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c6b60c38 | 1 | <chapter name="Timelike Showers"> |
2 | ||
3 | <h2>Timelike Showers</h2> | |
4 | ||
5 | The PYTHIA algorithm for timelike final-state showers is based on | |
6 | the article <ref>Sjo05</ref>, where a transverse-momentum-ordered | |
7 | evolution scheme is introduced, with the extension to fully interleaved | |
8 | evolution covered in <ref>Cor10a</ref>. This algorithm is influenced by | |
9 | the previous mass-ordered algorithm in PYTHIA <ref>Ben87</ref> and by | |
10 | the dipole-emission formulation in Ariadne <ref>Gus86</ref>. From the | |
11 | mass-ordered algorithm it inherits a merging procedure for first-order | |
12 | gluon-emission matrix elements in essentially all two-body decays | |
13 | in the standard model and its minimal supersymmetric extension | |
14 | <ref>Nor01</ref>. | |
15 | ||
16 | <p/> | |
17 | The normal user is not expected to call <code>TimeShower</code> directly, | |
18 | but only have it called from <code>Pythia</code>. Some of the parameters | |
19 | below, in particular <code>TimeShower:alphaSvalue</code>, would be of | |
20 | interest for a tuning exercise, however. | |
21 | ||
22 | <h3>Main variables</h3> | |
23 | ||
24 | Often the maximum scale of the FSR shower evolution is understood from the | |
25 | context. For instance, in a resonance decay half the resonance mass sets an | |
26 | absolute upper limit. For a hard process in a hadronic collision the choice | |
27 | is not as unique. Here the <aloc href="CouplingsAndScales">factorization | |
28 | scale</aloc> has been chosen as the maximum evolution scale. This would be | |
29 | the <ei>pT</ei> for a <ei>2 -> 2</ei> process, supplemented by mass terms | |
30 | for massive outgoing particles. For some special applications we do allow | |
31 | an alternative. | |
32 | ||
33 | <modepick name="TimeShower:pTmaxMatch" default="1" min="0" max="2"> | |
34 | Way in which the maximum shower evolution scale is set to match the | |
35 | scale of the hard process itself. | |
36 | <option value="0"><b>(i)</b> if the final state of the hard process | |
37 | (not counting subsequent resonance decays) contains at least one quark | |
38 | (<ei>u, d, s, c ,b</ei>), gluon or photon then <ei>pT_max</ei> | |
39 | is chosen to be the factorization scale for internal processes | |
40 | and the <code>scale</code> value for Les Houches input; | |
41 | <b>(ii)</b> if not, emissions are allowed to go all the way up to | |
42 | the kinematical limit (i.e. to half the dipole mass). | |
43 | This option agrees with the corresponding one for | |
44 | <aloc href="SpacelikeShowers">spacelike showers</aloc>. There the | |
45 | reasoning is that in the former set of processes the ISR | |
46 | emission of yet another quark, gluon or photon could lead to | |
47 | double-counting, while no such danger exists in the latter case. | |
48 | The argument is less compelling for timelike showers, but could | |
49 | be a reasonable starting point. | |
50 | </option> | |
51 | <option value="1">always use the factorization scale for an internal | |
52 | process and the <code>scale</code> value for Les Houches input, | |
53 | i.e. the lower value. This should avoid double-counting, but | |
54 | may leave out some emissions that ought to have been simulated. | |
55 | (Also known as wimpy showers.) | |
56 | </option> | |
57 | <option value="2">always allow emissions up to the kinematical limit | |
58 | (i.e. to half the dipole mass). This will simulate all possible event | |
59 | topologies, but may lead to double-counting. | |
60 | (Also known as power showers.) | |
61 | </option> | |
62 | <note>Note 1:</note> as enumerated in the text, these options take effect | |
63 | both for internal and external processes. Whether a particular option | |
64 | makes sense depends on the context. For instance, if events for the same | |
65 | basic process to different orders are to be matched, then option 1 would | |
66 | be a reasonable first guess. But in more sophisticated descriptions | |
67 | option 2 could be combined with UserHook vetoes on emissions that would | |
68 | lead to double-counting, using more flexible phase space boundaries. | |
69 | Option 0, finally, may be most realistic when only Born-level processes | |
70 | are involved, possibly in combination with a nonzero | |
