<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>. Nonetheless, 
some of the parameters 
below, in particular <code>TimeShower:alphaSvalue</code>, would be of 
interest for uncertainty estimates and tuning exercises. Note that 
PYTHIA also incorporates an 
<aloc href="Variations">automated framework</aloc> 
for shower uncertainty variations. 
 
<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 &rarr; 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/main152</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>. However, for Les Houches input the optional 
<code><aloc href="BeamParameters">Beams:strictLHEFscale = on</aloc></code> 
setting restricts all emissions, also in resonance decays, to be below 
the input <code>scale</code> value. 
</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="4"> 
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> 
<option value="3">as option 1, but in addition to the standard requirements 
for dampening it is further necessary to have at least two top or 
beyond-the-Standard-Model coloured particles in the final state. 
Examples include <ei>t tbar</ei> and <ei>squark gluino</ei> production. 
</option> 
<option value="4">as option 2, but in addition to the standard requirements 
for dampening it is further necessary to have at least two top or 
beyond-the-Standard-Model coloured particles in the final state. 
Examples include <ei>t tbar</ei> and <ei>squark gluino</ei> production. 
</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> 
 
<h3>Effective coupling constants</h3> 
 
<p/> 
The amount of QCD radiation in the shower is determined by 
<parm name="TimeShower:alphaSvalue" default="0.1365" 
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="3"> 
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> 
<option value="3">third order, with the same comment as for second 
order. The expression in the 2006 RPP is used here.</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="off"> 
<option value="off">Do not apply the CMW rescaling. </option> 
<option value="on">Apply the CMW rescaling, increasing 
 <ei>Lambda_QCD</ei> for timelike showers by a factor roughly 1.6. 
</option> 
</flag> 
 
<p/> 
The following options for taming (regularising) the effective value of 
the strong coupling at low (IR) scales are available: 
 
<parm name="TimeShower:alphaSmax" default="-1." min="-1." max="10."> 
For <code>alphaSmax &gt; 0</code>, the effective value of the strong 
coupling in timelike shower branchings is capped at this value, 
effectively freezing it in the infrared. Any value <code>alphaSmax 
&le; 0</code> is interpreted to mean that no such constraint should be 
imposed. 
</parm> 
 
<parm name="TimeShower:alphaSrenormShift" default="0." min="0." max="4."> 
The position of the Landau pole for timelike shower branchings is 
shifted by evaluating the strong coupling at <ei>scale2 &rarr; scale2 
+ x * Lambda_QCD(nF=3)^2</ei>, with <ei>x = 
<code>renormShift</code></ei>. The default value of <ei>x=0</ei> 
corresponds to no shift. A value of <ei>x=1</ei> corresponds to 
shifting the pole to an input scale of zero. For larger values, the 
effective coupling at zero input scale is finite and equal to <ei>4 pi 
/ (9 ln(x))</ei>. Since the scale argument is typically only shifted 
by a few hundred MeV, changes to the value of the effective coupling 
at perturbative input scales (well above <ei>Lambda_QCD(nF=3)</ei>) 
are generally small. The main effect is thus a suppression of the 
value of the effective coupling near the shower <code>pTmin</code> 
cutoff. For uncertainty estimates, variations of this parameter by a 
factor 2-4 in either direction (for a given central choice) may be a 
reasonable starting point. Detailed examinations of this assumption 
would be welcome. 
</parm> 
 
<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>. (Note that there is also an 
<aloc href="Variations">automated framework</aloc> for shower 
uncertainties.) 
 
<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> 
 
<h3>Lower cutoffs</h3> 
<p/> 
The rate of radiation if divergent in the <ei>pT &rarr; 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="0.5" min="0.1" max="2.0"> 
Parton shower cut-off <ei>pT</ei> for QCD emissions. 
</parm> 
 
<parm name="TimeShower:pTminChgQ" default="0.5" 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 &rarr; 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 &rarr; f fbar</ei> branching in the shower. 
</parm> 
 
<h3>QED Radiation in particle decays</h3> 
 
<p/> 
<b>Note:</b>This option only takes effect if <code>HadronLevel:QED = 
on</code>. 
 
