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1<html>
2<head>
3<title>Timelike Showers</title>
4<link rel="stylesheet" type="text/css" href="pythia.css"/>
5<link rel="shortcut icon" href="pythia32.gif"/>
6</head>
7<body>
8   
9<h2>Timelike Showers</h2>
10
11The PYTHIA algorithm for timelike final-state showers is based on
12the article [<a href="Bibliography.html" target="page">Sjo05</a>], where a transverse-momentum-ordered
13evolution scheme is introduced, with the extension to fully interleaved
14evolution covered in [<a href="Bibliography.html" target="page">Cor10a</a>]. This algorithm is influenced by
15the previous mass-ordered algorithm in PYTHIA [<a href="Bibliography.html" target="page">Ben87</a>] and by
16the dipole-emission formulation in Ariadne [<a href="Bibliography.html" target="page">Gus86</a>]. From the
17mass-ordered algorithm it inherits a merging procedure for first-order
18gluon-emission matrix elements in essentially all two-body decays
19in the standard model and its minimal supersymmetric extension
20[<a href="Bibliography.html" target="page">Nor01</a>].
21
22<p/>
23The normal user is not expected to call <code>TimeShower</code> directly,
24but only have it called from <code>Pythia</code>. Some of the parameters
25below, in particular <code>TimeShower:alphaSvalue</code>, would be of
26interest for a tuning exercise, however.
27
28<h3>Main variables</h3>
29
30Often the maximum scale of the FSR shower evolution is understood from the
31context. For instance, in a resonace decay half the resonance mass sets an
32absolute upper limit. For a hard process in a hadronic collision the choice
33is not as unique. Here the <a href="CouplingsAndScales.html" target="page">factorization
34scale</a> has been chosen as the maximum evolution scale. This would be
35the <i>pT</i> for a <i>2 -> 2</i> process, supplemented by mass terms
36for massive outgoing particles. For some special applications we do allow
37an alternative.
38
39<p/><code>mode&nbsp; </code><strong> TimeShower:pTmaxMatch &nbsp;</strong> 
40 (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
41Way in which the maximum shower evolution scale is set to match the
42scale of the hard process itself.
43<br/><code>option </code><strong> 0</strong> : <b>(i)</b> if the final state of the hard process
44(not counting subsequent resonance decays) contains at least one quark
45(<i>u, d, s, c ,b</i>), gluon or photon then <i>pT_max</i> 
46is chosen to be the factorization scale for internal processes
47and the <code>scale</code> value for Les Houches input;
48<b>(ii)</b> if not, emissions are allowed to go all the way up to
49the kinematical limit (i.e. to half the dipole mass).
50This option agrees with the corresponding one for
51<a href="SpacelikeShowers.html" target="page">spacelike showers</a>. There the
52reasoning is that in the former set of processes the ISR
53emission of yet another quark, gluon or photon could lead to
54doublecounting, while no such danger exists in the latter case.
55The argument is less compelling for timelike showers, but could
56be a reasonable starting point.
57 
58<br/><code>option </code><strong> 1</strong> : always use the factorization scale for an internal
59process and the <code>scale</code> value for Les Houches input,
60i.e. the lower value. This should avoid doublecounting, but
61may leave out some emissions that ought to have been simulated.
62(Also known as wimpy showers.)
63 
64<br/><code>option </code><strong> 2</strong> : always allow emissions up to the kinematical limit
65(i.e. to half the dipole mass). This will simulate all possible event
66topologies, but may lead to doublecounting.
67(Also known as power showers.)
68 
69<br/><b>Note:</b> These options only apply to the hard interaction.
70Emissions off subsequent multiparton interactions are always constrainted
71to be below the factorization scale of the process itself. They also
72assume you use interleaved evolution, so that FSR is in direct
73competition with ISR for the hardest emission. If you already
74generated a number of ISR partons at low <i>pT</i>, it would not
75make sense to have a later FSR shower up to the kinematical for all
76of them.
77 
78
79<p/><code>parm&nbsp; </code><strong> TimeShower:pTmaxFudge &nbsp;</strong> 
80 (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)<br/>
81In cases where the above <code>pTmaxMatch</code> rules would imply
82that <i>pT_max = pT_factorization</i>, <code>pTmaxFudge</code> 
83introduces a multiplicative factor <i>f</i> such that instead
84<i>pT_max = f * pT_factorization</i>. Only applies to the hardest
85interaction in an event, cf. below. It is strongly suggested that
86<i>f = 1</i>, but variations around this default can be useful to
87test this assumption.