71 | <code>TimeShower:pTdampMatch</code>. | |
72 | <note>Note 2:</note> These options only apply to the hard interaction. | |
73 | If a "second hard" process is present, the two are analyzed and | |
74 | set separately for the default 0 option, while both are affected | |
75 | the same way for non-default options 1 and 2. | |
76 | Emissions off subsequent multiparton interactions are always constrained | |
77 | to be below the factorization scale of each process itself. The options | |
78 | also assume that you use interleaved evolution, so that FSR is in direct | |
79 | competition with ISR for the hardest emission. If you already | |
80 | generated a number of ISR partons at low <ei>pT</ei>, it would not | |
81 | make sense to have a later FSR shower up to the kinematical limit | |
82 | for all of them. | |
83 | <note>Note 3:</note> Recall that resonance decays are not affected by | |
84 | this mode, but that showers there are always set to fill the full phase | |
85 | space, often with built-in matrix-element-matching that give a NLO | |
86 | accuracy. A modification of this behaviour would require you to | |
87 | work with <code>UserHooks</code>. | |
88 | </modepick> | |
89 | ||
90 | <parm name="TimeShower:pTmaxFudge" default="1.0" min="0.25" max="2.0"> | |
91 | In cases where the above <code>pTmaxMatch</code> rules would imply | |
92 | that <ei>pT_max = pT_factorization</ei>, <code>pTmaxFudge</code> | |
93 | introduces a multiplicative factor <ei>f</ei> such that instead | |
94 | <ei>pT_max = f * pT_factorization</ei>. Only applies to the hardest | |
95 | interaction in an event, and a "second hard" if there is such a one, | |
96 | cf. below. It is strongly suggested that <ei>f = 1</ei>, but variations | |
97 | around this default can be useful to test this assumption. | |
98 | <note>Note:</note>Scales for resonance decays are not affected, but can | |
99 | be set separately by <aloc href="UserHooks">user hooks</aloc>. | |
100 | </parm> | |
101 | ||
102 | <parm name="TimeShower:pTmaxFudgeMPI" default="1.0" min="0.25" max="2.0"> | |
103 | A multiplicative factor <ei>f</ei> such that | |
104 | <ei>pT_max = f * pT_factorization</ei>, as above, but here for the | |
105 | non-hardest interactions (when multiparton interactions are allowed). | |
106 | </parm> | |
107 | ||
108 | <modepick name="TimeShower:pTdampMatch" default="0" min="0" max="2"> | |
109 | These options only take effect when a process is allowed to radiate up | |
110 | to the kinematical limit by the above <code>pTmaxMatch</code> choice, | |
111 | and no matrix-element corrections are available. Then, in many processes, | |
112 | the fall-off in <ei>pT</ei> will be too slow by one factor of <ei>pT^2</ei>. | |
113 | That is, while showers have an approximate <ei>dpT^2/pT^2</ei> shape, often | |
114 | it should become more like <ei>dpT^2/pT^4</ei> at <ei>pT</ei> values above | |
115 | the scale of the hard process. This argument is more obvious and relevant | |
116 | for ISR, where emissions could go the the kinematical limit, whereas they | |
117 | are constrained by the respective dipole mass for FSR. Nevertheless this | |
118 | matching option is offered for FSR to have a (semi-)symmetric description. | |
119 | Note that a dampening factor is applied to all dipoles in the final state | |
120 | of the hard process, which is somewhat different from the ISR implementation. | |
121 | <option value="0">emissions go up to the kinematical limit, | |
122 | with no special dampening. | |
123 | </option> | |
124 | <option value="1">emissions go up to the kinematical limit, | |
125 | but dampened by a factor <ei>k^2 Q^2_fac/(pT^2 + k^2 Q^2_fac)</ei>, | |
126 | where <ei>Q_fac</ei> is the factorization scale and <ei>k</ei> is a | |
127 | multiplicative fudge factor stored in <code>pTdampFudge</code> below. | |
128 | </option> | |
129 | <option value="2">emissions go up to the kinematical limit, | |
130 | but dampened by a factor <ei>k^2 Q^2_ren/(pT^2 + k^2 Q^2_ren)</ei>, | |
131 | where <ei>Q_ren</ei> is the renormalization scale and <ei>k</ei> is a | |
132 | multiplicative fudge factor stored in <code>pTdampFudge</code> below. | |
133 | </option> | |
134 | <note>Note:</note> These options only apply to the hard interaction. | |
135 | Specifically, a "second hard" interaction would not be affected. | |
