3 <title>Timelike Showers</title>
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30 <h2>Timelike Showers</h2>
32 The PYTHIA algorithm for timelike final-state showers is based on
33 the article [<a href="Bibliography.php" target="page">Sjo05</a>], where a transverse-momentum-ordered
34 evolution scheme is introduced, with the extension to fully interleaved
35 evolution covered in [<a href="Bibliography.php" target="page">Cor10a</a>]. This algorithm is influenced by
36 the previous mass-ordered algorithm in PYTHIA [<a href="Bibliography.php" target="page">Ben87</a>] and by
37 the dipole-emission formulation in Ariadne [<a href="Bibliography.php" target="page">Gus86</a>]. From the
38 mass-ordered algorithm it inherits a merging procedure for first-order
39 gluon-emission matrix elements in essentially all two-body decays
40 in the standard model and its minimal supersymmetric extension
41 [<a href="Bibliography.php" target="page">Nor01</a>].
44 The normal user is not expected to call <code>TimeShower</code> directly,
45 but only have it called from <code>Pythia</code>. Some of the parameters
46 below, in particular <code>TimeShower:alphaSvalue</code>, would be of
47 interest for a tuning exercise, however.
49 <h3>Main variables</h3>
51 Often the maximum scale of the FSR shower evolution is understood from the
52 context. For instance, in a resonace decay half the resonance mass sets an
53 absolute upper limit. For a hard process in a hadronic collision the choice
54 is not as unique. Here the <?php $filepath = $_GET["filepath"];
55 echo "<a href='CouplingsAndScales.php?filepath=".$filepath."' target='page'>";?>factorization
56 scale</a> has been chosen as the maximum evolution scale. This would be
57 the <i>pT</i> for a <i>2 -> 2</i> process, supplemented by mass terms
58 for massive outgoing particles. For some special applications we do allow
61 <br/><br/><table><tr><td><strong>TimeShower:pTmaxMatch </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
62 Way in which the maximum shower evolution scale is set to match the
63 scale of the hard process itself.
65 <input type="radio" name="1" value="0"><strong>0 </strong>: <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 doublecounting, while no such danger exists in the latter case. The argument is less compelling for timelike showers, but could be a reasonable starting point. <br/>
66 <input type="radio" name="1" value="1" checked="checked"><strong>1 </strong>: 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 doublecounting, but may leave out some emissions that ought to have been simulated. (Also known as wimpy showers.) <br/>
67 <input type="radio" name="1" value="2"><strong>2 </strong>: always allow emissions up to the kinematical limit (i.e. to half the dipole mass). This will simulate all possible event topologies, but may lead to doublecounting. (Also known as power showers.) <br/>
68 <br/><b>Note:</b> These options only apply to the hard interaction.
69 Emissions off subsequent multiparton interactions are always constrainted
70 to be below the factorization scale of the process itself. They also
71 assume you use interleaved evolution, so that FSR is in direct
72 competition with ISR for the hardest emission. If you already
73 generated a number of ISR partons at low <ei>pT</ei>, it would not
74 make sense to have a later FSR shower up to the kinematical for all
77 <br/><br/><table><tr><td><strong>TimeShower:pTmaxFudge </td><td></td><td> <input type="text" name="2" value="1.0" size="20"/> (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)</td></tr></table>
78 In cases where the above <code>pTmaxMatch</code> rules would imply
79 that <i>pT_max = pT_factorization</i>, <code>pTmaxFudge</code>
80 introduces a multiplicative factor <i>f</i> such that instead
81 <i>pT_max = f * pT_factorization</i>. Only applies to the hardest
82 interaction in an event, cf. below. It is strongly suggested that
83 <i>f = 1</i>, but variations around this default can be useful to
85 <br/><b>Note:</b>Scales for resonance decays are not affected, but can
86 be set separately by <?php $filepath = $_GET["filepath"];
87 echo "<a href='UserHooks.php?filepath=".$filepath."' target='page'>";?>user hooks</a>.
90 <br/><br/><table><tr><td><strong>TimeShower:pTmaxFudgeMPI </td><td></td><td> <input type="text" name="3" value="1.0" size="20"/> (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)</td></tr></table>
91 A multiplicative factor <i>f</i> such that
92 <i>pT_max = f * pT_factorization</i>, as above, but here for the
93 non-hardest interactions (when multiparton interactions are allowed).
96 <br/><br/><table><tr><td><strong>TimeShower:pTdampMatch </td><td> (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
97 These options only take effect when a process is allowed to radiate up
98 to the kinematical limit by the above <code>pTmaxMatch</code> choice,
99 and no matrix-element corrections are available. Then, in many processes,
100 the fall-off in <ei>pT</ei> will be too slow by one factor of <ei>pT^2</ei>.
