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3<title>Timelike Showers</title>
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29   
30<h2>Timelike Showers</h2>
31
32The PYTHIA algorithm for timelike final-state showers is based on
33the article [<a href="Bibliography.php" target="page">Sjo05</a>], where a transverse-momentum-ordered
34evolution scheme is introduced, with the extension to fully interleaved
35evolution covered in [<a href="Bibliography.php" target="page">Cor10a</a>]. This algorithm is influenced by
36the previous mass-ordered algorithm in PYTHIA [<a href="Bibliography.php" target="page">Ben87</a>] and by
37the dipole-emission formulation in Ariadne [<a href="Bibliography.php" target="page">Gus86</a>]. From the
38mass-ordered algorithm it inherits a merging procedure for first-order
39gluon-emission matrix elements in essentially all two-body decays
40in the standard model and its minimal supersymmetric extension
41[<a href="Bibliography.php" target="page">Nor01</a>].
42
43<p/>
44The normal user is not expected to call <code>TimeShower</code> directly,
45but only have it called from <code>Pythia</code>. Some of the parameters
46below, in particular <code>TimeShower:alphaSvalue</code>, would be of
47interest for a tuning exercise, however.
48
49<h3>Main variables</h3>
50
51Often the maximum scale of the FSR shower evolution is understood from the
52context. For instance, in a resonace decay half the resonance mass sets an
53absolute upper limit. For a hard process in a hadronic collision the choice
54is not as unique. Here the <?php $filepath = $_GET["filepath"];
55echo "<a href='CouplingsAndScales.php?filepath=".$filepath."' target='page'>";?>factorization
56scale</a> has been chosen as the maximum evolution scale. This would be
57the <i>pT</i> for a <i>2 -> 2</i> process, supplemented by mass terms
58for massive outgoing particles. For some special applications we do allow
59an alternative.
60
61<br/><br/><table><tr><td><strong>TimeShower:pTmaxMatch </td><td>  &nbsp;&nbsp;(<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
62Way in which the maximum shower evolution scale is set to match the
63scale of the hard process itself.
64<br/>
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.
69Emissions off subsequent multiparton interactions are always constrainted
70to be below the factorization scale of the process itself. They also
71assume you use interleaved evolution, so that FSR is in direct
72competition with ISR for the hardest emission. If you already
73generated a number of ISR partons at low <ei>pT</ei>, it would not
74make sense to have a later FSR shower up to the kinematical for all
75of them.
76
77<br/><br/><table><tr><td><strong>TimeShower:pTmaxFudge </td><td></td><td> <input type="text" name="2" value="1.0" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)</td></tr></table>
78In cases where the above <code>pTmaxMatch</code> rules would imply
79that <i>pT_max = pT_factorization</i>, <code>pTmaxFudge</code>
80introduces a multiplicative factor <i>f</i> such that instead
81<i>pT_max = f * pT_factorization</i>. Only applies to the hardest
82interaction in an event, cf. below. It is strongly suggested that
83<i>f = 1</i>, but variations around this default can be useful to
84test this assumption.
85<br/><b>Note:</b>Scales for resonance decays are not affected, but can
86be set separately by <?php $filepath = $_GET["filepath"];
87echo "<a href='UserHooks.php?filepath=".$filepath."' target='page'>";?>user hooks</a>.
88 
89
90<br/><br/><table><tr><td><strong>TimeShower:pTmaxFudgeMPI </td><td></td><td> <input type="text" name="3" value="1.0" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)</td></tr></table>
91A multiplicative factor <i>f</i> such that
92<i>pT_max = f * pT_factorization</i>, as above, but here for the
93non-hardest interactions (when multiparton interactions are allowed).
94 
95
96<br/><br/><table><tr><td><strong>TimeShower:pTdampMatch </td><td>  &nbsp;&nbsp;(<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
97These options only take effect when a process is allowed to radiate up
98to the kinematical limit by the above <code>pTmaxMatch</code> choice,
99and no matrix-element corrections are available. Then, in many processes,
100the fall-off in <ei>pT</ei> will be too slow by one factor of <ei>pT^2</ei>.
101That is, while showers have an approximate <ei>dpT^2/pT^2</ei> shape, often
102it should become more like <ei>dpT^2/pT^4</ei> at <ei>pT</ei> values above
103the scale of the hard process. This argument is more obvious for ISR,
104but is taken over unchanged for FSR to have a symmetric description.
105<br/>
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.
110Emissions off subsequent multiparton interactions are always constrainted
111to be below the factorization scale of the process itself. 
112
113<br/><br/><table><tr><td><strong>TimeShower:pTdampFudge </td><td></td><td> <input type="text" name="5" value="1.0" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 4.0</code>)</td></tr></table>
114In cases 1 and 2 above, where a dampening is imposed at around the
115factorization or renormalization scale, respectively, this allows the
116<i>pT</i> scale of dampening of radiation by a half to be shifted
117by this factor relative to the default <i>Q_fac</i> or <i>Q_ren</i>.
118This number ought to be in the neighbourhood of unity, but variations
119away from this value could do better in some processes.
120 
121
122<p/>
123The 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"/>  &nbsp;&nbsp;(<code>default = <strong>0.1383</strong></code>; <code>minimum = 0.06</code>; <code>maximum = 0.25</code>)</td></tr></table>
125The <i>alpha_strong</i> value at scale <i>M_Z^2</i>. The default
126value corresponds to a crude tuning to LEP data, to be improved.
127 
128
129<p/>
130The 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>.
132
133<br/><br/><table><tr><td><strong>TimeShower:alphaSorder </td><td>  &nbsp;&nbsp;(<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
134Order at which <ei>alpha_strong</ei> runs,
135<br/>
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/>
139
140<p/>
141QED radiation is regulated by the <i>alpha_electromagnetic</i>
142value at the <i>pT^2</i> scale of a branching.