136 | Emissions off subsequent multiparton interactions are always constrained | |
137 | to be below the factorization scale of the process itself. | |
138 | </modepick> | |
139 | ||
140 | <parm name="TimeShower:pTdampFudge" default="1.0" min="0.25" max="4.0"> | |
141 | In cases 1 and 2 above, where a dampening is imposed at around the | |
142 | factorization or renormalization scale, respectively, this allows the | |
143 | <ei>pT</ei> scale of dampening of radiation by a half to be shifted | |
144 | by this factor relative to the default <ei>Q_fac</ei> or <ei>Q_ren</ei>. | |
145 | This number ought to be in the neighbourhood of unity, but variations | |
146 | away from this value could do better in some processes. | |
147 | </parm> | |
148 | ||
149 | <p/> | |
150 | The amount of QCD radiation in the shower is determined by | |
151 | <parm name="TimeShower:alphaSvalue" default="0.1383" | |
152 | min="0.06" max="0.25"> | |
153 | The <ei>alpha_strong</ei> value at scale <ei>M_Z^2</ei>. The default | |
154 | value corresponds to a crude tuning to LEP data, to be improved. | |
155 | </parm> | |
156 | ||
157 | <p/> | |
158 | The actual value is then regulated by the running to the scale | |
159 | <ei>pT^2</ei>, at which the shower evaluates <ei>alpha_strong</ei>. | |
160 | ||
161 | <modepick name="TimeShower:alphaSorder" default="1" min="0" max="2"> | |
162 | Order at which <ei>alpha_strong</ei> runs, | |
163 | <option value="0">zeroth order, i.e. <ei>alpha_strong</ei> is kept | |
164 | fixed.</option> | |
165 | <option value="1">first order, which is the normal value.</option> | |
166 | <option value="2">second order. Since other parts of the code do | |
167 | not go to second order there is no strong reason to use this option, | |
168 | but there is also nothing wrong with it.</option> | |
169 | </modepick> | |
170 | ||
171 | <p/> | |
172 | QED radiation is regulated by the <ei>alpha_electromagnetic</ei> | |
173 | value at the <ei>pT^2</ei> scale of a branching. | |
174 | ||
175 | <modepick name="TimeShower:alphaEMorder" default="1" min="-1" max="1"> | |
176 | The running of <ei>alpha_em</ei>. | |
177 | <option value="1">first-order running, constrained to agree with | |
178 | <code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass. | |
179 | </option> | |
180 | <option value="0">zeroth order, i.e. <ei>alpha_em</ei> is kept | |
181 | fixed at its value at vanishing momentum transfer.</option> | |
182 | <option value="-1">zeroth order, i.e. <ei>alpha_em</ei> is kept | |
183 | fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value | |
184 | at the <ei>Z^0</ei> mass. | |
185 | </option> | |
186 | </modepick> | |
187 | ||
188 | <p/> | |
189 | The natural scale for couplings, and PDFs for dipoles stretching out | |
190 | to the beam remnants, is <ei>pT^2</ei>. To explore uncertainties it | |
191 | is possibly to vary around this value, however, in analogy with what | |
192 | can be done for <aloc href="CouplingsAndScales">hard processes</aloc>. | |
193 | ||
194 | <parm name="TimeShower:renormMultFac" default="1." min="0.1" max="10."> | |
195 | The default <ei>pT^2</ei> renormalization scale is multiplied by | |
196 | this prefactor. For QCD this is equivalent to a change of | |
197 | <ei>Lambda^2</ei> in the opposite direction, i.e. to a change of | |
198 | <ei>alpha_strong(M_Z^2)</ei> (except that flavour thresholds | |
199 | remain at fixed scales). | |
200 | </parm> | |
201 | ||
202 | <parm name="TimeShower:factorMultFac" default="1." min="0.1" max="10."> | |
203 | The default <ei>pT^2</ei> factorization scale is multiplied by | |
204 | this prefactor. | |
205 | </parm> | |
206 | ||
207 | <p/> | |
208 | The rate of radiation if divergent in the <ei>pT -> 0</ei> limit. Here, | |
209 | however, perturbation theory is expected to break down. Therefore an | |
210 | effective <ei>pT_min</ei> cutoff parameter is introduced, below which | |
211 | no emissions are allowed. The cutoff may be different for QCD and QED | |
212 | radiation off quarks, and is mainly a technical parameter for QED | |
213 | radiation off leptons. | |
214 | ||
215 | <parm name="TimeShower:pTmin" default="0.4" min="0.1" max="2.0"> | |
216 | Parton shower cut-off <ei>pT</ei> for QCD emissions. | |
217 | </parm> | |
218 | ||
219 | <parm name="TimeShower:pTminChgQ" default="0.4" min="0.1" max="2.0"> | |