101 That is, while showers have an approximate <ei>dpT^2/pT^2</ei> shape, often
102 it should become more like <ei>dpT^2/pT^4</ei> at <ei>pT</ei> values above
103 the scale of the hard process. This argument is more obvious for ISR,
104 but is taken over unchanged for FSR to have a symmetric description.
106 <input type="radio" name="4" value="0" checked="checked"><strong>0 </strong>: emissions go up to the kinematical limit, with no special dampening. <br/>
107 <input type="radio" name="4" value="1"><strong>1 </strong>: 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. <br/>
108 <input type="radio" name="4" value="2"><strong>2 </strong>: 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. <br/>
109 <br/><b>Note:</b> These options only apply to the hard interaction.
110 Emissions off subsequent multiparton interactions are always constrainted
111 to be below the factorization scale of the process itself.
113 <br/><br/><table><tr><td><strong>TimeShower:pTdampFudge </td><td></td><td> <input type="text" name="5" value="1.0" size="20"/> (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 4.0</code>)</td></tr></table>
114 In cases 1 and 2 above, where a dampening is imposed at around the
115 factorization or renormalization scale, respectively, this allows the
116 <i>pT</i> scale of dampening of radiation by a half to be shifted
117 by this factor relative to the default <i>Q_fac</i> or <i>Q_ren</i>.
118 This number ought to be in the neighbourhood of unity, but variations
119 away from this value could do better in some processes.
123 The amount of QCD radiation in the shower is determined by
124 <br/><br/><table><tr><td><strong>TimeShower:alphaSvalue </td><td></td><td> <input type="text" name="6" value="0.1383" size="20"/> (<code>default = <strong>0.1383</strong></code>; <code>minimum = 0.06</code>; <code>maximum = 0.25</code>)</td></tr></table>
125 The <i>alpha_strong</i> value at scale <i>M_Z^2</i>. The default
126 value corresponds to a crude tuning to LEP data, to be improved.
130 The actual value is then regulated by the running to the scale
131 <i>pT^2</i>, at which the shower evaluates <i>alpha_strong</i>.
133 <br/><br/><table><tr><td><strong>TimeShower:alphaSorder </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
134 Order at which <ei>alpha_strong</ei> runs,
136 <input type="radio" name="7" value="0"><strong>0 </strong>: zeroth order, i.e. <ei>alpha_strong</ei> is kept fixed.<br/>
137 <input type="radio" name="7" value="1" checked="checked"><strong>1 </strong>: first order, which is the normal value.<br/>
138 <input type="radio" name="7" value="2"><strong>2 </strong>: 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.<br/>
141 QED radiation is regulated by the <i>alpha_electromagnetic</i>
142 value at the <i>pT^2</i> scale of a branching.
144 <br/><br/><table><tr><td><strong>TimeShower:alphaEMorder </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = -1</code>; <code>maximum = 1</code>)</td></tr></table>
145 The running of <ei>alpha_em</ei>.
147 <input type="radio" name="8" value="1" checked="checked"><strong>1 </strong>: first-order running, constrained to agree with <code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass. <br/>
148 <input type="radio" name="8" value="0"><strong>0 </strong>: zeroth order, i.e. <ei>alpha_em</ei> is kept fixed at its value at vanishing momentum transfer.<br/>
149 <input type="radio" name="8" value="-1"><strong>-1 </strong>: 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. <br/>
152 The natural scale for couplings, and PDFs for dipoles stretching out
153 to the beam remnants, is <i>pT^2</i>. To explore uncertainties it
154 is possibly to vary around this value, however, in analogy with what
155 can be done for <?php $filepath = $_GET["filepath"];
156 echo "<a href='CouplingsAndScales.php?filepath=".$filepath."' target='page'>";?>hard processes</a>.
158 <br/><br/><table><tr><td><strong>TimeShower:renormMultFac </td><td></td><td> <input type="text" name="9" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)</td></tr></table>
159 The default <i>pT^2</i> renormalization scale is multiplied by
160 this prefactor. For QCD this is equivalent to a change of
161 <i>Lambda^2</i> in the opposite direction, i.e. to a change of
162 <i>alpha_strong(M_Z^2)</i> (except that flavour thresholds
163 remain at fixed scales).
