Timelike Showers
The PYTHIA algorithm for timelike final-state showers is based on
the article [Sjo05], where a transverse-momentum-ordered
evolution scheme is introduced, with the extension to fully interleaved
evolution covered in [Cor10a]. 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
Often the maximum scale of the FSR shower evolution is understood from the
context. For instance, in a resonace decay half the resonance mass sets an
absolute upper limit. For a hard process in a hadronic collision the choice
is not as unique. Here the factorization
scale has been chosen as the maximum evolution scale. This would be
the pT for a 2 -> 2 process, supplemented by mass terms
for massive outgoing particles. For some special applications we do allow
an alternative.
mode
TimeShower:pTmaxMatch
(default = 1
; minimum = 0
; maximum = 2
)
Way in which the maximum shower evolution scale is set to match the
scale of the hard process itself.
option
0 : (i) if the final state of the hard process
(not counting subsequent resonance decays) contains at least one quark
(u, d, s, c ,b), gluon or photon then pT_max
is chosen to be the factorization scale for internal processes
and the scale
value for Les Houches input;
(ii) if not, emissions are allowed to go all the way up to
the kinematical limit (i.e. to half the dipole mass).
This option agrees with the corresponding one for
spacelike showers. There the
reasoning is that in the former set of processes the ISR
emission of yet another quark, gluon or photon could lead to
doublecounting, while no such danger exists in the latter case.
The argument is less compelling for timelike showers, but could
be a reasonable starting point.
option
1 : always use the factorization scale for an internal
process and the scale
value for Les Houches input,
i.e. the lower value. This should avoid doublecounting, but
may leave out some emissions that ought to have been simulated.
(Also known as wimpy showers.)
option
2 : always allow emissions up to the kinematical limit
(i.e. to half the dipole mass). This will simulate all possible event
topologies, but may lead to doublecounting.
(Also known as power showers.)
Note: These options only apply to the hard interaction.
Emissions off subsequent multiparton interactions are always constrainted
to be below the factorization scale of the process itself. They also
assume you use interleaved evolution, so that FSR is in direct
competition with ISR for the hardest emission. If you already
generated a number of ISR partons at low pT, it would not
make sense to have a later FSR shower up to the kinematical for all
of them.
parm
TimeShower:pTmaxFudge
(default = 1.0
; minimum = 0.25
; maximum = 2.0
)
In cases where the above pTmaxMatch
rules would imply
that pT_max = pT_factorization, pTmaxFudge
introduces a multiplicative factor f such that instead
pT_max = f * pT_factorization. Only applies to the hardest
interaction in an event, cf. below. It is strongly suggested that
f = 1, but variations around this default can be useful to
test this assumption.
Note:Scales for resonance decays are not affected, but can
be set separately by user hooks.
parm
TimeShower:pTmaxFudgeMPI
(default = 1.0
; minimum = 0.25
; maximum = 2.0
)
A multiplicative factor f such that
pT_max = f * pT_factorization, as above, but here for the
non-hardest interactions (when multiparton interactions are allowed).
mode
TimeShower:pTdampMatch
(default = 0
; minimum = 0
; maximum = 2
)
These options only take effect when a process is allowed to radiate up
to the kinematical limit by the above pTmaxMatch
choice,
and no matrix-element corrections are available. Then, in many processes,
the fall-off in pT will be too slow by one factor of pT^2.
That is, while showers have an approximate dpT^2/pT^2 shape, often
it should become more like dpT^2/pT^4 at pT values above
the scale of the hard process. This argument is more obvious for ISR,
but is taken over unchanged for FSR to have a symmetric description.
option
0 : emissions go up to the kinematical limit,
with no special dampening.
option
1 : emissions go up to the kinematical limit,
but dampened by a factor k^2 Q^2_fac/(pT^2 + k^2 Q^2_fac),
where Q_fac is the factorization scale and k is a
multiplicative fudge factor stored in pTdampFudge
below.
option
2 : emissions go up to the kinematical limit,
but dampened by a factor k^2 Q^2_ren/(pT^2 + k^2 Q^2_ren),
where Q_ren is the renormalization scale and k is a
multiplicative fudge factor stored in pTdampFudge
below.
Note: These options only apply to the hard interaction.
Emissions off subsequent multiparton interactions are always constrainted
to be below the factorization scale of the process itself.
parm
TimeShower:pTdampFudge
(default = 1.0
; minimum = 0.25
; maximum = 4.0
)
In cases 1 and 2 above, where a dampening is imposed at around the
factorization or renormalization scale, respectively, this allows the
pT scale of dampening of radiation by a half to be shifted
by this factor relative to the default Q_fac or Q_ren.
This number ought to be in the neighbourhood of unity, but variations
away from this value could do better in some processes.
The amount of QCD radiation in the shower is determined by
parm
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.
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 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.
parm
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).
parm
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.
parm
TimeShower:pTmin
(default = 0.4
; minimum = 0.1
; maximum = 2.0
)
Parton shower cut-off pT for QCD emissions.
parm
TimeShower:pTminChgQ
(default = 0.4
; 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
Multiparton interactions (MPI) and initial-state showers (ISR) are
always interleaved, as follows. Starting from the hard interaction,
the complete event is constructed by a set of steps. In each step
the pT scale of the previous step is used as starting scale
for a downwards evolution. The MPI and ISR components each make
their respective Monte Carlo choices for the next lower pT
value. The one with larger pT is allowed to carry out its
proposed action, thereby modifying the conditions for the next steps.
This is relevant since the two components compete for the energy
contained in the beam remnants: both an interaction and an emission
take avay some of the energy, leaving less for the future. The end
result is a combined chain of decreasing pT values, where
ones associated with new interactions and ones with new emissions
are interleaved.
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.
flag
TimeShower:interleave
(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.
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.
flag
TimeShower:dampenBeamRecoil
(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
The final-state algorithm is based on dipole-style recoils, where
one single parton takes the full recoil of a branching. This is unlike
the initial-state algorithm, where the complete already-existing
final state shares the recoil of each new emission. As an alternative,
also the final-state algorithm contains an option where the recoil
is shared between all partons in the final state. Thus the radiation
pattern is unrelated to colour correlations. This is especially
convenient for some matching algorithms, like MC@NLO, where a full
analytic knowledge of the shower radiation pattern is needed to avoid
doublecountning. (The pT-ordered shower is described in
[Sjo05], and the corrections for massive radiator and recoiler
in [Nor01].)
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.)
flag
TimeShower:globalRecoil
(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.
mode
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
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
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
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
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:MEafterFirst
(default = on
)
Use of matrix element corrections also after the first emission,
for dipole ends of the same system that did not yet radiate.
Only has a meaning if MEcorrections
above is
switched on.
flag
TimeShower:phiPolAsym
(default = on
)
Azimuthal asymmetry induced by gluon polarization; on/off = true/false.
flag
TimeShower:recoilToColoured
(default = on
)
In the decays of coloured resonances, say t -> b W, it is not
possible to set up dipoles with matched colours. Originally the
b radiator therefore has W as recoiler, and that
choice is unique. Once a gluon has been radiated, however, it is
possible either to have the unmatched colour (inherited by the gluon)
still recoiling against the W (off
), or else
let it recoil against the b also for this dipole
(on
). Before version 8.160 the former was the only
possibility, which could give unphysical radiation patterns. It is
kept as an option to check backwards compatibility. The same issue
exists for QED radiation, but obviously is less significant. Consider
the example W -> e nu, where originally the nu
takes the recoil. In the old (off
) scheme the nu
would remain recoiler, while in the new (on
) instead
each newly emitted photon becomes the new recoiler.