<chapter name="Timelike Showers">
<h2>Timelike Showers</h2>
The PYTHIA algorithm for timelike final-state showers is based on
the article <ref>Sjo05</ref>, where a transverse-momentum-ordered
evolution scheme is introduced, with the extension to fully interleaved
evolution covered in <ref>Cor10a</ref>. This algorithm is influenced by
the previous mass-ordered algorithm in PYTHIA <ref>Ben87</ref> and by
the dipole-emission formulation in Ariadne <ref>Gus86</ref>. 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
<ref>Nor01</ref>.
<p/>
The normal user is not expected to call <code>TimeShower</code> directly,
but only have it called from <code>Pythia</code>. Some of the parameters
below, in particular <code>TimeShower:alphaSvalue</code>, would be of
interest for a tuning exercise, however.
<h3>Main variables</h3>
Often the maximum scale of the FSR shower evolution is understood from the
context. For instance, in a resonance 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 <aloc href="CouplingsAndScales">factorization
scale</aloc> has been chosen as the maximum evolution scale. This would be
the <ei>pT</ei> for a <ei>2 → 2</ei> process, supplemented by mass terms
for massive outgoing particles. For some special applications we do allow
an alternative.
<modepick name="TimeShower:pTmaxMatch" default="1" min="0" max="2">
Way in which the maximum shower evolution scale is set to match the
scale of the hard process itself.
<option value="0"><b>(i)</b> if the final state of the hard process
(not counting subsequent resonance decays) contains at least one quark
(<ei>u, d, s, c ,b</ei>), gluon or photon then <ei>pT_max</ei>
is chosen to be the factorization scale for internal processes
and the <code>scale</code> value for Les Houches input;
<b>(ii)</b> 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
<aloc href="SpacelikeShowers">spacelike showers</aloc>. There the
reasoning is that in the former set of processes the ISR
emission of yet another quark, gluon or photon could lead to
double-counting, 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>
<option value="1">always use the factorization scale for an internal
process and the <code>scale</code> value for Les Houches input,
i.e. the lower value. This should avoid double-counting, but
may leave out some emissions that ought to have been simulated.
(Also known as wimpy showers.)
</option>
<option value="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 double-counting.
(Also known as power showers.)
</option>
<note>Note 1:</note> as enumerated in the text, these options take effect
both for internal and external processes. Whether a particular option
makes sense depends on the context. For instance, if events for the same
basic process to different orders are to be matched, then option 1 would
be a reasonable first guess. But in more sophisticated descriptions
option 2 could be combined with <code>UserHooks</code> vetoes on
emissions that would lead to double-counting, using more flexible
phase space boundaries. Further details are found in the
<aloc href="MatchingAndMerging">Matching and Merging</aloc> description,
with an example in <code>examples/main31</code>.
Option 0, finally, may be most realistic when only Born-level processes
are involved, possibly in combination with a nonzero
<code>TimeShower:pTdampMatch</code>.
<note>Note 2:</note> These options only apply to the hard interaction.
If a "second hard" process is present, the two are analyzed and
set separately for the default 0 option, while both are affected
the same way for non-default options 1 and 2.
Emissions off subsequent multiparton interactions are always constrained
to be below the factorization scale of each process itself. The options
also assume that 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 <ei>pT</ei>, it would not
make sense to have a later FSR shower up to the kinematical limit
for all of them.
<note>Note 3:</note> Recall that resonance decays are not affected by
this mode, but that showers there are always set to fill the full phase
space, often with built-in matrix-element-matching that give a NLO
accuracy. A modification of this behaviour would require you to
work with <code>UserHooks</code>.
</modepick>
<parm name="TimeShower:pTmaxFudge" default="1.0" min="0.25" max="2.0">
In cases where the above <code>pTmaxMatch</code> rules would imply
that <ei>pT_max = pT_factorization</ei>, <code>pTmaxFudge</code>
introduces a multiplicative factor <ei>f</ei> such that instead
<ei>pT_max = f * pT_factorization</ei>. Only applies to the hardest
interaction in an event, and a "second hard" if there is such a one,
cf. below. It is strongly suggested that <ei>f = 1</ei>, but variations
around this default can be useful to test this assumption.