166 <br/><br/><table><tr><td><strong>TimeShower:factorMultFac </td><td></td><td> <input type="text" name="10" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)</td></tr></table>
167 The default <i>pT^2</i> factorization scale is multiplied by
172 The rate of radiation if divergent in the <i>pT -> 0</i> limit. Here,
173 however, perturbation theory is expected to break down. Therefore an
174 effective <i>pT_min</i> cutoff parameter is introduced, below which
175 no emissions are allowed. The cutoff may be different for QCD and QED
176 radiation off quarks, and is mainly a technical parameter for QED
177 radiation off leptons.
179 <br/><br/><table><tr><td><strong>TimeShower:pTmin </td><td></td><td> <input type="text" name="11" value="0.4" size="20"/> (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)</td></tr></table>
180 Parton shower cut-off <i>pT</i> for QCD emissions.
183 <br/><br/><table><tr><td><strong>TimeShower:pTminChgQ </td><td></td><td> <input type="text" name="12" value="0.4" size="20"/> (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)</td></tr></table>
184 Parton shower cut-off <i>pT</i> for photon coupling to coloured particle.
187 <br/><br/><table><tr><td><strong>TimeShower:pTminChgL </td><td></td><td> <input type="text" name="13" value="0.0005" size="20"/> (<code>default = <strong>0.0005</strong></code>; <code>minimum = 0.0001</code>; <code>maximum = 2.0</code>)</td></tr></table>
188 Parton shower cut-off <i>pT</i> for pure QED branchings.
189 Assumed smaller than (or equal to) <code>pTminChgQ</code>.
193 Shower branchings <i>gamma -> f fbar</i>, where <i>f</i> is a
194 quark or lepton, in part compete with the hard processes involving
195 <i>gamma^*/Z^0</i> production. In order to avoid overlap it makes
196 sense to correlate the maximum <i>gamma</i> mass allowed in showers
197 with the minumum <i>gamma^*/Z^0</i> mass allowed in hard processes.
198 In addition, the shower contribution only contains the pure
199 <i>gamma^*</i> contribution, i.e. not the <i>Z^0</i> part, so
200 the mass spectrum above 50 GeV or so would not be well described.
202 <br/><br/><table><tr><td><strong>TimeShower:mMaxGamma </td><td></td><td> <input type="text" name="14" value="10.0" size="20"/> (<code>default = <strong>10.0</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 50.0</code>)</td></tr></table>
203 Maximum invariant mass allowed for the created fermion pair in a
204 <i>gamma -> f fbar</i> branching in the shower.
207 <h3>Interleaved evolution</h3>
209 Multiparton interactions (MPI) and initial-state showers (ISR) are
210 always interleaved, as follows. Starting from the hard interaction,
211 the complete event is constructed by a set of steps. In each step
212 the <i>pT</i> scale of the previous step is used as starting scale
213 for a downwards evolution. The MPI and ISR components each make
214 their respective Monte Carlo choices for the next lower <i>pT</i>
215 value. The one with larger <i>pT</i> is allowed to carry out its
216 proposed action, thereby modifying the conditions for the next steps.
217 This is relevant since the two components compete for the energy
218 contained in the beam remnants: both an interaction and an emission
219 take avay some of the energy, leaving less for the future. The end
220 result is a combined chain of decreasing <i>pT</i> values, where
221 ones associated with new interactions and ones with new emissions
225 There is no corresponding requirement for final-state radiation (FSR)
226 to be interleaved. Such an FSR emission does not compete directly for
227 beam energy (but see below), and also can be viewed as occuring after
228 the other two components in some kind of time sense. Interleaving is
229 allowed, however, since it can be argued that a high-<i>pT</i> FSR
230 occurs on shorter time scales than a low-<i>pT</i> MPI, say.
231 Backwards evolution of ISR is also an example that physical time
232 is not the only possible ordering principle, but that one can work
233 with conditional probabilities: given the partonic picture at a
234 specific <i>pT</i> resolution scale, what possibilities are open
235 for a modified picture at a slightly lower <i>pT</i> scale, either
236 by MPI, ISR or FSR? Complete interleaving of the three components also
237 offers advantages if one aims at matching to higher-order matrix
238 elements above some given scale.
240 <br/><br/><strong>TimeShower:interleave</strong> <input type="radio" name="15" value="on" checked="checked"><strong>On</strong>
241 <input type="radio" name="15" value="off"><strong>Off</strong>
242 (<code>default = <strong>on</strong></code>)<br/>
243 If on, final-state emissions are interleaved in the same
244 decreasing-<i>pT</i> chain as multiparton interactions and initial-state
245 emissions. If off, final-state emissions are only addressed after the
246 multiparton interactions and initial-state radiation have been considered.