220 | Parton shower cut-off <ei>pT</ei> for photon coupling to coloured particle. | |
221 | </parm> | |
222 | ||
223 | <parm name="TimeShower:pTminChgL" default="1e-6" min="1e-10" max="2.0"> | |
224 | Parton shower cut-off <ei>pT</ei> for pure QED branchings. | |
225 | Assumed smaller than (or equal to) <code>pTminChgQ</code>. | |
226 | </parm> | |
227 | ||
228 | <p/> | |
229 | Shower branchings <ei>gamma -> f fbar</ei>, where <ei>f</ei> is a | |
230 | quark or lepton, in part compete with the hard processes involving | |
231 | <ei>gamma^*/Z^0</ei> production. In order to avoid overlap it makes | |
232 | sense to correlate the maximum <ei>gamma</ei> mass allowed in showers | |
233 | with the minimum <ei>gamma^*/Z^0</ei> mass allowed in hard processes. | |
234 | In addition, the shower contribution only contains the pure | |
235 | <ei>gamma^*</ei> contribution, i.e. not the <ei>Z^0</ei> part, so | |
236 | the mass spectrum above 50 GeV or so would not be well described. | |
237 | ||
238 | <parm name="TimeShower:mMaxGamma" default="10.0" min="0.001" | |
239 | max="50.0"> | |
240 | Maximum invariant mass allowed for the created fermion pair in a | |
241 | <ei>gamma -> f fbar</ei> branching in the shower. | |
242 | </parm> | |
243 | ||
244 | <h3>Interleaved evolution</h3> | |
245 | ||
246 | Multiparton interactions (MPI) and initial-state showers (ISR) are | |
247 | always interleaved, as follows. Starting from the hard interaction, | |
248 | the complete event is constructed by a set of steps. In each step | |
249 | the <ei>pT</ei> scale of the previous step is used as starting scale | |
250 | for a downwards evolution. The MPI and ISR components each make | |
251 | their respective Monte Carlo choices for the next lower <ei>pT</ei> | |
252 | value. The one with larger <ei>pT</ei> is allowed to carry out its | |
253 | proposed action, thereby modifying the conditions for the next steps. | |
254 | This is relevant since the two components compete for the energy | |
255 | contained in the beam remnants: both an interaction and an emission | |
256 | take away some of the energy, leaving less for the future. The end | |
257 | result is a combined chain of decreasing <ei>pT</ei> values, where | |
258 | ones associated with new interactions and ones with new emissions | |
259 | are interleaved. | |
260 | ||
261 | <p/> | |
262 | There is no corresponding requirement for final-state radiation (FSR) | |
263 | to be interleaved. Such an FSR emission does not compete directly for | |
264 | beam energy (but see below), and also can be viewed as occurring after | |
265 | the other two components in some kind of time sense. Interleaving is | |
266 | allowed, however, since it can be argued that a high-<ei>pT</ei> FSR | |
267 | occurs on shorter time scales than a low-<ei>pT</ei> MPI, say. | |
268 | Backwards evolution of ISR is also an example that physical time | |
269 | is not the only possible ordering principle, but that one can work | |
270 | with conditional probabilities: given the partonic picture at a | |
271 | specific <ei>pT</ei> resolution scale, what possibilities are open | |
272 | for a modified picture at a slightly lower <ei>pT</ei> scale, either | |
273 | by MPI, ISR or FSR? Complete interleaving of the three components also | |
274 | offers advantages if one aims at matching to higher-order matrix | |
275 | elements above some given scale. | |
276 | ||
277 | <flag name="TimeShower:interleave" default="on"> | |
278 | If on, final-state emissions are interleaved in the same | |
279 | decreasing-<ei>pT</ei> chain as multiparton interactions and initial-state | |
280 | emissions. If off, final-state emissions are only addressed after the | |
281 | multiparton interactions and initial-state radiation have been considered. | |
282 | </flag> | |
283 | ||
284 | <p/> | |
285 | As an aside, it should be noted that such interleaving does not affect | |
286 | showering in resonance decays, such as a <ei>Z^0</ei>. These decays are | |
287 | only introduced after the production process has been considered in full, | |
288 | and the subsequent FSR is carried out inside the resonance, with | |
289 | preserved resonance mass. | |
290 | ||
291 | <p/> | |
292 | One aspect of FSR for a hard process in hadron collisions is that often | |
