription would come to be used. Instead, without ME corrections, a process-independent emission rate is obtained, and ";?>user hooks can provide the desired process-specific rejection factors.

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.

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.

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