88<br/><b>Note:</b>Scales for resonance decays are not affected, but can
89be set separately by <a href="UserHooks.html" target="page">user hooks</a>.
90 
91
92<p/><code>parm&nbsp; </code><strong> TimeShower:pTmaxFudgeMPI &nbsp;</strong> 
93 (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)<br/>
94A multiplicative factor <i>f</i> such that
95<i>pT_max = f * pT_factorization</i>, as above, but here for the
96non-hardest interactions (when multiparton interactions are allowed).
97 
98
99<p/><code>mode&nbsp; </code><strong> TimeShower:pTdampMatch &nbsp;</strong> 
100 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
101These options only take effect when a process is allowed to radiate up
102to the kinematical limit by the above <code>pTmaxMatch</code> choice,
103and no matrix-element corrections are available. Then, in many processes,
104the fall-off in <i>pT</i> will be too slow by one factor of <i>pT^2</i>.
105That is, while showers have an approximate <i>dpT^2/pT^2</i> shape, often
106it should become more like <i>dpT^2/pT^4</i> at <i>pT</i> values above
107the scale of the hard process. This argument is more obvious for ISR,
108but is taken over unchanged for FSR to have a symmetric description.
109<br/><code>option </code><strong> 0</strong> : emissions go up to the kinematical limit,
110with no special dampening.
111 
112<br/><code>option </code><strong> 1</strong> : emissions go up to the kinematical limit, 
113but dampened by a factor <i>k^2 Q^2_fac/(pT^2 + k^2 Q^2_fac)</i>,
114where <i>Q_fac</i> is the factorization scale and <i>k</i> is a
115multiplicative fudge factor stored in <code>pTdampFudge</code> below.
116 
117<br/><code>option </code><strong> 2</strong> : emissions go up to the kinematical limit,
118but dampened by a factor <i>k^2 Q^2_ren/(pT^2 + k^2 Q^2_ren)</i>,
119where <i>Q_ren</i> is the renormalization scale and <i>k</i> is a
120multiplicative fudge factor stored in <code>pTdampFudge</code> below.
121 
122<br/><b>Note:</b> These options only apply to the hard interaction.
123Emissions off subsequent multiparton interactions are always constrainted
124to be below the factorization scale of the process itself. 
125 
126
127<p/><code>parm&nbsp; </code><strong> TimeShower:pTdampFudge &nbsp;</strong> 
128 (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 4.0</code>)<br/>
129In cases 1 and 2 above, where a dampening is imposed at around the
130factorization or renormalization scale, respectively, this allows the
131<i>pT</i> scale of dampening of radiation by a half to be shifted
132by this factor relative to the default <i>Q_fac</i> or <i>Q_ren</i>.
133This number ought to be in the neighbourhood of unity, but variations
134away from this value could do better in some processes.
135 
136
137<p/>
138The amount of QCD radiation in the shower is determined by
139<p/><code>parm&nbsp; </code><strong> TimeShower:alphaSvalue &nbsp;</strong> 
140 (<code>default = <strong>0.1383</strong></code>; <code>minimum = 0.06</code>; <code>maximum = 0.25</code>)<br/>
141The <i>alpha_strong</i> value at scale <i>M_Z^2</i>. The default
142value corresponds to a crude tuning to LEP data, to be improved.
143 
144
145<p/>
146The actual value is then regulated by the running to the scale
147<i>pT^2</i>, at which the shower evaluates <i>alpha_strong</i>.
148
149<p/><code>mode&nbsp; </code><strong> TimeShower:alphaSorder &nbsp;</strong> 
150 (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/>
151Order at which <i>alpha_strong</i> runs,
152<br/><code>option </code><strong> 0</strong> : zeroth order, i.e. <i>alpha_strong</i> is kept
153fixed. 
154<br/><code>option </code><strong> 1</strong> : first order, which is the normal value. 
155<br/><code>option </code><strong> 2</strong> : second order. Since other parts of the code do
156not go to second order there is no strong reason to use this option,
157but there is also nothing wrong with it. 
158 
159
160<p/>
161QED radiation is regulated by the <i>alpha_electromagnetic</i>
162value at the <i>pT^2</i> scale of a branching.