<note>Note:</note>Scales for resonance decays are not affected, but can
be set separately by <aloc href="UserHooks">user hooks</aloc>.
</parm>
<parm name="TimeShower:pTmaxFudgeMPI" default="1.0" min="0.25" max="2.0">
A multiplicative factor <ei>f</ei> such that
<ei>pT_max = f * pT_factorization</ei>, as above, but here for the
non-hardest interactions (when multiparton interactions are allowed).
</parm>
<modepick name="TimeShower:pTdampMatch" default="0" min="0" max="2">
These options only take effect when a process is allowed to radiate up
to the kinematical limit by the above <code>pTmaxMatch</code> choice,
and no matrix-element corrections are available. Then, in many processes,
the fall-off in <ei>pT</ei> will be too slow by one factor of <ei>pT^2</ei>.
That is, while showers have an approximate <ei>dpT^2/pT^2</ei> shape, often
it should become more like <ei>dpT^2/pT^4</ei> at <ei>pT</ei> values above
the scale of the hard process. This argument is more obvious and relevant
for ISR, where emissions could go the the kinematical limit, whereas they
are constrained by the respective dipole mass for FSR. Nevertheless this
matching option is offered for FSR to have a (semi-)symmetric description.
Note that a dampening factor is applied to all dipoles in the final state
of the hard process, which is somewhat different from the ISR implementation.
<option value="0">emissions go up to the kinematical limit,
with no special dampening.
</option>
<option value="1">emissions go up to the kinematical limit,
but dampened by a factor <ei>k^2 Q^2_fac/(pT^2 + k^2 Q^2_fac)</ei>,
where <ei>Q_fac</ei> is the factorization scale and <ei>k</ei> is a
multiplicative fudge factor stored in <code>pTdampFudge</code> below.
</option>
<option value="2">emissions go up to the kinematical limit,
but dampened by a factor <ei>k^2 Q^2_ren/(pT^2 + k^2 Q^2_ren)</ei>,
where <ei>Q_ren</ei> is the renormalization scale and <ei>k</ei> is a
multiplicative fudge factor stored in <code>pTdampFudge</code> below.
</option>
<note>Note:</note> These options only apply to the hard interaction.
Specifically, a "second hard" interaction would not be affected.
Emissions off subsequent multiparton interactions are always constrained
to be below the factorization scale of the process itself.
</modepick>
<parm name="TimeShower:pTdampFudge" default="1.0" min="0.25" max="4.0">
In cases 1 and 2 above, where a dampening is imposed at around the
factorization or renormalization scale, respectively, this allows the
<ei>pT</ei> scale of dampening of radiation by a half to be shifted
by this factor relative to the default <ei>Q_fac</ei> or <ei>Q_ren</ei>.
This number ought to be in the neighbourhood of unity, but variations
away from this value could do better in some processes.
</parm>
<p/>
The amount of QCD radiation in the shower is determined by
<parm name="TimeShower:alphaSvalue" default="0.1383"
min="0.06" max="0.25">
The <ei>alpha_strong</ei> value at scale <ei>M_Z^2</ei>. The default
value corresponds to a crude tuning to LEP data, to be improved.
</parm>
<p/>
The actual value is then regulated by the running to the scale
<ei>pT^2</ei>, at which the shower evaluates <ei>alpha_strong</ei>.
<modepick name="TimeShower:alphaSorder" default="1" min="0" max="2">
Order at which <ei>alpha_strong</ei> runs,
<option value="0">zeroth order, i.e. <ei>alpha_strong</ei> is kept
fixed.</option>
<option value="1">first order, which is the normal value.</option>
<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.</option>
</modepick>
<p/>
The CMW rescaling of <ei>Lambda_QCD</ei> (see the section on
<aloc href="StandardModelParameters">StandardModelParameters</aloc>)
can be applied to the <ei>alpha_strong</ei> values used for
timelike showers. Note that tunes using this option need lower values of
<ei>alpha_strong(m_Z^2)</ei> than tunes that do not.
<flag name="TimeShower:alphaSuseCMW" default="false">
<option value="false">Do not apply the CMW rescaling. </option>
<option value="true">Apply the CMW rescaling, increasing
<ei>Lambda_QCD</ei> for timelike showers by a factor roughly 1.6.