<p/> 
Traditionally, PYTHIA did not have a generic machinery for handling 
QED radiation in hadron (and tau) decays. In order to include this, a 
program like PHOTOS <ref>Bar94, Dav10</ref> could be used as an 
afterburner. The options below can be used to enable PYTHIA's internal 
shower machinery for QED radiation. 
<br/> 
<b>Note 1:</b> Only two-body decays can be handled.<br/> 
<b>Note 2:</b> The f &rarr; f&gamma; DGLAP kernels are used indiscriminately 
irrespective of actual spins.<br/> 
<b>Note 3:</b> First-order matrix-element corrections for the first 
(hardest) photon emission are applied to <ei>V0 &rarr; ll and V&pm; 
&rarr; l nu</ei> since such decays are mediated by <ei>gamma^*/Z^0/ 
W^+-</ei> exchange, for which PYTHIA does have an existing machinery 
that can be applied. 
 
<modepick name="TimeShower:gammaModeHad" default="1" min="1" max="2"> 
When <code>HadronLevel:QED = on</code> and the simple-shower model is 
used, this switch determines how to handle hadron-level photon 
radiation. 
<option value="1">Photon radiation only in two-body decays to a lepton 
pair, see above. Matrix element corrections are only applied in the 
case of <ei>V0 &rarr; ll and V&pm; &rarr; l nu</ei>, based on the 
equivalent corrections for <ei>Z</ei> and <ei>W</ei> decays. 
</option> 
<option value="2">Photon radiation in all two-body hadron 
decays. Note: this option is mainly intended for comparisons and not 
for serious studies. Since the simple shower's splitting kernels do 
not encode the correct Lorentz structures for hadron decays in many 
cases, nor are the correct matrix-element corrections implemented, 
this option is not expected to deliver a faithful description of QED 
radiation in hadron decays. (Nor are hadronic form factors or photon 
VMD effects taken into account.) 
</option> 
</modepick> 
 
<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/> 
Whether such interleaving affects resonance decays or not is 
controlled by the following switch: 
<flag name="TimeShower:interleaveResDec" default="off"> 
When this flag is set to <code>off</code>, the interleaved evolution 
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. When this 
flag is set to <code>on</code>, resonance decays are inserted in the 
final-state shower evolution when it reaches the <ei>pT</ei> scale 
defined by <code>TimeShower:resDecScaleChoice</code> below. 
</flag> 
 
<p/>When <code>TimeShower:interleaveResDec</code> is set to 
<code>on</code>, the <ei>pT</ei> scale at which interleaved resonance 
decays are inserted in the shower evolution is determined by the value 
of the following switch: 
<modepick name="TimeShower:resDecScaleChoice" default="1" min="0" max="2"> 
<option value="0">The on-shell width of the resonance.</option> 
<option value="1">Off-shellness determined by <ei>|m<sup>2</sup> - 
m0<sup>2</sup>|/m0</ei>. This implies, e.g., that the decay of a 
resonance which has <ei>m = m0 &pm; &Gamma;</ei> will be performed at 
a scale <ei>pT ~ sqrt(2) &Gamma;</ei>. 
</option> 
<option value="2"> Off-shellness determined by <ei>sqrt(|m<sup>2</sup> 
- m0<sup>2</sup>|)</ei>. This implies, e.g., that the decay of a 
resonance which has <ei>m = m0 &pm; &Gamma;</ei> will be performed at 
a scale <ei>pT ~ sqrt(2 &Gamma; m0 )</ei>. 
</option> 
</modepick> 
 
<p/>Technically, the following steps happen when an interleaved 
resonance decay is inserted in the evolution: 
<ul> 
<li>The resonance is replaced by its decay products;</li> 
<li>A final-state resonance shower is performed within the 
resonance-decay system (with preserved resonance mass) bringing it 
down to the same <ei>pT</ei> scale that the rest of the evolution had 
reached before the decay was inserted.</li> 
<li>The overall final-state shower evolution is continued from that 
<ei>pT</ei> scale downwards, now with the resonance replaced by its 
decay products together with any branchings that happened during the 
resonance shower in the previous step.</li> 
</ul> 
This can take place in nested sequences, such as in 
<ei>t&rarr;bW</ei> followed by <ei>W&rarr; qq'</ei>, where the 
<ei>W</ei> decay may happen either during the top-decay resonance shower, or 
after it, depending on whether the scale associated with the 
<ei>W</ei> decay is higher, or lower, than that of the top. 
 