163 
164<p/><code>mode&nbsp; </code><strong> TimeShower:alphaEMorder &nbsp;</strong> 
165 (<code>default = <strong>1</strong></code>; <code>minimum = -1</code>; <code>maximum = 1</code>)<br/>
166The running of <i>alpha_em</i>.
167<br/><code>option </code><strong> 1</strong> : first-order running, constrained to agree with
168<code>StandardModel:alphaEMmZ</code> at the <i>Z^0</i> mass.
169 
170<br/><code>option </code><strong> 0</strong> : zeroth order, i.e. <i>alpha_em</i> is kept
171fixed at its value at vanishing momentum transfer. 
172<br/><code>option </code><strong> -1</strong> : zeroth order, i.e. <i>alpha_em</i> is kept
173fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value
174at the <i>Z^0</i> mass.
175   
176 
177
178<p/>
179The natural scale for couplings, and PDFs for dipoles stretching out
180to the beam remnants, is <i>pT^2</i>. To explore uncertainties it
181is possibly to vary around this value, however, in analogy with what
182can be done for <a href="CouplingsAndScales.html" target="page">hard processes</a>.
183
184<p/><code>parm&nbsp; </code><strong> TimeShower:renormMultFac &nbsp;</strong> 
185 (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)<br/>
186The default <i>pT^2</i> renormalization scale is multiplied by
187this prefactor. For QCD this is equivalent to a change of
188<i>Lambda^2</i> in the opposite direction, i.e. to a change of
189<i>alpha_strong(M_Z^2)</i> (except that flavour thresholds
190remain at fixed scales).
191 
192
193<p/><code>parm&nbsp; </code><strong> TimeShower:factorMultFac &nbsp;</strong> 
194 (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)<br/>
195The default <i>pT^2</i> factorization scale is multiplied by
196this prefactor.
197 
198 
199<p/>
200The rate of radiation if divergent in the <i>pT -> 0</i> limit. Here,
201however, perturbation theory is expected to break down. Therefore an
202effective <i>pT_min</i> cutoff parameter is introduced, below which
203no emissions are allowed. The cutoff may be different for QCD and QED
204radiation off quarks, and is mainly a technical parameter for QED
205radiation off leptons.
206
207<p/><code>parm&nbsp; </code><strong> TimeShower:pTmin &nbsp;</strong> 
208 (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)<br/>
209Parton shower cut-off <i>pT</i> for QCD emissions.
210 
211
212<p/><code>parm&nbsp; </code><strong> TimeShower:pTminChgQ &nbsp;</strong> 
213 (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)<br/>
214Parton shower cut-off <i>pT</i> for photon coupling to coloured particle.
215 
216
217<p/><code>parm&nbsp; </code><strong> TimeShower:pTminChgL &nbsp;</strong> 
218 (<code>default = <strong>0.0005</strong></code>; <code>minimum = 0.0001</code>; <code>maximum = 2.0</code>)<br/>
219Parton shower cut-off <i>pT</i> for pure QED branchings.
220Assumed smaller than (or equal to) <code>pTminChgQ</code>.
221 
222
223<p/> 
224Shower branchings <i>gamma -> f fbar</i>, where <i>f</i> is a
225quark or lepton, in part compete with the hard processes involving
226<i>gamma^*/Z^0</i> production. In order to avoid overlap it makes
227sense to correlate the maximum <i>gamma</i> mass allowed in showers
228with the minumum <i>gamma^*/Z^0</i> mass allowed in hard processes.
229In addition, the shower contribution only contains the pure
230<i>gamma^*</i> contribution, i.e. not the <i>Z^0</i> part, so
231the mass spectrum above 50 GeV or so would not be well described.
232
233<p/><code>parm&nbsp; </code><strong> TimeShower:mMaxGamma &nbsp;</strong> 
234 (<code>default = <strong>10.0</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 50.0</code>)<br/>
235Maximum invariant mass allowed for the created fermion pair in a
236<i>gamma -> f fbar</i> branching in the shower.
237 
238
239<h3>Interleaved evolution</h3>
240
241Multiparton interactions (MPI) and initial-state showers (ISR) are
242always interleaved, as follows. Starting from the hard interaction,
243the complete event is constructed by a set of steps. In each step
244the <i>pT</i> scale of the previous step is used as starting scale
245for a downwards evolution. The MPI and ISR components each make
246their respective Monte Carlo choices for the next lower <i>pT</i> 
247value. The one with larger <i>pT</i> is allowed to carry out its
248proposed action, thereby modifying the conditions for the next steps.