</option>
</flag>
<p/>
QED radiation is regulated by the <ei>alpha_electromagnetic</ei>
value at the <ei>pT^2</ei> scale of a branching.
<modepick name="TimeShower:alphaEMorder" default="1" min="-1" max="1">
The running of <ei>alpha_em</ei>.
<option value="1">first-order running, constrained to agree with
<code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass.
</option>
<option value="0">zeroth order, i.e. <ei>alpha_em</ei> is kept
fixed at its value at vanishing momentum transfer.</option>
<option value="-1">zeroth order, i.e. <ei>alpha_em</ei> is kept
fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value
at the <ei>Z^0</ei> mass.
</option>
</modepick>
<p/>
The natural scale for couplings, and PDFs for dipoles stretching out
to the beam remnants, is <ei>pT^2</ei>. To explore uncertainties it
is possibly to vary around this value, however, in analogy with what
can be done for <aloc href="CouplingsAndScales">hard processes</aloc>.
<parm name="TimeShower:renormMultFac" default="1." min="0.1" max="10.">
The default <ei>pT^2</ei> renormalization scale is multiplied by
this prefactor. For QCD this is equivalent to a change of
<ei>Lambda^2</ei> in the opposite direction, i.e. to a change of
<ei>alpha_strong(M_Z^2)</ei> (except that flavour thresholds
remain at fixed scales).
</parm>
<parm name="TimeShower:factorMultFac" default="1." min="0.1" max="10.">
The default <ei>pT^2</ei> factorization scale is multiplied by
this prefactor.
</parm>
<p/>
The rate of radiation if divergent in the <ei>pT → 0</ei> limit. Here,
however, perturbation theory is expected to break down. Therefore an
effective <ei>pT_min</ei> 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="0.4" min="0.1" max="2.0">
Parton shower cut-off <ei>pT</ei> for QCD emissions.
</parm>
<parm name="TimeShower:pTminChgQ" default="0.4" min="0.1" max="2.0">
Parton shower cut-off <ei>pT</ei> for photon coupling to coloured particle.
</parm>
<parm name="TimeShower:pTminChgL" default="1e-6" min="1e-10" max="2.0">
Parton shower cut-off <ei>pT</ei> for pure QED branchings.
Assumed smaller than (or equal to) <code>pTminChgQ</code>.
</parm>
<p/>
Shower branchings <ei>gamma → f fbar</ei>, where <ei>f</ei> is a
quark or lepton, in part compete with the hard processes involving
<ei>gamma^*/Z^0</ei> production. In order to avoid overlap it makes
sense to correlate the maximum <ei>gamma</ei> mass allowed in showers
with the minimum <ei>gamma^*/Z^0</ei> mass allowed in hard processes.
In addition, the shower contribution only contains the pure
<ei>gamma^*</ei> contribution, i.e. not the <ei>Z^0</ei> 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="5000.0">
Maximum invariant mass allowed for the created fermion pair in a
<ei>gamma → f fbar</ei> branching in the shower.
</parm>
<h3>Interleaved evolution</h3>
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 <ei>pT</ei> 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 <ei>pT</ei>
value. The one with larger <ei>pT</ei> 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 away some of the energy, leaving less for the future. The end
result is a combined chain of decreasing <ei>pT</ei> values, where
ones associated with new interactions and ones with new emissions
are interleaved.
<p/>
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 occurring after
the other two components in some kind of time sense. Interleaving is
allowed, however, since it can be argued that a high-<ei>pT</ei> FSR
occurs on shorter time scales than a low-<ei>pT</ei> 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 <ei>pT</ei> resolution scale, what possibilities are open
for a modified picture at a slightly lower <ei>pT</ei> 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 name="TimeShower:interleave" default="on">
If on, final-state emissions are interleaved in the same
decreasing-<ei>pT</ei> 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.
</flag>
<p/>
As an aside, it should be noted that such interleaving does not affect
showering in resonance decays, such as a <ei>Z^0</ei>. 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.
<p/>
One aspect of FSR for a hard process in hadron collisions is that often
colour dipoles 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
bookkept by increasing the <ei>x</ei> value assigned to the incoming
scattering parton, and a reweighting factor
<ei>x_new f(x_new, pT^2) / x_old f(x_old, pT^2)</ei>
in the emission probability ensures that not unphysically large
<ei>x_new</ei> values are reached. Usually such <ei>x</ei> changes are
small, and they can be viewed as a higher-order effect beyond the
accuracy of the leading-log initial-state showers.
