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[u/mrichter/AliRoot.git] / PYTHIA8 / pythia8130 / xmldoc / TimelikeShowers.xml
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5ad4eb21 1<chapter name="Timelike Showers">
2
3<h2>Timelike Showers</h2>
4
5The PYTHIA algorithm for timelike final-state showers is based on
6the recent article <ref>Sjo05</ref>, where a transverse-momentum-ordered
7evolution scheme is introduced. This algorithm is influenced by
8the previous mass-ordered algorithm in PYTHIA <ref>Ben87</ref> and by
9the dipole-emission formulation in Ariadne <ref>Gus86</ref>. From the
10mass-ordered algorithm it inherits a merging procedure for first-order
11gluon-emission matrix elements in essentially all two-body decays
12in the standard model and its minimal supersymmetric extension
13<ref>Nor01</ref>.
14
15<p/>
16The normal user is not expected to call <code>TimeShower</code> directly,
17but only have it called from <code>Pythia</code>. Some of the parameters
18below, in particular <code>TimeShower:alphaSvalue</code>, would be of
19interest for a tuning exercise, however.
20
21<h3>Main variables</h3>
22
23Often the maximum scale of the FSR shower evolution is understood from the
24context. For instance, in a resonace decay half the resonance mass sets an
25absolute upper limit. For a hard process in a hadronic collision the choice
26is not as unique. Here the factorization scale has been chosen as the
27maximum evolution scale. This would be the <ei>pT</ei> for a
28<ei>2 -> 2</ei> process, supplemented by mass terms for massive outgoing
29particles. Some small amount of freedom is offered by
30<parm name="TimeShower:pTmaxFudge" default="1.0" min="0.5" max="2.0">
31While the above rules would imply that <ei>pT_max = pT_factorization</ei>,
32<code>pTmaxFudge</code> introduced a multiplicative factor <ei>f</ei> such
33that instead <ei>pT_max = f * pT_factorization</ei>. Only applies to the
34hardest interaction in an event. It is strongly suggested that
35<ei>f = 1</ei>, but variations around this default can be useful to test
36this assumption.
37</parm>
38
39<p/>
40The amount of QCD radiation in the shower is determined by
41<parm name="TimeShower:alphaSvalue" default="0.137"
42min="0.06" max="0.25">
43The <ei>alpha_strong</ei> value at scale <ei>M_Z^2</ei>. The default
44value corresponds to a crude tuning to LEP data, to be improved.
45</parm>
46
47<p/>
48The actual value is then regulated by the running to the scale
49<ei>pT^2</ei>, at which the shower evaluates <ei>alpha_strong</ei>
50
51<modepick name="TimeShower:alphaSorder" default="1" min="0" max="2">
52Order at which <ei>alpha_strong</ei> runs,
53<option value="0">zeroth order, i.e. <ei>alpha_strong</ei> is kept
54fixed.</option>
55<option value="1">first order, which is the normal value.</option>
56<option value="2">second order. Since other parts of the code do
57not go to second order there is no strong reason to use this option,
58but there is also nothing wrong with it.</option>
59</modepick>
60
61<p/>
62QED radiation is regulated by the <ei>alpha_electromagnetic</ei>
63value at the <ei>pT^2</ei> scale of a branching.
64
65<modepick name="TimeShower:alphaEMorder" default="1" min="-1" max="1">
66The running of <ei>alpha_em</ei>.
67<option value="1">first-order running, constrained to agree with
68<code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass.
69</option>
70<option value="0">zeroth order, i.e. <ei>alpha_em</ei> is kept
71fixed at its value at vanishing momentum transfer.</option>
72<option value="-1">zeroth order, i.e. <ei>alpha_em</ei> is kept
73fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value
74at the <ei>Z^0</ei> mass.
75</option>
76</modepick>
77
78<p/>
79The rate of radiation if divergent in the <ei>pT -> 0</ei> limit. Here,
80however, perturbation theory is expected to break down. Therefore an
81effective <ei>pT_min</ei> cutoff parameter is introduced, below which
82no emissions are allowed. The cutoff may be different for QCD and QED
83radiation off quarks, and is mainly a technical parameter for QED
84radiation off leptons.