249This is relevant since the two components compete for the energy
250contained in the beam remnants: both an interaction and an emission
251take avay some of the energy, leaving less for the future. The end
252result is a combined chain of decreasing <i>pT</i> values, where
253ones associated with new interactions and ones with new emissions
254are interleaved. 
255
256<p/>
257There is no corresponding requirement for final-state radiation (FSR)
258to be interleaved. Such an FSR emission does not compete directly for
259beam energy (but see below), and also can be viewed as occuring after
260the other two components in some kind of time sense. Interleaving is
261allowed, however, since it can be argued that a high-<i>pT</i> FSR
262occurs on shorter time scales than a low-<i>pT</i> MPI, say.
263Backwards evolution of ISR is also an example that physical time
264is not the only possible ordering principle, but that one can work
265with conditional probabilities: given the partonic picture at a 
266specific <i>pT</i> resolution scale, what possibilities are open
267for a modified picture at a slightly lower <i>pT</i> scale, either
268by MPI, ISR or FSR? Complete interleaving of the three components also
269offers advantages if one aims at matching to higher-order matrix
270elements above some given scale.
271
272<p/><code>flag&nbsp; </code><strong> TimeShower:interleave &nbsp;</strong> 
273 (<code>default = <strong>on</strong></code>)<br/>
274If on, final-state emissions are interleaved in the same
275decreasing-<i>pT</i> chain as multiparton interactions and initial-state
276emissions. If off, final-state emissions are only addressed after the
277multiparton interactions and initial-state radiation have been considered.
278 
279
280<p/>
281As an aside, it should be noted that such interleaving does not affect
282showering in resonance decays, such as a <i>Z^0</i>. These decays are
283only introduced after the production process has been considered in full,
284and the subsequent FSR is carried out inside the resonance, with
285preserved resonance mass.
286
287<p/>
288One aspect of FSR for a hard process in hadron collisions is that often
289colour diples are formed between a scattered parton and a beam remnant,
290or rather the hole left behind by an incoming partons. If such holes
291are allowed as dipole ends and take the recoil when the scattered parton
292undergoes a branching then this translates into the need to take some
293amount of remnant energy also in the case of FSR, i.e. the roles of
294ISR and FSR are not completely decoupled. The energy taken away is
295bokkept by increasing the <i>x</i> value assigned to the incoming
296scattering parton, and a reweighting factor
297<i>x_new f(x_new, pT^2) / x_old f(x_old, pT^2)</i> 
298in the emission probability ensures that not unphysically large
299<i>x_new</i> values are reached. Usually such <i>x</i> changes are
300small, and they can be viewed as a higher-order effect beyond the
301accuracy of the leading-log initial-state showers.
302
303<p/>
304This choice is not unique, however. As an alternative, if nothing else
305useful for cross-checks, one could imagine that the FSR is completely
306decoupled from the ISR and beam remnants.
307
308<p/><code>flag&nbsp; </code><strong> TimeShower:allowBeamRecoil &nbsp;</strong> 
309 (<code>default = <strong>on</strong></code>)<br/>
310If on, the final-state shower is allowed to borrow energy from
311the beam remnants as described above, thereby changing the mass of the
312scattering subsystem. If off, the partons in the scattering subsystem
313are constrained to borrow energy from each other, such that the total
314four-momentum of the system is preserved. This flag has no effect
315on resonance decays, where the shower always preserves the resonance
316mass, cf. the comment above about showers for resonances never being
317interleaved.
318 
319
320<p/><code>flag&nbsp; </code><strong> TimeShower:dampenBeamRecoil &nbsp;</strong> 
321 (<code>default = <strong>on</strong></code>)<br/>
322When beam recoil is allowed there is still some ambiguity how far
323into the beam end of the dipole that emission should be allowed.
324It is dampened in the beam region, but probably not enough.
325When on an additional suppression factor
326<i>4 pT2_hard / (4 pT2_hard + m2)</i> is multiplied on to the
327emission probability. Here <i>pT_hard</i> is the transverse momentum
328of the radiating parton and <i>m</i> the off-shell mass it acquires
329by the branching, <i>m2 = pT2/(z(1-z))</i>. Note that
330<i>m2 = 4 pT2_hard</i> is the kinematical limit for a scattering
331at 90 degrees without beam recoil.   