<p/>
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 name="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>
<flag name="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
<ei>4 pT2_hard / (4 pT2_hard + m2)</ei> is multiplied on to the
emission probability. Here <ei>pT_hard</ei> is the transverse momentum
of the radiating parton and <ei>m</ei> the off-shell mass it acquires
by the branching, <ei>m2 = pT2/(z(1-z))</ei>. Note that
<ei>m2 = 4 pT2_hard</ei> is the kinematical limit for a scattering
at 90 degrees without beam recoil.
</flag>
<h3>Global recoil</h3>
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
double-counting. (The <ei>pT</ei>-ordered shower is described in
<ref>Sjo05</ref>, and the corrections for massive radiator and recoiler
in <ref>Nor01</ref>.)
<p/>
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.
<p/>
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.
<p/>
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 name="TimeShower:globalRecoil" default="off">
Alternative approach as above, where all final-state particles share
the recoil of an emission.
<br/>If off, then use the standard dipole-recoil approach.
<br/>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 <code>TimeShower:nMaxGlobalRecoil</code> before the
branching.
</flag>
<modeopen name="TimeShower:nMaxGlobalRecoil" default="2" min="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 <ei>Z^0</ei>. 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.
</modeopen>
<p/>
Two variations of the scheme outlined above are also available,
(motivated by comparative studies within aMC@NLO). These studies indicate
that global recoils should be used as sparsely as possible, in order to
retain desirable features of the radiation pattern produced with the local
recoil prescription.
<modepick name="TimeShower:globalRecoilMode" default="0" min="0" max="2">
Choice which splittings are produced with the global recoil approach.
<option value="0">Global recoil mode as outlined above, i.e. using global
recoils until the number of final state particles exceeds
<code>TimeShower:nMaxGlobalRecoil</code>.</option>
<option value="1">Global recoil only for the first branching of
final state legs that have an ancestor in the hard process, and
if the maximal number of branchings generated according to the global
recoil scheme (see <code>TimeShower:nMaxGlobalBranch</code> below) has
not yet been reached.</option>
<option value="2">Global recoil only if the first branching in
the whole evolution is a timelike splitting of a parton in an
event with Born-like kinematics (i.e.\ an S-event).
The impact of global recoils should be minimal in this case.
This option is only sensible for interleaved evolution.
</option>
</modepick>
<modeopen name="TimeShower:nMaxGlobalBranch" default="-1">
The maximum number of splittings in the final state for which
the next final-state emission can be performed with the global recoil
strategy. This number has to be set if <code>TimeShower:globalRecoilMode = 1
</code> or <code>TimeShower:globalRecoilMode = 2</code>
</modeopen>
<modeopen name="TimeShower:nPartonsInBorn" default="-1">
The number of partons for Born-like phase space points. This number needs
to be set if a different treatment of S-events (with Born-like kinematics)
and H-events (with real-emission kinematics) is desired. This number has
to be set if <code>TimeShower:globalRecoilMode = 2</code>.
</modeopen>
<flag name="TimeShower:limitPTmaxGlobal" default="off">
If on, limit the maximal pT produced in branchings in the global recoil scheme
exactly as in the default (local) scheme. This means that the mass of the
splitting dipole will set an upper bound for the pT of an emission.
To be more explicit, this disallows emissions with pT larger than
<ei>min{μ<sub>start </sub><sup>2</sup>, m<sub>D</sub><sup>2</sup>/4}</ei>,
with <ei>m<sub>D</sub><sup>2</sup> =
(√<span style="text-decoration:overline;color:green"> (p<sub>r
</sub>+p<sub>s</sub>)<sup>2</sup> </span>-m<sub>0,s</sub>)<sup>2</sup>
- m<sub>0,r</sub><sup>2</sup> </ei>, where
the shower starting scale is <ei>μ<sub>start</sub></ei> (i.e. SCALUP when
reading LHE files, and <code> Info.QFac()</code> otherwise), <ei>r</ei> the
radiating parton, and <ei>s</ei> the recoiling particle that would have been
used in the local recoil scheme. This option is only used if wimpy showers are
enabled.