250 As an aside, it should be noted that such interleaving does not affect
251 showering in resonance decays, such as a <i>Z^0</i>. These decays are
252 only introduced after the production process has been considered in full,
253 and the subsequent FSR is carried out inside the resonance, with
254 preserved resonance mass.
257 One aspect of FSR for a hard process in hadron collisions is that often
258 colour diples are formed between a scattered parton and a beam remnant,
259 or rather the hole left behind by an incoming partons. If such holes
260 are allowed as dipole ends and take the recoil when the scattered parton
261 undergoes a branching then this translates into the need to take some
262 amount of remnant energy also in the case of FSR, i.e. the roles of
263 ISR and FSR are not completely decoupled. The energy taken away is
264 bokkept by increasing the <i>x</i> value assigned to the incoming
265 scattering parton, and a reweighting factor
266 <i>x_new f(x_new, pT^2) / x_old f(x_old, pT^2)</i>
267 in the emission probability ensures that not unphysically large
268 <i>x_new</i> values are reached. Usually such <i>x</i> changes are
269 small, and they can be viewed as a higher-order effect beyond the
270 accuracy of the leading-log initial-state showers.
273 This choice is not unique, however. As an alternative, if nothing else
274 useful for cross-checks, one could imagine that the FSR is completely
275 decoupled from the ISR and beam remnants.
277 <br/><br/><strong>TimeShower:allowBeamRecoil</strong> <input type="radio" name="16" value="on" checked="checked"><strong>On</strong>
278 <input type="radio" name="16" value="off"><strong>Off</strong>
279 (<code>default = <strong>on</strong></code>)<br/>
280 If on, the final-state shower is allowed to borrow energy from
281 the beam remnants as described above, thereby changing the mass of the
282 scattering subsystem. If off, the partons in the scattering subsystem
283 are constrained to borrow energy from each other, such that the total
284 four-momentum of the system is preserved. This flag has no effect
285 on resonance decays, where the shower always preserves the resonance
286 mass, cf. the comment above about showers for resonances never being
290 <br/><br/><strong>TimeShower:dampenBeamRecoil</strong> <input type="radio" name="17" value="on" checked="checked"><strong>On</strong>
291 <input type="radio" name="17" value="off"><strong>Off</strong>
292 (<code>default = <strong>on</strong></code>)<br/>
293 When beam recoil is allowed there is still some ambiguity how far
294 into the beam end of the dipole that emission should be allowed.
295 It is dampened in the beam region, but probably not enough.
296 When on an additional suppression factor
297 <i>4 pT2_hard / (4 pT2_hard + m2)</i> is multiplied on to the
298 emission probability. Here <i>pT_hard</i> is the transverse momentum
299 of the radiating parton and <i>m</i> the off-shell mass it acquires
300 by the branching, <i>m2 = pT2/(z(1-z))</i>. Note that
301 <i>m2 = 4 pT2_hard</i> is the kinematical limit for a scattering
302 at 90 degrees without beam recoil.
305 <h3>Global recoil</h3>
307 The final-state algorithm is based on dipole-style recoils, where
308 one single parton takes the full recoil of a branching. This is unlike
309 the initial-state algorithm, where the complete already-existing
310 final state shares the recoil of each new emission. As an alternative,
311 also the final-state algorithm contains an option where the recoil
312 is shared between all partons in the final state. Thus the radiation
313 pattern is unrelated to colour correlations. This is especially
314 convenient for some matching algorithms, like MC@NLO, where a full
315 analytic knowledge of the shower radiation pattern is needed to avoid
316 doublecountning. (The <i>pT</i>-ordered shower is described in
317 [<a href="Bibliography.php" target="page">Sjo05</a>], and the corrections for massive radiator and recoiler
318 in [<a href="Bibliography.php" target="page">Nor01</a>].)
321 Technically, the radiation pattern is most conveniently represented
322 in the rest frame of the final state of the hard subprocess. Then, for
323 each parton at a time, the rest of the final state can be viewed as
324 a single effective parton. This "parton" has a fixed invariant mass
325 during the emission process, and takes the recoil without any changed
326 direction of motion. The momenta of the individual new recoilers are
327 then obtained by a simple common boost of the original ones.
330 This alternative approach will miss out on the colour coherence
331 phenomena. Specifically, with the whole subcollision mass as "dipole"
332 mass, the phase space for subsequent emissions is larger than for
333 the normal dipole algorithm. The phase space difference grows as
334 more and more gluons are created, and thus leads to a way too steep
335 multiplication of soft gluons. Therefore the main application is
336 for the first one or few emissions of the shower, where a potential
337 overestimate of the emission rate is to be corrected for anyway,
338 by matching to the relevant matrix elements. Thereafter, subsequent
339 emissions should be handled as before, i.e. with dipoles spanned
340 between nearby partons. Furthermore, only the first (hardest)
341 subcollision is handled with global recoils, since subsequent MPI's
342 would not be subject to matrix element corrections anyway.