332 
333
334<h3>Global recoil</h3>
335
336The final-state algorithm is based on dipole-style recoils, where
337one single parton takes the full recoil of a branching. This is unlike
338the initial-state algorithm, where the complete already-existing
339final state shares the recoil of each new emission. As an alternative,
340also the final-state algorithm contains an option where the recoil
341is shared between all partons in the final state. Thus the radiation
342pattern is unrelated to colour correlations. This is especially
343convenient for some matching algorithms, like MC@NLO, where a full
344analytic knowledge of the shower radiation pattern is needed to avoid
345doublecountning. (The <i>pT</i>-ordered shower is described in
346[<a href="Bibliography.html" target="page">Sjo05</a>], and the corrections for massive radiator and recoiler
347in [<a href="Bibliography.html" target="page">Nor01</a>].)
348
349<p/> 
350Technically, the radiation pattern is most conveniently represented
351in the rest frame of the final state of the hard subprocess. Then, for
352each parton at a time, the rest of the final state can be viewed as
353a single effective parton. This "parton" has a fixed invariant mass
354during the emission process, and takes the recoil without any changed
355direction of motion. The momenta of the individual new recoilers are
356then obtained by a simple common boost of the original ones.
357
358<p/> 
359This alternative approach will miss out on the colour coherence
360phenomena. Specifically, with the whole subcollision mass as "dipole"
361mass, the phase space for subsequent emissions is larger than for
362the normal dipole algorithm. The phase space difference grows as
363more and more gluons are created, and thus leads to a way too steep
364multiplication of soft gluons. Therefore the main application is
365for the first one or few emissions of the shower, where a potential
366overestimate of the emission rate is to be corrected for anyway,
367by matching to the relevant matrix elements. Thereafter, subsequent
368emissions should be handled as before, i.e. with dipoles spanned
369between nearby partons. Furthermore, only the first (hardest)
370subcollision is handled with global recoils, since subsequent MPI's
371would not be subject to matrix element corrections anyway.
372
373<p/> 
374In order for the mid-shower switch from global to local recoils
375to work, colours are traced and bookkept just as for normal showers;
376it is only that this information is not used in those steps where
377a global recoil is requested. (Thus, e.g., a gluon is still bookkept
378as one colour and one anticolour dipole end, with half the charge
379each, but with global recoil those two ends radiate identically.)
380
381<p/><code>flag&nbsp; </code><strong> TimeShower:globalRecoil &nbsp;</strong> 
382 (<code>default = <strong>off</strong></code>)<br/>
383Alternative approach as above, where all final-state particles share
384the recoil of an emission.
385<br/>If off, then use the standard dipole-recoil approach.
386<br/>If on, use the alternative global recoil, but only for the first
387interaction, and only while the number of particles in the final state
388is at most <code>TimeShower:nMaxGlobalRecoil</code> before the
389branching.
390 
391 
392<p/><code>mode&nbsp; </code><strong> TimeShower:nMaxGlobalRecoil &nbsp;</strong> 
393 (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>)<br/>
394Represents the maximum number of particles in the final state for which
395the next final-state emission can be performed with the global recoil
396strategy. This number counts all particles, whether they are
397allowed to radiate or not, e.g. also <i>Z^0</i>. Also partons
398created by initial-state radiation emissions counts towards this sum,
399as part of the interleaved evolution. Without interleaved evolution
400this option would not make sense, since then a varying and large
401number of partons could already have been created by the initial-state
402radiation before the first final-state one, and then there is not
403likely to be any matrix elements available for matching.
404 
405
406<p/> 
407The global-recoil machinery does not work well with rescattering in the
408MPI machinery, since then the recoiling system is not uniquely defined.
409<code>MultipartonInteractions:allowRescatter = off</code> by default,
410so this is not a main issue. If both options are switched on,
411rescattering will only be allowed to kick in after the global recoil
412has ceased to be active, i.e. once the <code>nMaxGlobalRecoil</code> 
413limit has been exceeded. This should not be a major conflict,
414since rescattering is mainly of interest at later stages of the
415downwards <i>pT</i> evolution.
416
417<p/> 
418Further, it is strongly recommended to set
419<code>TimeShower:MEcorrections = off</code> (not default!), i.e. not
420to correct the emission probability to the internal matrix elements.
421The internal ME options do not cover any cases relevant for a multibody
422recoiler anyway, so no guarantees are given what prescription would
423come to be used. Instead, without ME corrections,  a process-independent
424emission rate is obtained, and  <a href="UserHooks.html" target="page">user hooks</a> 
425can provide the desired process-specific rejection factors.