<p/> 
Note that, since interleaving of resonance decays only affects the 
shower evolution below the scale at which the resonance decays occur, 
only mild effects are expected for SM resonances like t, Z, and W, which 
all have widths not much larger than 1 GeV. The dynamic scale choices, 
especially <code>TimeShower:resDecScaleChoice = 2</code>, however, 
allow for potentially larger effects in the tails. 
 
<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> 
 
<p/> 
When there is no interleaving, a number of MPIs may have been generated 
before FSR is considered. In principle there could be colour correlations 
between the MPIs, such that a final-state colour of one MPI could be 
matched by the corresponding final-state anticolour of another MPI. 
These thereby would form a colour dipole, but one that does not come out 
from a common vertex, and therefore presumably could not radiate in full. 
Currently the standard procedure is to match colours between MPIs 
only after FSR, so MPI systems would radiate independently, with 
recoils taken by the beam remnant, where necessary. This could change, 
however, and the following switch would then regulate the choice of 
behaviour. 
 
<flag name="TimeShower:allowMPIdipole" default="off"> 
If on, and if interleaving is off, then dipoles are allowed to be 
formed between matching final-state colour-anticolour pairs also 
between two different MPIs. Else dipoles can normally only form 
inside the same MPI, and the could-have-been dipoles between different 
MPIs instead appear as dipoles stretched to the beam remnants. 
In either case a dipole can still form between two MPIs if a final-state 
colour cannot be matched inside the same MPI. This should normally 
not happen, except if rescattering is allowed, whereby two or more 
MPIs get interconnected. 
</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{&mu;<sub>start </sub><sup>2</sup>, m<sub>D</sub><sup>2</sup>/4}</ei>, 
with <ei>m<sub>D</sub><sup>2</sup> = 
(&radic;<span style="text-decoration:overline;color:green">&nbsp;(p<sub>r 
</sub>+p<sub>s</sub>)<sup>2</sup>&nbsp;</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>&mu;<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>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 radiation modification options</h3> 
 
There are several possibilities you can use to modify the behaviour 
of the shower, in general or for specific branchings. These options 
should be modified from default only after due consideration. 
 
<h4>Matrix-element corrections</h4> 
<flag name="TimeShower:MEcorrections" default="on"> 
Use of matrix element corrections where available; on/off = true/false. 
</flag> 
 
<flag name="TimeShower:MEextended" default="on"> 
Use matrix element corrections also for <ei>1 &rarr; n</ei> and 
<ei>2 &rarr; n</ei> processes where no matrix elements are encoded, 
by an attempt to match on to one of the <ei>1 &rarr; 2</ei> processes 
that are implemented. This should at least provide relevant mass dampening 
for massive radiators and recoilers. Only has a meaning if 
<code>MEcorrections</code> above is switched on. 
</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. Switching off this option currently does not take effect 
for a few rare types of secondary branchings, where ME corrections 
play a central role. 
</flag> 
 
<flag name="TimeShower:skipFirstMECinHardProc" default="off"> 
Allow control of matrix element corrections (MECs) in the hard 
process. By default, a matching is made between the final state of a 
hard process and the suite of decay MECs. When this option is "on", 
no MEC is used until after the first emission. This allows 
compatability with various NLO-correct merging schemes. 
</flag> 
 
<mvec name="TimeShower:skipFirstMECinResDecIDs" default="{}"> 
Allow control of matrix element corrections (MECs) in resonance 
decays, similarly to the treatment of the hard process. See above 
explanation. Only those resonance with the listed PDG identifiers are 
affected. 
</mvec> 
 