</flag>
<p/>
The global-recoil machinery does not work well with rescattering in the
MPI machinery, since then the recoiling system is not uniquely defined.
<code>MultipartonInteractions:allowRescatter = off</code> 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 <code>nMaxGlobalRecoil</code>
limit has been exceeded. This should not be a major conflict,
since rescattering is mainly of interest at later stages of the
downwards <ei>pT</ei> evolution.
<p/>
Further, it is strongly recommended to set
<code>TimeShower:MEcorrections = off</code> (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 <aloc href="UserHooks">user hooks</aloc>
can provide the desired process-specific rejection factors.
<h3>Radiation off octet onium states</h3>
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 <ei>2 → 2</ei> hard processes
such as <ei>g g → (onium) g</ei>.
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.)
<p/>
There could be two parts to such a shower. Firstly a gluon (or even a
quark, though less likely) produced in a hard <ei>2 → 2</ei> 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.
<p/>
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
<ei>q → q g</ei> 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
<ei>q → q g</ei> branching kernel is roughly equivalent to always
following the harder gluon in a <ei>g → g g</ei> 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.
<p/>
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.
</parm>
<parm name="TimeShower:octetOniumColFac" default="2." min="0." max="4." >
The colour factor used used in the splitting kernel for those octet onium
states that are allowed to radiate, normalized to the <ei>q → q g</ei>
splitting kernel. Thus the default corresponds to twice the radiation
off a quark. The physically preferred range would be between 1 and 9/4.
</parm>
<h3>Weak showers</h3>
The emission of weak gauge bosons is an integrated part of the initial-
and final-state radiation, see <aloc href="WeakShowers">Weak Showers</aloc>.
The following settings are those specifically related to the final-state
weak radiation, while common settings are found in the
<aloc href="WeakShowers">Weak Showers</aloc> description.
<flag name="TimeShower:weakShower" default="off">
Allow a weak shower, yes or no.
</flag>
<modepick name="TimeShower:weakShowerMode" default="0" min="0" max="2">
Determine which branchings are allowed.
<option value="0"> both <ei>W^+-</ei> and <ei>Z^0</ei> branchings.
</option>
<option value="1"> only <ei>W^+-</ei> branchings. </option>
<option value="2"> only <ei>Z^0</ei> branchings. </option>
</modepick>
<parm name ="TimeShower:pTminWeak" default="1.0" min="0.1" max="2.0">
Parton shower cut-off <ei>pT</ei> for weak branchings.
</parm>
<h3>Further variables</h3>
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 <ei>q → q g</ei>,
<ei>g → g g</ei> and <ei>g → q qbar</ei>; on/off = true/false.
</flag>
<modeopen name="TimeShower:nGluonToQuark" default="5" min="0" max="5">
Number of allowed quark flavours in <ei>g → q qbar</ei> branchings
(phase space permitting). A change to 4 would exclude
<ei>g → b bbar</ei>, etc.
</modeopen>
<modepick name="TimeShower:weightGluonToQuark" default="1" min="1" max="8">
Different options to assign kinematics distributions and weights
for <ei>g → q qbar</ei> branchings, notably for charm and bottom
quarks. These options also have the corresponding effect on
<ei>gamma → f fbar</ei> branchings.
Notation: <ei>r_q = m_q^2/m_qq^2</ei>, <ei>beta = sqrt(1 - 4r_q)</ei>, with
<ei>m_q</ei> the quark mass and <ei>m_qq</ei> the <ei>q qbar</ei> pair
invariant mass. The scale factor <ei>k</ei> is described below,
<code>TimeShower:scaleGluonToQuark</code>.