426 
427<h3>Radiation off octet onium states</h3>
428
429In the current implementation, charmonium and bottomonium production
430can proceed either through colour singlet or colour octet mechanisms,
431both of them implemented in terms of <i>2 -> 2</i> hard processes
432such as <i>g g -> (onium) g</i>.
433In the former case the state does not radiate and the onium therefore
434is produced in isolation, up to normal underlying-event activity. In
435the latter case the situation is not so clear, but it is sensible to
436assume that a shower can evolve. (Assuming, of course, that the
437transverse momentum of the onium state is sufficiently high that 
438radiation is of relevance.)
439
440<p/> 
441There could be two parts to such a shower. Firstly a gluon (or even a
442quark, though less likely) produced in a hard <i>2 -> 2</i> process
443can undergo showering into many gluons, whereof one branches into the
444heavy-quark pair. Secondly, once the pair has been produced, each quark
445can radiate further gluons. This latter kind of emission could easily
446break up a semibound quark pair, but might also create a new semibound
447state where before an unbound pair existed, and to some approximation
448these two effects should balance in the onium production rate.
449The showering "off an onium state" as implemented here therefore should
450not be viewed as an accurate description of the emission history
451step by step, but rather as an effective approach to ensure that the
452octet onium produced "in the hard process" is embedded in a realistic
453amount of jet activity.
454Of course both the isolated singlet and embedded octet are likely to
455be extremes, but hopefully the mix of the two will strike a reasonable
456balance. However, it is possible that some part of the octet production
457occurs in channels where it should not be accompanied by (hard) radiation.
458Therefore reducing the fraction of octet onium states allowed to radiate
459is a valid variation to explore uncertainties.
460
461<p/>
462If an octet onium state is chosen to radiate, the simulation of branchings
463is based on the assumption that the full radiation is provided by an
464incoherent sum of radiation off the quark and off the antiquark of the
465onium state. Thus the splitting kernel is taken to be the normal
466<i>q -> q g</i> one, multiplied by a factor of two. Obviously this is
467a simplification of a more complex picture, averaging over factors pulling
468in different directions. Firstly, radiation off a gluon ought
469to be enhanced by a factor 9/4 relative to a quark rather than the 2
470now used, but this is a minor difference. Secondly, our use of the
471<i>q -> q g</i> branching kernel is roughly equivalent to always
472following the harder gluon in a <i>g -> g g</i> branching. This could
473give us a bias towards producing too hard onia. A soft gluon would have
474little phase space to branch into a heavy-quark pair however, so the
475bias may not be as big as it would seem at first glance. Thirdly,
476once the gluon has branched into a quark pair, each quark carries roughly
477only half of the onium energy. The maximum energy per emitted gluon should
478then be roughly half the onium energy rather than the full, as it is now.
479Thereby the energy of radiated gluons is exaggerated, i.e. onia become too
480soft. So the second and the third points tend to cancel each other.
481
482<p/>
483Finally, note that the lower cutoff scale of the shower evolution depends
484on the onium mass rather than on the quark mass, as it should be. Gluons
485below the octet-onium scale should only be part of the octet-to-singlet
486transition.
487
488<p/><code>parm&nbsp; </code><strong> TimeShower:octetOniumFraction &nbsp;</strong> 
489 (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/>
490Allow colour-octet charmonium and bottomonium states to radiate gluons.
4910 means that no octet-onium states radiate, 1 that all do, with possibility
492to interpolate between these two extremes.
493 
494
495<p/><code>parm&nbsp; </code><strong> TimeShower:octetOniumColFac &nbsp;</strong> 
496 (<code>default = <strong>2.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 4.</code>)<br/>
497The colour factor used used in the splitting kernel for those octet onium
498states that are allowed to radiate, normalized to the <i>q -> q g</i>
499splitting kernel. Thus the default corresponds to twice the radiation
500off a quark. The physically preferred range would be between 1 and 9/4.
501 
502
503<h3>Further variables</h3>
504
505There are several possibilities you can use to switch on or off selected
506branching types in the shower, or in other respects simplify the shower.
507These should normally not be touched. Their main function is for
508cross-checks.