<h4>Weights for gluon (and photon) splittings</h4> 
<modepick name="TimeShower:weightGluonToQuark" default="4" min="1" max="8"> 
Different options to assign kinematics distributions and weights 
for <ei>g &rarr; q qbar</ei> branchings, notably for charm and bottom 
quarks. These options also have the corresponding effect on 
<ei>gamma &rarr; f fbar</ei> branchings. The rationale for the options 
is described in <a href="../pdfdoc/g2qqbarsplit.pdf">this note</a>. 
<br/>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> 
 
<h4>Gluon polarization effects</h4> 
<flag name="TimeShower:phiPolAsym" default="on"> 
Azimuthal asymmetry induced by gluon polarization; on/off = true/false. 
</flag> 
 
<flag name="TimeShower:phiPolAsymHard" default="on"> 
Extend the above azimuthal asymmetry (if on) also back to gluons produced 
in the hard process itself, where feasible; on/off = true/false. 
</flag> 
 
<h4>Dead cone effect</h4> 
<flag name="TimeShower:recoilDeadCone" default="on"> 
For topologies where a gluon recoils against a massive quark (or another 
massive coloured particle) there are no suitable ME corrections implemented 
into PYTHIA. When the dipole radiation pattern is split into two ends, 
with a smooth transition between the two, this means that the  gluon end 
can radiate into the quark hemisphere as if the quark were massless. The 
"dead cone" effect, that radiation collinear with a massive quark is 
strongly suppressed, thereby is not fully respected. (Unlike  radiation 
from the quark end itself, where mass effects are included.) With this 
switch on, a further suppression is therefore introduced for 
<ei>g &rarr; g g</ei> branchings, derived as the massive/massless ratio 
of the eikonal expression for dipole radiation, which kills radiation 
collinear with the quark. The <ei>g &rarr; q qbar</ei> branchings currently 
are not affected; the absence of a soft singularity implies that there 
is hardly any radiation into the recoiler hemisphere anyway. 
</flag> 
 
<h4>Resonance-final dipoles</h4> 
<modepick name="TimeShower:recoilStrategyRF" default="0" min="0" max="1"> 
In the decays of coloured resonances, notably <ei>t &rarr; b W</ei>, it 
is not possible to set up dipoles with matched colours inside the final 
state. In the first emission the <ei>b</ei> radiator therefore has 
<ei>W</ei> as recoiler, and that choice is unique. A matrix-element 
correction is also applied for this branching. Once a gluon has 
been radiated, however, there are two dipoles to consider. One colour 
line connects the gluon to the <ei>b</ei>, and the other to the 
<ei>t</ei>. The first line is a traditional dipole, so no problem, 
but the second resonance-final (RF) one needs attention. Also in 
subsequent shower steps there will always be one RF colour line. This 
switch allows two different alternative strategies to be applied for 
radiation off the final-state end of such a dipole. 
<option value="0">Let the <ei>W</ei> act as recoiler when the parton 
with the top colour radiates. Before version 8.160 this was the only 
possibility, which could give too much wide-angle radiation. From 
version 8.314 onwards, the parameter <code>TimeShower:weightRF</code> 
allows to suppress this wide-angle radiation by a factor proportional to 
the RF eikonal, which should deliver a better description of RF 
radiation patterns. 
</option> 
<option value="1">Assign the <ei>b</ei> as recoiler for both colour 
lines of the first emitted gluon, i.e. also the one with the top 
colour. This assignment then is inherited in the subsequent shower 
evolution. This option was the default between versions 8.160 and 
8.313. 
</option> 
</modepick> 
 
<note>Note 1: Up to and including version 8.309 options 0 and 1 
were available as the <code>off/on</code> options of the 
<code>TimeShower:recoilToColoured</code> flag. 
</note> 
<note>Note 2: The same issue  exists for QED radiation, but 
obviously is less significant. Consider the example 
<ei>W &rarr; e nu</ei>,  where originally the <ei>nu</ei> takes the 
recoil. In option 0 the <ei>nu</ei> would remain recoiler, while in 
option 1 instead each newly emitted photon becomes the new recoiler. 
</note> 
 
<p/> 
For <code>TimeShower:recoilStrategyRF = 0</code>, the following 
parameter and flag allow to apply a correction to the emission 
pattern for RF dipoles. The intention is that the radiation pattern should 
attach to the one expected for a final-initial dipole, 
while the recoil of this radiation is taken by the final particle that 
best correlates with the original top momentum. 
 