85
86<parm name="TimeShower:pTmin" default="0.5" min="0.1" max="2.0">
87Parton shower cut-off <ei>pT</ei> for QCD emissions.
88</parm>
89
90<parm name="TimeShower:pTminChgQ" default="0.5" min="0.1" max="2.0">
91Parton shower cut-off <ei>pT</ei> for photon coupling to coloured particle.
92</parm>
93
94<parm name="TimeShower:pTminChgL" default="0.0005" min="0.0001" max="2.0">
95Parton shower cut-off <ei>pT</ei> for pure QED branchings.
96Assumed smaller than (or equal to) <code>pTminChgQ</code>.
97</parm>
98
99<p/>
100Shower branchings <ei>gamma -> f fbar</ei>, where <ei>f</ei> is a
101quark or lepton, in part compete with the hard processes involving
102<ei>gamma^*/Z^0</ei> production. In order to avoid overlap it makes
103sense to correlate the maximum <ei>gamma</ei> mass allowed in showers
104with the minumum <ei>gamma^*/Z^0</ei> mass allowed in hard processes.
105In addition, the shower contribution only contains the pure
106<ei>gamma^*</ei> contribution, i.e. not the <ei>Z^0</ei> part, so
107the mass spectrum above 50 GeV or so would not be well described.
108
109<parm name="TimeShower:mMaxGamma" default="10.0" min="0.001"
110max="50.0">
111Maximum invariant mass allowed for the created fermion pair in a
112<ei>gamma -> f fbar</ei> branching in the shower.
113</parm>
114
115<h3>Interleaved evolution</h3>
116
117Multiple interactions (MI) and initial-state showers (ISR) are
118always interleaved, as follows. Starting from the hard interaction,
119the complete event is constructed by a set of steps. In each step
120the <ei>pT</ei> scale of the previous step is used as starting scale
121for a downwards evolution. The MI and ISR components each make
122their respective Monte Carlo choices for the next lower <ei>pT</ei>
123value. The one with larger <ei>pT</ei> is allowed to carry out its
124proposed action, thereby modifying the conditions for the next steps.
125This is relevant since the two components compete for the energy
126contained in the beam remnants: both an interaction and an emission
127take avay some of the energy, leaving less for the future. The end
128result is a combined chain of decreasing <ei>pT</ei> values, where
129ones associated with new interactions and ones with new emissions
130are interleaved.
131
132<p/>
133There is no corresponding requirement for final-state radiation (FSR)
134to be interleaved. Such an FSR emission does not compete directly for
135beam energy (but see below), and also can be viewed as occuring after
136the other two components in some kind of time sense. Interleaving is
137allowed, however, since it can be argued that a high-<ei>pT</ei> FSR
138occurs on shorter time scales than a low-<ei>pT</ei> MI, say.
139Backwards evolution of ISR is also an example that physical time
140is not the only possible ordering principle, but that one can work
141with conditional probabilities: given the partonic picture at a
142specific <ei>pT</ei> resolution scale, what possibilities are open
143for a modified picture at a slightly lower <ei>pT</ei> scale, either
144by MI, ISR or FSR? Complete interleaving of the three components also
145offers advantages if one aims at matching to higher-order matrix
146elements above some given scale.
147
148<flag name="TimeShower:interleave" default="on">
149If on, final-state emissions are interleaved in the same
150decreasing-<ei>pT</ei> chain as multiple interactions and initial-state
151emissions. If off, final-state emissions are only addressed after the
152multiple interactions and initial-state radiation have been considered.
153</flag>
154
155<p/>
156As an aside, it should be noted that such interleaving does not affect
157showering in resonance decays, such as a <ei>Z^0</ei>. These decays are
158only introduced after the production process has been considered in full,
159and the subsequent FSR is carried out inside the resonance, with
160preserved resonance mass.