<option value="1">same splitting kernel <ei>(1/2) (z^2 + (1-z)^2)</ei> for
massive as massless quarks, only with an extra <ei>beta</ei> phase
space factor.</option>
<option value="2">a splitting kernel
<ei>(beta/2) (z^2 + (1-z)^2 + 8r_q z(1-z))</ei>.</option>
<option value="3">a splitting kernel <ei>z^2 + (1-z)^2 + 8r_q z(1-z)</ei>,
normalized so that the <ei>z</ei>-integrated rate is
<ei>(beta/3) (1 + r/2)</ei>.</option>
<option value="4">same as 3, but additionally a suppression factor
<ei>(1 - m_qq^2/m_dipole^2)^3</ei>, which reduces the rate of high-mass
<ei>q qbar</ei> pairs.</option>
<option value="5">same as 1, but reweighted to an <ei>alpha_s(k m_qq^2)</ei>
rather than the normal <ei>alpha_s(pT^2)</ei>.</option>
<option value="6">same as 2, but reweighted to an <ei>alpha_s(k m_qq^2)</ei>
rather than the normal <ei>alpha_s(pT^2)</ei>.</option>
<option value="7">same as 3, but reweighted to an <ei>alpha_s(k m_qq^2)</ei>
rather than the normal <ei>alpha_s(pT^2)</ei>.</option>
<option value="8">same as 4, but reweighted to an <ei>alpha_s(k m_qq^2)</ei>
rather than the normal <ei>alpha_s(pT^2)</ei>.</option>
</modepick>
<parm name="TimeShower:scaleGluonToQuark" default="1.0" min="0.25" max="1.0">
Extra scale parameter <ei>k</ei> for <code>TimeShower:weightGluonToQuark</code>
options 5 - 8. Comes on top of <code>TimeShower:renormMultFac</code>, which
affects <ei>alpha_s(pT^2)</ei> alike.
</parm>
<flag name="TimeShower:QEDshowerByQ" default="on">
Allow quarks to radiate photons, i.e. branchings <ei>q → q gamma</ei>;
on/off = true/false.
</flag>
<flag name="TimeShower:QEDshowerByL" default="on">
Allow leptons to radiate photons, i.e. branchings <ei>l → l gamma</ei>;
on/off = true/false.
</flag>
<flag name="TimeShower:QEDshowerByGamma" default="on">
Allow photons to branch into lepton or quark pairs, i.e. branchings
<ei>gamma → l+ l-</ei> and <ei>gamma → q qbar</ei>;
on/off = true/false.
</flag>
<modeopen name="TimeShower:nGammaToQuark" default="5" min="0" max="5">
Number of allowed quark flavours in <ei>gamma → q qbar</ei> branchings
(phase space permitting). A change to 4 would exclude
<ei>g → b bbar</ei>, etc.
</modeopen>
<modeopen name="TimeShower:nGammaToLepton" default="3" min="0" max="3">
Number of allowed lepton flavours in <ei>gamma → l+ l-</ei> branchings
(phase space permitting). A change to 2 would exclude
<ei>gamma → tau+ tau-</ei>, and a change to 1 also
<ei>gamma → mu+ mu-</ei>.
</modeopen>
<flag name="TimeShower:MEcorrections" default="on">
Use of matrix element corrections where available; on/off = true/false.
</flag>
<flag name="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 <code>MEcorrections</code> above is
switched on.
</flag>
<flag name="TimeShower:phiPolAsym" default="on">
Azimuthal asymmetry induced by gluon polarization; on/off = true/false.
</flag>
<flag name="TimeShower:recoilToColoured" default="on">
In the decays of coloured resonances, say <ei>t → b W</ei>, it is not
possible to set up dipoles with matched colours. Originally the
<ei>b</ei> radiator therefore has <ei>W</ei> 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 <ei>W</ei> (<code>off</code>), or else
let it recoil against the <ei>b</ei> also for this dipole
(<code>on</code>). 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 <ei>W → e nu</ei>, where originally the <ei>nu</ei>
takes the recoil. In the old (<code>off</code>) scheme the <ei>nu</ei>
would remain recoiler, while in the new (<code>on</code>) instead
each newly emitted photon becomes the new recoiler.
</flag>
<flag name="TimeShower:useFixedFacScale" default="off">
Allow the possibility to use a fixed factorization scale, set by
the <code>parm</code> below. This option is unphysical and only
intended for toy-model and debug studies.
</flag>
<parm name="TimeShower:fixedFacScale" default="100." min="1.">
The fixed factorization scale, in GeV, that would be used in the
evaluation of parton densities if the <code>flag</code> above is on.
</parm>
</chapter>
<!-- Copyright (C) 2014 Torbjorn Sjostrand -->
Marcin Chrzaszcz