<parm name="TimeShower:weightRF" default="1." min="0." max="1."> 
In RF dipoles such as that which carries the colour of the top quark 
in <ei>t &rarr; b W</ei>, for <code>TimeShower:recoilStrategyRF = 
0</code> the W is chosen as recoiler not only for the first emission 
but also for subsequent emissions. The emission probability is 
corrected by a factor <ei>1. + <code>weightRF</code> (eikTop/eikW - 
1.)</ei>, where <ei>eikTop</ei> is an eikonal factor in which the top 
is considered to be the recoiler while <ei>eikW</ei> is an eikonal 
factor in which the <ei>W</ei> is considered to be the recoiler. Thus, 
for <code>weightRF = 0</code> the radiation pattern is uncorrected 
(and then corresponds to that for the <ei>W</ei> as recoiler), while 
for <code>weightRF = 1</code> it is corrected by a factor 
<ei>eikTop/eikW</ei>. As a technical note, the denominator eikonal 
factor depends on the <code>TimeShower:recoilDeadCone</code> flag. If 
on, the radiation pattern has already been corrected for the 
<ei>W</ei> mass effects. Therefore the denominator eikonal will also 
contain the <ei>W</ei> mass term. If off, the denominator will not 
contain this term, such that the ratio introduces the mass correction. 
For <code>TimeShower:recoilStrategyRF = 0</code>, this parameter 
allows to smoothly interpolate between applying the full RF eikonal 
reweighting factor (obtained with the default value of <code>weightRF 
= 1.</code>) and no reweighting (for <code>weightRF = 0.</code>). 
</parm> 
 
<flag name="TimeShower:recoilRFUseParents" default="off"> 
The <code>weightRF</code> factor above is normally evaluated with the 
four-momenta of the three partons that have been produced by the 
dipole emission. If this flag is set to <code>on</code>, instead the 
radiator and recoiler momenta before the emission are used. The 
radiated parton obviously only exists afterwards, so there the choice 
is unique. The eikonal is valid in the soft-emission limit, where the 
two choices agree, but the <code>off</code> option better attaches to 
the singularity structure of matrix elements also for harder 
emissions. The <code>on</code> still represents a valid variation. 
</flag> 
 
<note>Note: <code>weightRF</code> and <code>recoilRFuseParents</code> 
have no effect for <code>TimeShower:recoilStrategyRF = 1.</code></note> 
 
<h4>Factorization scale and PDFs</h4> 
<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> 
 
<modepick name="TimeShower:pdfMode" default="0" min="0" max="2"> 
This setting should not be touched by non-experts. Deviating 
from the default setting will only lead to consistent results 
after explicit external intervention. This setting can be useful 
in the context of interfaces to external code as done when using 
the flag <code>Merging:runtimeAMCATNLOInterface</code> described under 
<aloc href="CKKWLMerging">Merging</aloc>. 
<option value="0">this default setting corresponds to the typical 
shower treatment of including PDF ratios for dipole recoils in the 
initial state, leading to the generation of normal no-emission 
probabilities. 
</option> 
<option value="1">disable the PDF dependence, which leads to the 
generation of Sudakov factors according to the momentum sum rule. 
</option> 
<option value="2">disable the PDF dependence, which leads to the 
generation of Sudakov factors like option 1, but with a lower cut-off 
<ei>zMin = 0.5</ei> on the energy-fraction integral. 
</option> 
</modepick> 
 