161
162<p/>
163One aspect of FSR for a hard process in hadron collisions is that often
164colour diples are formed between a scattered parton and a beam remnant,
165or rather the hole left behind by an incoming partons. If such holes
166are allowed as dipole ends and take the recoil when the scattered parton
167undergoes a branching then this translates into the need to take some
168amount of remnant energy also in the case of FSR, i.e. the roles of
169ISR and FSR are not completely decoupled. The energy taken away is
170bokkept by increasing the <ei>x</ei> value assigned to the incoming
171scattering parton, and a reweighting factor
172<ei>x_new f(x_new, pT^2) / x_old f(x_old, pT^2)</ei>
173in the emission probability ensures that not unphysically large
174<ei>x_new</ei> values are reached. Usually such <ei>x</ei> changes are
175small, and they can be viewed as a higher-order effect beyond the
176accuracy of the leading-log initial-state showers.
177
178<p/>
179This choice is not unique, however. As an alternative, if nothing else
180useful for cross-checks, one could imagine that the FSR is completely
181decoupled from the ISR and beam remnants.
182
183<flag name="TimeShower:allowBeamRecoil" default="on">
184If on, the final-state shower is allowed to borrow energy from
185the beam remnants as described above, thereby changing the mass of the
186scattering subsystem. If off, the partons in the scattering subsystem
187are constrained to borrow energy from each other, such that the total
188four-momentum of the system is preserved. This flag has no effect
189on resonance decays, where the shower always preserves the resonance
190mass, cf. the comment above about showers for resonances never being
191interleaved.
192</flag>
193
194
195<h3>Radiation off octet onium states</h3>
196
197In the current implementation, charmonium and bottomonium production
198can proceed either through colour singlet or colour octet mechanisms,
199both of them implemented in terms of <ei>2 -> 2</ei> hard processes
200such as <ei>g g -> (onium) g</ei>.
201In the former case the state does not radiate and the onium therefore
202is produced in isolation, up to normal underlying-event activity. In
203the latter case the situation is not so clear, but it is sensible to
204assume that a shower can evolve. (Assuming, of course, that the
205transverse momentum of the onium state is sufficiently high that
206radiation is of relevance.)
207
208<p/>
209There could be two parts to such a shower. Firstly a gluon (or even a
210quark, though less likely) produced in a hard <ei>2 -> 2</ei> process
211can undergo showering into many gluons, whereof one branches into the
212heavy-quark pair. Secondly, once the pair has been produced, each quark
213can radiate further gluons. This latter kind of emission could easily
214break up a semibound quark pair, but might also create a new semibound
215state where before an unbound pair existed, and to some approximation
216these two effects should balance in the onium production rate.
217The showering "off an onium state" as implemented here therefore should
218not be viewed as an accurate description of the emission history
219step by step, but rather as an effective approach to ensure that the
220octet onium produced "in the hard process" is embedded in a realistic
221amount of jet activity.
222Of course both the isolated singlet and embedded octet are likely to
223be extremes, but hopefully the mix of the two will strike a reasonable
224balance. However, it is possible that some part of the octet production
225occurs in channels where it should not be accompanied by (hard) radiation.
226Therefore reducing the fraction of octet onium states allowed to radiate
227is a valid variation to explore uncertainties.
228
229<p/>
230If an octet onium state is chosen to radiate, the simulation of branchings
231is based on the assumption that the full radiation is provided by an
232incoherent sum of radiation off the quark and off the antiquark of the
233onium state. Thus the splitting kernel is taken to be the normal
234<ei>q -> q g</ei> one, multiplied by a factor of two. Obviously this is
235a simplification of a more complex picture, averaging over factors pulling
236in different directions. Firstly, radiation off a gluon ought
237to be enhanced by a factor 9/4 relative to a quark rather than the 2
238now used, but this is a minor difference. Secondly, our use of the
239<ei>q -> q g</ei> branching kernel is roughly equivalent to always
240following the harder gluon in a <ei>g -> g g</ei> branching. This could
241give us a bias towards producing too hard onia. A soft gluon would have
242little phase space to branch into a heavy-quark pair however, so the
243bias may not be as big as it would seem at first glance. Thirdly,
244once the gluon has branched into a quark pair, each quark carries roughly
245only half of the onium energy. The maximum energy per emitted gluon should
246then be roughly half the onium energy rather than the full, as it is now.