293 | colour dipoles are formed between a scattered parton and a beam remnant, | |
294 | or rather the hole left behind by an incoming partons. If such holes | |
295 | are allowed as dipole ends and take the recoil when the scattered parton | |
296 | undergoes a branching then this translates into the need to take some | |
297 | amount of remnant energy also in the case of FSR, i.e. the roles of | |
298 | ISR and FSR are not completely decoupled. The energy taken away is | |
299 | bookkept by increasing the <ei>x</ei> value assigned to the incoming | |
300 | scattering parton, and a reweighting factor | |
301 | <ei>x_new f(x_new, pT^2) / x_old f(x_old, pT^2)</ei> | |
302 | in the emission probability ensures that not unphysically large | |
303 | <ei>x_new</ei> values are reached. Usually such <ei>x</ei> changes are | |
304 | small, and they can be viewed as a higher-order effect beyond the | |
305 | accuracy of the leading-log initial-state showers. | |
306 | ||
307 | <p/> | |
308 | This choice is not unique, however. As an alternative, if nothing else | |
309 | useful for cross-checks, one could imagine that the FSR is completely | |
310 | decoupled from the ISR and beam remnants. | |
311 | ||
312 | <flag name="TimeShower:allowBeamRecoil" default="on"> | |
313 | If on, the final-state shower is allowed to borrow energy from | |
314 | the beam remnants as described above, thereby changing the mass of the | |
315 | scattering subsystem. If off, the partons in the scattering subsystem | |
316 | are constrained to borrow energy from each other, such that the total | |
317 | four-momentum of the system is preserved. This flag has no effect | |
318 | on resonance decays, where the shower always preserves the resonance | |
319 | mass, cf. the comment above about showers for resonances never being | |
320 | interleaved. | |
321 | </flag> | |
322 | ||
323 | <flag name="TimeShower:dampenBeamRecoil" default="on"> | |
324 | When beam recoil is allowed there is still some ambiguity how far | |
325 | into the beam end of the dipole that emission should be allowed. | |
326 | It is dampened in the beam region, but probably not enough. | |
327 | When on an additional suppression factor | |
328 | <ei>4 pT2_hard / (4 pT2_hard + m2)</ei> is multiplied on to the | |
329 | emission probability. Here <ei>pT_hard</ei> is the transverse momentum | |
330 | of the radiating parton and <ei>m</ei> the off-shell mass it acquires | |
331 | by the branching, <ei>m2 = pT2/(z(1-z))</ei>. Note that | |
332 | <ei>m2 = 4 pT2_hard</ei> is the kinematical limit for a scattering | |
333 | at 90 degrees without beam recoil. | |
334 | </flag> | |
335 | ||
336 | <h3>Global recoil</h3> | |
337 | ||
338 | The final-state algorithm is based on dipole-style recoils, where | |
339 | one single parton takes the full recoil of a branching. This is unlike | |
340 | the initial-state algorithm, where the complete already-existing | |
341 | final state shares the recoil of each new emission. As an alternative, | |
342 | also the final-state algorithm contains an option where the recoil | |
343 | is shared between all partons in the final state. Thus the radiation | |
344 | pattern is unrelated to colour correlations. This is especially | |
345 | convenient for some matching algorithms, like MC@NLO, where a full | |
346 | analytic knowledge of the shower radiation pattern is needed to avoid | |
347 | double-counting. (The <ei>pT</ei>-ordered shower is described in | |
348 | <ref>Sjo05</ref>, and the corrections for massive radiator and recoiler | |
349 | in <ref>Nor01</ref>.) | |
350 | ||
351 | <p/> | |
352 | Technically, the radiation pattern is most conveniently represented | |
353 | in the rest frame of the final state of the hard subprocess. Then, for | |
354 | each parton at a time, the rest of the final state can be viewed as | |
355 | a single effective parton. This "parton" has a fixed invariant mass | |
356 | during the emission process, and takes the recoil without any changed | |
357 | direction of motion. The momenta of the individual new recoilers are | |
358 | then obtained by a simple common boost of the original ones. | |
359 | ||
360 | <p/> | |
361 | This alternative approach will miss out on the colour coherence | |
362 | phenomena. Specifically, with the whole subcollision mass as "dipole" | |