509
510<p/><code>flag&nbsp; </code><strong> TimeShower:QCDshower &nbsp;</strong> 
511 (<code>default = <strong>on</strong></code>)<br/>
512Allow a QCD shower, i.e. branchings <i>q -> q g</i>, <i>g -> g g</i> 
513and <i>g -> q qbar</i>; on/off = true/false.
514 
515
516<p/><code>mode&nbsp; </code><strong> TimeShower:nGluonToQuark &nbsp;</strong> 
517 (<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)<br/>
518Number of allowed quark flavours in <i>g -> q qbar</i> branchings
519(phase space permitting). A change to 4 would exclude
520<i>g -> b bbar</i>, etc.
521 
522
523<p/><code>flag&nbsp; </code><strong> TimeShower:QEDshowerByQ &nbsp;</strong> 
524 (<code>default = <strong>on</strong></code>)<br/>
525Allow quarks to radiate photons, i.e. branchings <i>q -> q gamma</i>;
526on/off = true/false.
527 
528
529<p/><code>flag&nbsp; </code><strong> TimeShower:QEDshowerByL &nbsp;</strong> 
530 (<code>default = <strong>on</strong></code>)<br/>
531Allow leptons to radiate photons, i.e. branchings <i>l -> l gamma</i>; 
532on/off = true/false.
533 
534
535<p/><code>flag&nbsp; </code><strong> TimeShower:QEDshowerByGamma &nbsp;</strong> 
536 (<code>default = <strong>on</strong></code>)<br/>
537Allow photons to branch into lepton or quark pairs, i.e. branchings
538<i>gamma -> l+ l-</i> and <i>gamma -> q qbar</i>;
539on/off = true/false.
540 
541
542<p/><code>mode&nbsp; </code><strong> TimeShower:nGammaToQuark &nbsp;</strong> 
543 (<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)<br/>
544Number of allowed quark flavours in <i>gamma -> q qbar</i> branchings
545(phase space permitting). A change to 4 would exclude
546<i>g -> b bbar</i>, etc.
547 
548
549<p/><code>mode&nbsp; </code><strong> TimeShower:nGammaToLepton &nbsp;</strong> 
550 (<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)<br/>
551Number of allowed lepton flavours in <i>gamma -> l+ l-</i> branchings
552(phase space permitting). A change to 2 would exclude
553<i>gamma -> tau+ tau-</i>, and a change to 1 also
554<i>gamma -> mu+ mu-</i>.
555 
556
557<p/><code>flag&nbsp; </code><strong> TimeShower:MEcorrections &nbsp;</strong> 
558 (<code>default = <strong>on</strong></code>)<br/>
559Use of matrix element corrections where available; on/off = true/false.
560 
561
562<p/><code>flag&nbsp; </code><strong> TimeShower:MEafterFirst &nbsp;</strong> 
563 (<code>default = <strong>on</strong></code>)<br/>
564Use of matrix element corrections also after the first emission,
565for dipole ends of the same system that did not yet radiate.
566Only has a meaning if <code>MEcorrections</code> above is
567switched on.
568 
569
570<p/><code>flag&nbsp; </code><strong> TimeShower:phiPolAsym &nbsp;</strong> 
571 (<code>default = <strong>on</strong></code>)<br/>
572Azimuthal asymmetry induced by gluon polarization; on/off = true/false.
573 
574
575<p/><code>flag&nbsp; </code><strong> TimeShower:recoilToColoured &nbsp;</strong> 
576 (<code>default = <strong>on</strong></code>)<br/>
577In the decays of coloured resonances, say <i>t -> b W</i>, it is not
578possible to set up dipoles with matched colours. Originally the
579<i>b</i> radiator therefore has <i>W</i> as recoiler, and that
580choice is unique. Once a gluon has been radiated, however, it is
581possible either to have the unmatched colour (inherited by the gluon)
582still recoiling against the <i>W</i> (<code>off</code>), or else
583let it recoil against the <i>b</i> also for this dipole
584(<code>on</code>). Before version 8.160 the former was the only
585possibility, which could give unphysical radiation patterns. It is
586kept as an option to check backwards compatibility. The same issue
587exists for QED radiation, but obviously is less significant. Consider
588the example <i>W -> e nu</i>, where originally the <i>nu</i> 
589takes the recoil. In the old (<code>off</code>) scheme the <i>nu</i> 
590would remain recoiler, while in the new (<code>on</code>) instead
591each newly emitted photon becomes the new recoiler.
592 
593
594</body>
595</html>
596
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