247Thereby the energy of radiated gluons is exaggerated, i.e. onia become too
248soft. So the second and the third points tend to cancel each other.
249
250<p/>
251Finally, note that the lower cutoff scale of the shower evolution depends
252on the onium mass rather than on the quark mass, as it should be. Gluons
253below the octet-onium scale should only be part of the octet-to-singlet
254transition.
255
256<parm name="TimeShower:octetOniumFraction" default="1." min="0." max="1." >
257Allow colour-octet charmonium and bottomonium states to radiate gluons.
2580 means that no octet-onium states radiate, 1 that all do, with possibility
259to interpolate between these two extremes.
260</parm>
261
262<parm name="TimeShower:octetOniumColFac" default="2." min="0." max="4." >
263The colour factor used used in the splitting kernel for those octet onium
264states that are allowed to radiate, normalized to the <ei>q -> q g</ei>
265splitting kernel. Thus the default corresponds to twice the radiation
266off a quark. The physically preferred range would be between 1 and 9/4.
267</parm>
268
269<h3>Further variables</h3>
270
271There are several possibilities you can use to switch on or off selected
272branching types in the shower, or in other respects simplify the shower.
273These should normally not be touched. Their main function is for
274cross-checks.
275
276<flag name="TimeShower:QCDshower" default="on">
277Allow a QCD shower, i.e. branchings <ei>q -> q g</ei>, <ei>g -> g g</ei>
278and <ei>g -> q qbar</ei>; on/off = true/false.
279</flag>
280
281<modeopen name="TimeShower:nGluonToQuark" default="5" min="0" max="5">
282Number of allowed quark flavours in <ei>g -> q qbar</ei> branchings
283(phase space permitting). A change to 4 would exclude
284<ei>g -> b bbar</ei>, etc.
285</modeopen>
286
287<flag name="TimeShower:QEDshowerByQ" default="on">
288Allow quarks to radiate photons, i.e. branchings <ei>q -> q gamma</ei>;
289on/off = true/false.
290</flag>
291
292<flag name="TimeShower:QEDshowerByL" default="on">
293Allow leptons to radiate photons, i.e. branchings <ei>l -> l gamma</ei>;
294on/off = true/false.
295</flag>
296
297<flag name="TimeShower:QEDshowerByGamma" default="on">
298Allow photons to branch into lepton or quark pairs, i.e. branchings
299<ei>gamma -> l+ l-</ei> and <ei>gamma -> q qbar</ei>;
300on/off = true/false.
301</flag>
302
303<modeopen name="TimeShower:nGammaToQuark" default="5" min="0" max="5">
304Number of allowed quark flavours in <ei>gamma -> q qbar</ei> branchings
305(phase space permitting). A change to 4 would exclude
306<ei>g -> b bbar</ei>, etc.
307</modeopen>
308
309<modeopen name="TimeShower:nGammaToLepton" default="3" min="0" max="3">
310Number of allowed lepton flavours in <ei>gamma -> l+ l-</ei> branchings
311(phase space permitting). A change to 2 would exclude
312<ei>gamma -> tau+ tau-</ei>, and a change to 1 also
313<ei>gamma -> mu+ mu-</ei>.
314</modeopen>
315
316<flag name="TimeShower:MEcorrections" default="on">
317Use of matrix element corrections where available; on/off = true/false.
318</flag>
319
320<flag name="TimeShower:phiPolAsym" default="on">
321Azimuthal asymmetry induced by gluon polarization; on/off = true/false.
322</flag>
323
324</chapter>
325
326<!-- Copyright (C) 2008 Torbjorn Sjostrand -->