363 | mass, the phase space for subsequent emissions is larger than for | |
364 | the normal dipole algorithm. The phase space difference grows as | |
365 | more and more gluons are created, and thus leads to a way too steep | |
366 | multiplication of soft gluons. Therefore the main application is | |
367 | for the first one or few emissions of the shower, where a potential | |
368 | overestimate of the emission rate is to be corrected for anyway, | |
369 | by matching to the relevant matrix elements. Thereafter, subsequent | |
370 | emissions should be handled as before, i.e. with dipoles spanned | |
371 | between nearby partons. Furthermore, only the first (hardest) | |
372 | subcollision is handled with global recoils, since subsequent MPI's | |
373 | would not be subject to matrix element corrections anyway. | |
374 | ||
375 | <p/> | |
376 | In order for the mid-shower switch from global to local recoils | |
377 | to work, colours are traced and bookkept just as for normal showers; | |
378 | it is only that this information is not used in those steps where | |
379 | a global recoil is requested. (Thus, e.g., a gluon is still bookkept | |
380 | as one colour and one anticolour dipole end, with half the charge | |
381 | each, but with global recoil those two ends radiate identically.) | |
382 | ||
383 | <flag name="TimeShower:globalRecoil" default="off"> | |
384 | Alternative approach as above, where all final-state particles share | |
385 | the recoil of an emission. | |
386 | <br/>If off, then use the standard dipole-recoil approach. | |
387 | <br/>If on, use the alternative global recoil, but only for the first | |
388 | interaction, and only while the number of particles in the final state | |
389 | is at most <code>TimeShower:nMaxGlobalRecoil</code> before the | |
390 | branching. | |
391 | </flag> | |
392 | ||
393 | <modeopen name="TimeShower:nMaxGlobalRecoil" default="2" min="1"> | |
394 | Represents the maximum number of particles in the final state for which | |
395 | the next final-state emission can be performed with the global recoil | |
396 | strategy. This number counts all particles, whether they are | |
397 | allowed to radiate or not, e.g. also <ei>Z^0</ei>. Also partons | |
398 | created by initial-state radiation emissions counts towards this sum, | |
399 | as part of the interleaved evolution. Without interleaved evolution | |
400 | this option would not make sense, since then a varying and large | |
401 | number of partons could already have been created by the initial-state | |
402 | radiation before the first final-state one, and then there is not | |
403 | likely to be any matrix elements available for matching. | |
404 | </modeopen> | |
405 | ||
406 | <p/> | |
407 | The global-recoil machinery does not work well with rescattering in the | |
408 | MPI machinery, since then the recoiling system is not uniquely defined. | |
409 | <code>MultipartonInteractions:allowRescatter = off</code> by default, | |
410 | so this is not a main issue. If both options are switched on, | |
411 | rescattering will only be allowed to kick in after the global recoil | |
412 | has ceased to be active, i.e. once the <code>nMaxGlobalRecoil</code> | |
413 | limit has been exceeded. This should not be a major conflict, | |
414 | since rescattering is mainly of interest at later stages of the | |
415 | downwards <ei>pT</ei> evolution. | |
416 | ||
417 | <p/> | |
418 | Further, it is strongly recommended to set | |
419 | <code>TimeShower:MEcorrections = off</code> (not default!), i.e. not | |
420 | to correct the emission probability to the internal matrix elements. | |
421 | The internal ME options do not cover any cases relevant for a multibody | |
422 | recoiler anyway, so no guarantees are given what prescription would | |
423 | come to be used. Instead, without ME corrections, a process-independent | |
424 | emission rate is obtained, and <aloc href="UserHooks">user hooks</aloc> | |
425 | can provide the desired process-specific rejection factors. | |
426 | ||
427 | <h3>Radiation off octet onium states</h3> | |
428 | ||
429 | In the current implementation, charmonium and bottomonium production | |
430 | can proceed either through colour singlet or colour octet mechanisms, | |
431 | both of them implemented in terms of <ei>2 -> 2</ei> hard processes | |