<h3>Options for non-singular and higher-order terms</h3> 
 
<p>The parameters below are intended to explore 
uncertainties/variations arising from process-dependent non-singular 
terms and/or undetermined higher-order corrections to the effective 
branching kernels, beyond LL accuracy. This uses generalized forms of 
the shower splitting kernels, for gluon emissions and splittings 
respectively, 
</p> 
&nbsp;&nbsp;&nbsp;<img src="pq2qgBLL.png" height="53"></img><br/> 
&nbsp;&nbsp;&nbsp;<img src="pg2qqBLL.png" height="64"></img> 
<p> 
where <ei>&mu;<sub>s</sub></ei> is the standard renormalisation scale 
used for shower branchings and we take the scale for the second-order 
correction terms to be <ei>&mu;<sub>h</sub> = mDip/4</ei>.  The form 
used for the <ei>g&rarr;gg</ei> kernel is completely analogous to the 
one for <ei>q&rarr;qg</ei> above, with its own <ei>c</ei> coefficient 
but the same <ei>h</ei> coefficients. 
</p> 
 
<h4>First-order non-singular terms</h4> 
 
<p>For processes that do not have matrix-element corrections (MECs), 
the parameters below allow to add a constant (non-singular) term to 
the effective LO kernels for QCD branchings. For positive (negative) 
values, this increases (decreases) the branching probabilities. These 
terms are analogous to the ones called <code>cNS</code> in the context 
of <aloc href="Variations">uncertainty variations</aloc>, and have the 
effect of modifying the splitting kernels as <ei>P(z)/Q2 &rarr; 
P(z)/Q2 + c</ei>. 
<parm name="TimeShower:cEmitQ" default="0.0" min="-5.0" max="5.0"> 
Non-singular term, <ei>c</ei>, for <ei>Q&rarr;QG</ei> branchings. 
</parm> 
<parm name="TimeShower:cEmitC" default="0.0" min="-5.0" max="5.0"> 
Additional non-singular term for <ei>C&rarr;CG</ei> branchings so that 
the total for such branchings is <code>cEmitQ</code> + <code>cEmitC</code>. 
</parm> 
<parm name="TimeShower:cEmitB" default="0.0" min="-5.0" max="5.0"> 
Additional non-singular term for <ei>B&rarr;BG</ei> branchings so that 
the total for such branchings is <code>cEmitQ</code> + <code>cEmitB</code>. 
</parm> 
<parm name="TimeShower:cEmitG" default="0.0" min="-5.0" max="5.0"> 
Non-singular term, <ei>c</ei>, for <ei>G&rarr;GG</ei> branchings. 
</parm> 
<parm name="TimeShower:cSplit" default="0.0" min="-5.0" max="5.0"> 
Non-singular term, <ei>c</ei>, for <ei>G&rarr;QQbar</ei> splittings. 
</parm> 
<parm name="TimeShower:cSplitC" default="0.0" min="-5.0" max="5.0"> 
Additional non-singular term for <ei>G&rarr;CCbar</ei> splittings so that 
the total for such splittings is <code>cSplit</code> + <code>cSplitC</code>. 
</parm> 
<parm name="TimeShower:cSplitB" default="0.0" min="-5.0" max="5.0"> 
Additional non-singular term for <ei>G&rarr;BBbar</ei> splittings so that 
the total for such splittings is <code>cSplit</code> + <code>cSplitB</code>. 
</parm> 
</p> 
 