345 In order for the mid-shower switch from global to local recoils
346 to work, colours are traced and bookkept just as for normal showers;
347 it is only that this information is not used in those steps where
348 a global recoil is requested. (Thus, e.g., a gluon is still bookkept
349 as one colour and one anticolour dipole end, with half the charge
350 each, but with global recoil those two ends radiate identically.)
352 <br/><br/><strong>TimeShower:globalRecoil</strong> <input type="radio" name="18" value="on"><strong>On</strong>
353 <input type="radio" name="18" value="off" checked="checked"><strong>Off</strong>
354 (<code>default = <strong>off</strong></code>)<br/>
355 Alternative approach as above, where all final-state particles share
356 the recoil of an emission.
357 <br/>If off, then use the standard dipole-recoil approach.
358 <br/>If on, use the alternative global recoil, but only for the first
359 interaction, and only while the number of particles in the final state
360 is at most <code>TimeShower:nMaxGlobalRecoil</code> before the
364 <br/><br/><table><tr><td><strong>TimeShower:nMaxGlobalRecoil </td><td></td><td> <input type="text" name="19" value="2" size="20"/> (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>)</td></tr></table>
365 Represents the maximum number of particles in the final state for which
366 the next final-state emission can be performed with the global recoil
367 strategy. This number counts all particles, whether they are
368 allowed to radiate or not, e.g. also <i>Z^0</i>. Also partons
369 created by initial-state radiation emissions counts towards this sum,
370 as part of the interleaved evolution. Without interleaved evolution
371 this option would not make sense, since then a varying and large
372 number of partons could already have been created by the initial-state
373 radiation before the first final-state one, and then there is not
374 likely to be any matrix elements available for matching.
378 The global-recoil machinery does not work well with rescattering in the
379 MPI machinery, since then the recoiling system is not uniquely defined.
380 <code>MultipartonInteractions:allowRescatter = off</code> by default,
381 so this is not a main issue. If both options are switched on,
382 rescattering will only be allowed to kick in after the global recoil
383 has ceased to be active, i.e. once the <code>nMaxGlobalRecoil</code>
384 limit has been exceeded. This should not be a major conflict,
385 since rescattering is mainly of interest at later stages of the
386 downwards <i>pT</i> evolution.
389 Further, it is strongly recommended to set
390 <code>TimeShower:MEcorrections = off</code> (not default!), i.e. not
391 to correct the emission probability to the internal matrix elements.
392 The internal ME options do not cover any cases relevant for a multibody
393 recoiler anyway, so no guarantees are given what prescription would
394 come to be used. Instead, without ME corrections, a process-independent
395 emission rate is obtained, and <?php $filepath = $_GET["filepath"];
396 echo "<a href='UserHooks.php?filepath=".$filepath."' target='page'>";?>user hooks</a>
397 can provide the desired process-specific rejection factors.
399 <h3>Radiation off octet onium states</h3>
401 In the current implementation, charmonium and bottomonium production
402 can proceed either through colour singlet or colour octet mechanisms,
403 both of them implemented in terms of <i>2 -> 2</i> hard processes
404 such as <i>g g -> (onium) g</i>.
405 In the former case the state does not radiate and the onium therefore
406 is produced in isolation, up to normal underlying-event activity. In
407 the latter case the situation is not so clear, but it is sensible to
408 assume that a shower can evolve. (Assuming, of course, that the
409 transverse momentum of the onium state is sufficiently high that
410 radiation is of relevance.)
413 There could be two parts to such a shower. Firstly a gluon (or even a
414 quark, though less likely) produced in a hard <i>2 -> 2</i> process
415 can undergo showering into many gluons, whereof one branches into the
416 heavy-quark pair. Secondly, once the pair has been produced, each quark
417 can radiate further gluons. This latter kind of emission could easily
418 break up a semibound quark pair, but might also create a new semibound
419 state where before an unbound pair existed, and to some approximation
420 these two effects should balance in the onium production rate.
421 The showering "off an onium state" as implemented here therefore should
422 not be viewed as an accurate description of the emission history
423 step by step, but rather as an effective approach to ensure that the
424 octet onium produced "in the hard process" is embedded in a realistic
425 amount of jet activity.