432 | such as <ei>g g -> (onium) g</ei>. | |
433 | In the former case the state does not radiate and the onium therefore | |
434 | is produced in isolation, up to normal underlying-event activity. In | |
435 | the latter case the situation is not so clear, but it is sensible to | |
436 | assume that a shower can evolve. (Assuming, of course, that the | |
437 | transverse momentum of the onium state is sufficiently high that | |
438 | radiation is of relevance.) | |
439 | ||
440 | <p/> | |
441 | There could be two parts to such a shower. Firstly a gluon (or even a | |
442 | quark, though less likely) produced in a hard <ei>2 -> 2</ei> process | |
443 | can undergo showering into many gluons, whereof one branches into the | |
444 | heavy-quark pair. Secondly, once the pair has been produced, each quark | |
445 | can radiate further gluons. This latter kind of emission could easily | |
446 | break up a semibound quark pair, but might also create a new semibound | |
447 | state where before an unbound pair existed, and to some approximation | |
448 | these two effects should balance in the onium production rate. | |
449 | The showering "off an onium state" as implemented here therefore should | |
450 | not be viewed as an accurate description of the emission history | |
451 | step by step, but rather as an effective approach to ensure that the | |
452 | octet onium produced "in the hard process" is embedded in a realistic | |
453 | amount of jet activity. | |
454 | Of course both the isolated singlet and embedded octet are likely to | |
455 | be extremes, but hopefully the mix of the two will strike a reasonable | |
456 | balance. However, it is possible that some part of the octet production | |
457 | occurs in channels where it should not be accompanied by (hard) radiation. | |
458 | Therefore reducing the fraction of octet onium states allowed to radiate | |
459 | is a valid variation to explore uncertainties. | |
460 | ||
461 | <p/> | |
462 | If an octet onium state is chosen to radiate, the simulation of branchings | |
463 | is based on the assumption that the full radiation is provided by an | |
464 | incoherent sum of radiation off the quark and off the antiquark of the | |
465 | onium state. Thus the splitting kernel is taken to be the normal | |
466 | <ei>q -> q g</ei> one, multiplied by a factor of two. Obviously this is | |
467 | a simplification of a more complex picture, averaging over factors pulling | |
468 | in different directions. Firstly, radiation off a gluon ought | |
469 | to be enhanced by a factor 9/4 relative to a quark rather than the 2 | |
470 | now used, but this is a minor difference. Secondly, our use of the | |
471 | <ei>q -> q g</ei> branching kernel is roughly equivalent to always | |
472 | following the harder gluon in a <ei>g -> g g</ei> branching. This could | |
473 | give us a bias towards producing too hard onia. A soft gluon would have | |
474 | little phase space to branch into a heavy-quark pair however, so the | |
475 | bias may not be as big as it would seem at first glance. Thirdly, | |
476 | once the gluon has branched into a quark pair, each quark carries roughly | |
477 | only half of the onium energy. The maximum energy per emitted gluon should | |
478 | then be roughly half the onium energy rather than the full, as it is now. | |
479 | Thereby the energy of radiated gluons is exaggerated, i.e. onia become too | |
480 | soft. So the second and the third points tend to cancel each other. | |
481 | ||
482 | <p/> | |
483 | Finally, note that the lower cutoff scale of the shower evolution depends | |
484 | on the onium mass rather than on the quark mass, as it should be. Gluons | |
485 | below the octet-onium scale should only be part of the octet-to-singlet | |
486 | transition. | |
487 | ||
488 | <parm name="TimeShower:octetOniumFraction" default="1." min="0." max="1." > | |
489 | Allow colour-octet charmonium and bottomonium states to radiate gluons. | |
490 | 0 means that no octet-onium states radiate, 1 that all do, with possibility | |
491 | to interpolate between these two extremes. | |
492 | </parm> | |
493 | ||
494 | <parm name="TimeShower:octetOniumColFac" default="2." min="0." max="4." > | |
495 | The colour factor used used in the splitting kernel for those octet onium | |
496 | states that are allowed to radiate, normalized to the <ei>q -> q g</ei> | |