<h4>Higher-order terms</h4> 
 
<p>The following parameters allow to add terms that are suppressed by 
an additional power of the strong coupling, representing variations of 
the effective branching kernels beyond LO and hence active also in the 
presence of MECs. 
<parm name="TimeShower:hEmitHard" default="0.0" min="-40.0" max="40.0"> 
Non-singular 2nd-order term added to <ei>Q&rarr;QG</ei> and 
<ei>G&rarr;GG</ei> branchings. Acts in the same way as the LO 
<ei>c</ei> parameters above but is suppressed by an extra power of 
<ei>&alpha;<sub>S</sub>/(2&pi;)</ei>. 
</parm> 
<parm name="TimeShower:hEmitColl" default="0.0" min="-20.0" max="20.0"> 
Collinear-singular 2nd-order term added to <ei>Q&rarr;QG</ei> and 
<ei>G&rarr;GG</ei> branchings, proportional to 
<ei>(&alpha;<sub>S</sub>/(2&pi;))<sup>2</sup> 
z*P(z)/Q<sup>2</sup></ei>. 
</parm> 
<parm name="TimeShower:hEmitSoft" default="0.0" min="-20.0" max="20.0"> 
Soft-singular 2nd-order term added to <ei>Q&rarr;QG</ei> and 
<ei>G&rarr;GG</ei> branchings, proportional to 
<ei>(&alpha;<sub>S</sub>/(2&pi;))<sup>2</sup> 
(1-z)*P(z)/Q<sup>2</sup></ei>.  Note that, when using the CMW scheme 
for the strong coupling, this parameter should not be allowed to 
differ significantly from zero (though small values could still be 
used to explore effective 3rd-order variations). 
</parm> 
<parm name="TimeShower:hSplitHard" default="0.0" min="-40.0" max="40.0"> 
Non-singular 2nd-order term added to <ei>G&rarr;QQ</ei> branchings. 
Acts in the same way as the LO <ei>c</ei> parameters above but is 
suppressed by an extra power of <ei>&alpha;<sub>S</sub>/(2&pi;)</ei>. 
</parm> 
<parm name="TimeShower:hSplitColl" default="0.0" min="-20.0" max="20.0"> 
Collinear-singular 2nd-order term added to <ei>G&rarr;QQ</ei> 
branchings, proportional to 
<ei>(&alpha;<sub>S</sub>/(2&pi;))<sup>2</sup> P(z)/Q<sup>2</sup></ei>. 
</parm> 
</p> 
 
<h3>Switch off branching types</h3> 
 
There are several possibilities you can use to switch on or off 
selected branching types in 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 &rarr; q g</ei>, 
<ei>g &rarr; g g</ei> and <ei>g &rarr; 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 &rarr; q qbar</ei> branchings 
(phase space permitting). A change to 4 would exclude 
<ei>g &rarr; b bbar</ei>, etc. 
</modeopen> 
 
<flag name="TimeShower:QEDshowerByQ" default="on"> 
Allow quarks to radiate photons, i.e. branchings <ei>q &rarr; q gamma</ei>; 
on/off = true/false. 
</flag> 
 
<flag name="TimeShower:QEDshowerByL" default="on"> 
Allow leptons to radiate photons, i.e. branchings <ei>l &rarr; l gamma</ei>; 
on/off = true/false. 
</flag> 
 
<flag name="TimeShower:QEDshowerByOther" default="on"> 
Allow charged resonances to radiate photons, i.e. branchings 
<ei>q&sim; &rarr; q&sim; gamma</ei>; on/off = true/false. This will 
also allow the W boson to radiate. 
</flag> 
 
<flag name="TimeShower:QEDshowerByGamma" default="on"> 
Allow photons to branch into lepton or quark pairs, i.e. branchings 
<ei>gamma &rarr; l+ l-</ei> and <ei>gamma &rarr; 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 &rarr; q qbar</ei> branchings 
(phase space permitting). A change to 4 would exclude 
<ei>gamma &rarr; b bbar</ei>, etc. 
</modeopen> 
 
<modeopen name="TimeShower:nGammaToLepton" default="3" min="0" max="3"> 
Number of allowed lepton flavours in <ei>gamma &rarr; l+ l-</ei> branchings 
(phase space permitting). A change to 2 would exclude 
<ei>gamma &rarr; tau+ tau-</ei>, and a change to 1 also 
<ei>gamma &rarr; mu+ mu-</ei>. 
</modeopen> 
 
<flag name="TimeShower:recoilToColoured" default="on"> 
In the decays of coloured resonances, say <ei>t &rarr; 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 &rarr; 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> 
 
</chapter> 
 
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