426 Of course both the isolated singlet and embedded octet are likely to
427 be extremes, but hopefully the mix of the two will strike a reasonable
428 balance. However, it is possible that some part of the octet production
429 occurs in channels where it should not be accompanied by (hard) radiation.
430 Therefore reducing the fraction of octet onium states allowed to radiate
431 is a valid variation to explore uncertainties.
434 If an octet onium state is chosen to radiate, the simulation of branchings
435 is based on the assumption that the full radiation is provided by an
436 incoherent sum of radiation off the quark and off the antiquark of the
437 onium state. Thus the splitting kernel is taken to be the normal
438 <i>q -> q g</i> one, multiplied by a factor of two. Obviously this is
439 a simplification of a more complex picture, averaging over factors pulling
440 in different directions. Firstly, radiation off a gluon ought
441 to be enhanced by a factor 9/4 relative to a quark rather than the 2
442 now used, but this is a minor difference. Secondly, our use of the
443 <i>q -> q g</i> branching kernel is roughly equivalent to always
444 following the harder gluon in a <i>g -> g g</i> branching. This could
445 give us a bias towards producing too hard onia. A soft gluon would have
446 little phase space to branch into a heavy-quark pair however, so the
447 bias may not be as big as it would seem at first glance. Thirdly,
448 once the gluon has branched into a quark pair, each quark carries roughly
449 only half of the onium energy. The maximum energy per emitted gluon should
450 then be roughly half the onium energy rather than the full, as it is now.
451 Thereby the energy of radiated gluons is exaggerated, i.e. onia become too
452 soft. So the second and the third points tend to cancel each other.
455 Finally, note that the lower cutoff scale of the shower evolution depends
456 on the onium mass rather than on the quark mass, as it should be. Gluons
457 below the octet-onium scale should only be part of the octet-to-singlet
460 <br/><br/><table><tr><td><strong>TimeShower:octetOniumFraction </td><td></td><td> <input type="text" name="20" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)</td></tr></table>
461 Allow colour-octet charmonium and bottomonium states to radiate gluons.
462 0 means that no octet-onium states radiate, 1 that all do, with possibility
463 to interpolate between these two extremes.
466 <br/><br/><table><tr><td><strong>TimeShower:octetOniumColFac </td><td></td><td> <input type="text" name="21" value="2." size="20"/> (<code>default = <strong>2.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 4.</code>)</td></tr></table>
467 The colour factor used used in the splitting kernel for those octet onium
468 states that are allowed to radiate, normalized to the <i>q -> q g</i>
469 splitting kernel. Thus the default corresponds to twice the radiation
470 off a quark. The physically preferred range would be between 1 and 9/4.
473 <h3>Further variables</h3>
475 There are several possibilities you can use to switch on or off selected
476 branching types in the shower, or in other respects simplify the shower.
477 These should normally not be touched. Their main function is for
480 <br/><br/><strong>TimeShower:QCDshower</strong> <input type="radio" name="22" value="on" checked="checked"><strong>On</strong>
481 <input type="radio" name="22" value="off"><strong>Off</strong>
482 (<code>default = <strong>on</strong></code>)<br/>
483 Allow a QCD shower, i.e. branchings <i>q -> q g</i>, <i>g -> g g</i>
484 and <i>g -> q qbar</i>; on/off = true/false.
487 <br/><br/><table><tr><td><strong>TimeShower:nGluonToQuark </td><td></td><td> <input type="text" name="23" value="5" size="20"/> (<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)</td></tr></table>
488 Number of allowed quark flavours in <i>g -> q qbar</i> branchings
489 (phase space permitting). A change to 4 would exclude
490 <i>g -> b bbar</i>, etc.
493 <br/><br/><strong>TimeShower:QEDshowerByQ</strong> <input type="radio" name="24" value="on" checked="checked"><strong>On</strong>
494 <input type="radio" name="24" value="off"><strong>Off</strong>
495 (<code>default = <strong>on</strong></code>)<br/>
496 Allow quarks to radiate photons, i.e. branchings <i>q -> q gamma</i>;
500 <br/><br/><strong>TimeShower:QEDshowerByL</strong> <input type="radio" name="25" value="on" checked="checked"><strong>On</strong>
501 <input type="radio" name="25" value="off"><strong>Off</strong>
502 (<code>default = <strong>on</strong></code>)<br/>
503 Allow leptons to radiate photons, i.e. branchings <i>l -> l gamma</i>;
507 <br/><br/><strong>TimeShower:QEDshowerByGamma</strong> <input type="radio" name="26" value="on" checked="checked"><strong>On</strong>
508 <input type="radio" name="26" value="off"><strong>Off</strong>
509 (<code>default = <strong>on</strong></code>)<br/>
510 Allow photons to branch into lepton or quark pairs, i.e. branchings
511 <i>gamma -> l+ l-</i> and <i>gamma -> q qbar</i>;
515 <br/><br/><table><tr><td><strong>TimeShower:nGammaToQuark </td><td></td><td> <input type="text" name="27" value="5" size="20"/> (<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)</td></tr></table>
516 Number of allowed quark flavours in <i>gamma -> q qbar</i> branchings
517 (phase space permitting). A change to 4 would exclude
518 <i>g -> b bbar</i>, etc.
