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.