497 | splitting kernel. Thus the default corresponds to twice the radiation | |
498 | off a quark. The physically preferred range would be between 1 and 9/4. | |
499 | </parm> | |
500 | ||
501 | <h3>Further variables</h3> | |
502 | ||
503 | There are several possibilities you can use to switch on or off selected | |
504 | branching types in the shower, or in other respects simplify the shower. | |
505 | These should normally not be touched. Their main function is for | |
506 | cross-checks. | |
507 | ||
508 | <flag name="TimeShower:QCDshower" default="on"> | |
509 | Allow a QCD shower, i.e. branchings <ei>q -> q g</ei>, <ei>g -> g g</ei> | |
510 | and <ei>g -> q qbar</ei>; on/off = true/false. | |
511 | </flag> | |
512 | ||
513 | <modeopen name="TimeShower:nGluonToQuark" default="5" min="0" max="5"> | |
514 | Number of allowed quark flavours in <ei>g -> q qbar</ei> branchings | |
515 | (phase space permitting). A change to 4 would exclude | |
516 | <ei>g -> b bbar</ei>, etc. | |
517 | </modeopen> | |
518 | ||
519 | <flag name="TimeShower:QEDshowerByQ" default="on"> | |
520 | Allow quarks to radiate photons, i.e. branchings <ei>q -> q gamma</ei>; | |
521 | on/off = true/false. | |
522 | </flag> | |
523 | ||
524 | <flag name="TimeShower:QEDshowerByL" default="on"> | |
525 | Allow leptons to radiate photons, i.e. branchings <ei>l -> l gamma</ei>; | |
526 | on/off = true/false. | |
527 | </flag> | |
528 | ||
529 | <flag name="TimeShower:QEDshowerByGamma" default="on"> | |
530 | Allow photons to branch into lepton or quark pairs, i.e. branchings | |
531 | <ei>gamma -> l+ l-</ei> and <ei>gamma -> q qbar</ei>; | |
532 | on/off = true/false. | |
533 | </flag> | |
534 | ||
535 | <modeopen name="TimeShower:nGammaToQuark" default="5" min="0" max="5"> | |
536 | Number of allowed quark flavours in <ei>gamma -> q qbar</ei> branchings | |
537 | (phase space permitting). A change to 4 would exclude | |
538 | <ei>g -> b bbar</ei>, etc. | |
539 | </modeopen> | |
540 | ||
541 | <modeopen name="TimeShower:nGammaToLepton" default="3" min="0" max="3"> | |
542 | Number of allowed lepton flavours in <ei>gamma -> l+ l-</ei> branchings | |
543 | (phase space permitting). A change to 2 would exclude | |
544 | <ei>gamma -> tau+ tau-</ei>, and a change to 1 also | |
545 | <ei>gamma -> mu+ mu-</ei>. | |
546 | </modeopen> | |
547 | ||
548 | <flag name="TimeShower:MEcorrections" default="on"> | |
549 | Use of matrix element corrections where available; on/off = true/false. | |
550 | </flag> | |
551 | ||
552 | <flag name="TimeShower:MEafterFirst" default="on"> | |
553 | Use of matrix element corrections also after the first emission, | |
554 | for dipole ends of the same system that did not yet radiate. | |
555 | Only has a meaning if <code>MEcorrections</code> above is | |
556 | switched on. | |
557 | </flag> | |
558 | ||
559 | <flag name="TimeShower:phiPolAsym" default="on"> | |
560 | Azimuthal asymmetry induced by gluon polarization; on/off = true/false. | |
561 | </flag> | |
562 | ||
563 | <flag name="TimeShower:recoilToColoured" default="on"> | |
564 | In the decays of coloured resonances, say <ei>t -> b W</ei>, it is not | |
565 | possible to set up dipoles with matched colours. Originally the | |
566 | <ei>b</ei> radiator therefore has <ei>W</ei> as recoiler, and that | |
567 | choice is unique. Once a gluon has been radiated, however, it is | |
568 | possible either to have the unmatched colour (inherited by the gluon) | |
569 | still recoiling against the <ei>W</ei> (<code>off</code>), or else | |
570 | let it recoil against the <ei>b</ei> also for this dipole | |
571 | (<code>on</code>). Before version 8.160 the former was the only | |
572 | possibility, which could give unphysical radiation patterns. It is | |
573 | kept as an option to check backwards compatibility. The same issue | |
574 | exists for QED radiation, but obviously is less significant. Consider | |
575 | the example <ei>W -> e nu</ei>, where originally the <ei>nu</ei> | |
576 | takes the recoil. In the old (<code>off</code>) scheme the <ei>nu</ei> | |
577 | would remain recoiler, while in the new (<code>on</code>) instead | |
578 | each newly emitted photon becomes the new recoiler. | |
579 | </flag> | |
580 | ||
581 | </chapter> | |
582 | ||
583 | <!-- Copyright (C) 2013 Torbjorn Sjostrand --> |