521 <br/><br/><table><tr><td><strong>TimeShower:nGammaToLepton </td><td></td><td> <input type="text" name="28" value="3" size="20"/> (<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)</td></tr></table>
522 Number of allowed lepton flavours in <i>gamma -> l+ l-</i> branchings
523 (phase space permitting). A change to 2 would exclude
524 <i>gamma -> tau+ tau-</i>, and a change to 1 also
525 <i>gamma -> mu+ mu-</i>.
528 <br/><br/><strong>TimeShower:MEcorrections</strong> <input type="radio" name="29" value="on" checked="checked"><strong>On</strong>
529 <input type="radio" name="29" value="off"><strong>Off</strong>
530 (<code>default = <strong>on</strong></code>)<br/>
531 Use of matrix element corrections where available; on/off = true/false.
534 <br/><br/><strong>TimeShower:MEafterFirst</strong> <input type="radio" name="30" value="on" checked="checked"><strong>On</strong>
535 <input type="radio" name="30" value="off"><strong>Off</strong>
536 (<code>default = <strong>on</strong></code>)<br/>
537 Use of matrix element corrections also after the first emission,
538 for dipole ends of the same system that did not yet radiate.
539 Only has a meaning if <code>MEcorrections</code> above is
543 <br/><br/><strong>TimeShower:phiPolAsym</strong> <input type="radio" name="31" value="on" checked="checked"><strong>On</strong>
544 <input type="radio" name="31" value="off"><strong>Off</strong>
545 (<code>default = <strong>on</strong></code>)<br/>
546 Azimuthal asymmetry induced by gluon polarization; on/off = true/false.
549 <br/><br/><strong>TimeShower:recoilToColoured</strong> <input type="radio" name="32" value="on" checked="checked"><strong>On</strong>
550 <input type="radio" name="32" value="off"><strong>Off</strong>
551 (<code>default = <strong>on</strong></code>)<br/>
552 In the decays of coloured resonances, say <i>t -> b W</i>, it is not
553 possible to set up dipoles with matched colours. Originally the
554 <i>b</i> radiator therefore has <i>W</i> as recoiler, and that
555 choice is unique. Once a gluon has been radiated, however, it is
556 possible either to have the unmatched colour (inherited by the gluon)
557 still recoiling against the <i>W</i> (<code>off</code>), or else
558 let it recoil against the <i>b</i> also for this dipole
559 (<code>on</code>). Before version 8.160 the former was the only
560 possibility, which could give unphysical radiation patterns. It is
561 kept as an option to check backwards compatibility. The same issue
562 exists for QED radiation, but obviously is less significant. Consider
563 the example <i>W -> e nu</i>, where originally the <i>nu</i>
564 takes the recoil. In the old (<code>off</code>) scheme the <i>nu</i>
565 would remain recoiler, while in the new (<code>on</code>) instead
566 each newly emitted photon becomes the new recoiler.
569 <input type="hidden" name="saved" value="1"/>
572 echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
574 <table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
579 if($_POST["saved"] == 1)
581 $filepath = $_POST["filepath"];
582 $handle = fopen($filepath, 'a');
584 if($_POST["1"] != "1")
586 $data = "TimeShower:pTmaxMatch = ".$_POST["1"]."\n";
587 fwrite($handle,$data);
589 if($_POST["2"] != "1.0")
591 $data = "TimeShower:pTmaxFudge = ".$_POST["2"]."\n";
592 fwrite($handle,$data);
594 if($_POST["3"] != "1.0")
596 $data = "TimeShower:pTmaxFudgeMPI = ".$_POST["3"]."\n";
597 fwrite($handle,$data);
599 if($_POST["4"] != "0")
601 $data = "TimeShower:pTdampMatch = ".$_POST["4"]."\n";
602 fwrite($handle,$data);
604 if($_POST["5"] != "1.0")
606 $data = "TimeShower:pTdampFudge = ".$_POST["5"]."\n";
607 fwrite($handle,$data);
609 if($_POST["6"] != "0.1383")
611 $data = "TimeShower:alphaSvalue = ".$_POST["6"]."\n";
612 fwrite($handle,$data);
614 if($_POST["7"] != "1")
616 $data = "TimeShower:alphaSorder = ".$_POST["7"]."\n";
617 fwrite($handle,$data);
619 if($_POST["8"] != "1")
621 $data = "TimeShower:alphaEMorder = ".$_POST["8"]."\n";
622 fwrite($handle,$data);
624 if($_POST["9"] != "1.")
626 $data = "TimeShower:renormMultFac = ".$_POST["9"]."\n";
627 fwrite($handle,$data);
629 if($_POST["10"] != "1.")
631 $data = "TimeShower:factorMultFac = ".$_POST["10"]."\n";
632 fwrite($handle,$data);
634 if($_POST["11"] != "0.4")
636 $data = "TimeShower:pTmin = ".$_POST["11"]."\n";
637 fwrite($handle,$data);
639 if($_POST["12"] != "0.4")
641 $data = "TimeShower:pTminChgQ = ".$_POST["12"]."\n";
642 fwrite($handle,$data);
644 if($_POST["13"] != "0.0005")
646 $data = "TimeShower:pTminChgL = ".$_POST["13"]."\n";
647 fwrite($handle,$data);
649 if($_POST["14"] != "10.0")
651 $data = "TimeShower:mMaxGamma = ".$_POST["14"]."\n";
652 fwrite($handle,$data);
654 if($_POST["15"] != "on")
656 $data = "TimeShower:interleave = ".$_POST["15"]."\n";
657 fwrite($handle,$data);
659 if($_POST["16"] != "on")
661 $data = "TimeShower:allowBeamRecoil = ".$_POST["16"]."\n";
662 fwrite($handle,$data);
664 if($_POST["17"] != "on")
666 $data = "TimeShower:dampenBeamRecoil = ".$_POST["17"]."\n";
667 fwrite($handle,$data);
669 if($_POST["18"] != "off")
671 $data = "TimeShower:globalRecoil = ".$_POST["18"]."\n";
672 fwrite($handle,$data);
674 if($_POST["19"] != "2")
676 $data = "TimeShower:nMaxGlobalRecoil = ".$_POST["19"]."\n";
677 fwrite($handle,$data);
679 if($_POST["20"] != "1.")
681 $data = "TimeShower:octetOniumFraction = ".$_POST["20"]."\n";
682 fwrite($handle,$data);
684 if($_POST["21"] != "2.")
686 $data = "TimeShower:octetOniumColFac = ".$_POST["21"]."\n";
687 fwrite($handle,$data);
689 if($_POST["22"] != "on")
691 $data = "TimeShower:QCDshower = ".$_POST["22"]."\n";
692 fwrite($handle,$data);
694 if($_POST["23"] != "5")
696 $data = "TimeShower:nGluonToQuark = ".$_POST["23"]."\n";
697 fwrite($handle,$data);
699 if($_POST["24"] != "on")
701 $data = "TimeShower:QEDshowerByQ = ".$_POST["24"]."\n";
702 fwrite($handle,$data);
704 if($_POST["25"] != "on")
706 $data = "TimeShower:QEDshowerByL = ".$_POST["25"]."\n";
707 fwrite($handle,$data);
709 if($_POST["26"] != "on")
711 $data = "TimeShower:QEDshowerByGamma = ".$_POST["26"]."\n";
712 fwrite($handle,$data);
714 if($_POST["27"] != "5")
716 $data = "TimeShower:nGammaToQuark = ".$_POST["27"]."\n";
717 fwrite($handle,$data);
719 if($_POST["28"] != "3")
721 $data = "TimeShower:nGammaToLepton = ".$_POST["28"]."\n";
722 fwrite($handle,$data);
724 if($_POST["29"] != "on")
726 $data = "TimeShower:MEcorrections = ".$_POST["29"]."\n";
727 fwrite($handle,$data);
729 if($_POST["30"] != "on")
731 $data = "TimeShower:MEafterFirst = ".$_POST["30"]."\n";
732 fwrite($handle,$data);
734 if($_POST["31"] != "on")
736 $data = "TimeShower:phiPolAsym = ".$_POST["31"]."\n";
737 fwrite($handle,$data);
739 if($_POST["32"] != "on")
741 $data = "TimeShower:recoilToColoured = ".$_POST["32"]."\n";
742 fwrite($handle,$data);
751 <!-- Copyright (C) 2012 Torbjorn Sjostrand -->