143 
144<br/><br/><table><tr><td><strong>TimeShower:alphaEMorder </td><td>  &nbsp;&nbsp;(<code>default = <strong>1</strong></code>; <code>minimum = -1</code>; <code>maximum = 1</code>)</td></tr></table>
145The running of <ei>alpha_em</ei>.
146<br/>
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/>
150
151<p/>
152The natural scale for couplings, and PDFs for dipoles stretching out
153to the beam remnants, is <i>pT^2</i>. To explore uncertainties it
154is possibly to vary around this value, however, in analogy with what
155can be done for <?php $filepath = $_GET["filepath"];
156echo "<a href='CouplingsAndScales.php?filepath=".$filepath."' target='page'>";?>hard processes</a>.
157
158<br/><br/><table><tr><td><strong>TimeShower:renormMultFac </td><td></td><td> <input type="text" name="9" value="1." size="20"/>  &nbsp;&nbsp;(<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)</td></tr></table>
159The default <i>pT^2</i> renormalization scale is multiplied by
160this 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
163remain at fixed scales).
164 
165
166<br/><br/><table><tr><td><strong>TimeShower:factorMultFac </td><td></td><td> <input type="text" name="10" value="1." size="20"/>  &nbsp;&nbsp;(<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)</td></tr></table>
167The default <i>pT^2</i> factorization scale is multiplied by
168this prefactor.
169 
170 
171<p/>
172The rate of radiation if divergent in the <i>pT -> 0</i> limit. Here,
173however, perturbation theory is expected to break down. Therefore an
174effective <i>pT_min</i> cutoff parameter is introduced, below which
175no emissions are allowed. The cutoff may be different for QCD and QED
176radiation off quarks, and is mainly a technical parameter for QED
177radiation off leptons.
178
179<br/><br/><table><tr><td><strong>TimeShower:pTmin </td><td></td><td> <input type="text" name="11" value="0.4" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)</td></tr></table>
180Parton shower cut-off <i>pT</i> for QCD emissions.
181 
182
183<br/><br/><table><tr><td><strong>TimeShower:pTminChgQ </td><td></td><td> <input type="text" name="12" value="0.4" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)</td></tr></table>
184Parton shower cut-off <i>pT</i> for photon coupling to coloured particle.
185 
186
187<br/><br/><table><tr><td><strong>TimeShower:pTminChgL </td><td></td><td> <input type="text" name="13" value="0.0005" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.0005</strong></code>; <code>minimum = 0.0001</code>; <code>maximum = 2.0</code>)</td></tr></table>
188Parton shower cut-off <i>pT</i> for pure QED branchings.
189Assumed smaller than (or equal to) <code>pTminChgQ</code>.
190 
191
192<p/> 
193Shower branchings <i>gamma -> f fbar</i>, where <i>f</i> is a
194quark or lepton, in part compete with the hard processes involving
195<i>gamma^*/Z^0</i> production. In order to avoid overlap it makes
196sense to correlate the maximum <i>gamma</i> mass allowed in showers
197with the minumum <i>gamma^*/Z^0</i> mass allowed in hard processes.
198In addition, the shower contribution only contains the pure
199<i>gamma^*</i> contribution, i.e. not the <i>Z^0</i> part, so
200the mass spectrum above 50 GeV or so would not be well described.
201
202<br/><br/><table><tr><td><strong>TimeShower:mMaxGamma </td><td></td><td> <input type="text" name="14" value="10.0" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>10.0</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 50.0</code>)</td></tr></table>
203Maximum invariant mass allowed for the created fermion pair in a
204<i>gamma -> f fbar</i> branching in the shower.
205 
206
207<h3>Interleaved evolution</h3>
208
209Multiparton interactions (MPI) and initial-state showers (ISR) are
210always interleaved, as follows. Starting from the hard interaction,
211the complete event is constructed by a set of steps. In each step
212the <i>pT</i> scale of the previous step is used as starting scale
213for a downwards evolution. The MPI and ISR components each make
214their respective Monte Carlo choices for the next lower <i>pT</i>
215value. The one with larger <i>pT</i> is allowed to carry out its
216proposed action, thereby modifying the conditions for the next steps.
217This is relevant since the two components compete for the energy
218contained in the beam remnants: both an interaction and an emission
219take avay some of the energy, leaving less for the future. The end
220result is a combined chain of decreasing <i>pT</i> values, where
221ones associated with new interactions and ones with new emissions
222are interleaved. 
223
224<p/>
225There is no corresponding requirement for final-state radiation (FSR)
226to be interleaved. Such an FSR emission does not compete directly for
227beam energy (but see below), and also can be viewed as occuring after
228the other two components in some kind of time sense. Interleaving is
229allowed, however, since it can be argued that a high-<i>pT</i> FSR
230occurs on shorter time scales than a low-<i>pT</i> MPI, say.
231Backwards evolution of ISR is also an example that physical time
232is not the only possible ordering principle, but that one can work
233with conditional probabilities: given the partonic picture at a 
234specific <i>pT</i> resolution scale, what possibilities are open
235for a modified picture at a slightly lower <i>pT</i> scale, either
236by MPI, ISR or FSR? Complete interleaving of the three components also
237offers advantages if one aims at matching to higher-order matrix
238elements above some given scale.
239
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
243If on, final-state emissions are interleaved in the same
244decreasing-<i>pT</i> chain as multiparton interactions and initial-state
245emissions. If off, final-state emissions are only addressed after the
246multiparton interactions and initial-state radiation have been considered.
247 
248
249<p/>
250As an aside, it should be noted that such interleaving does not affect
251showering in resonance decays, such as a <i>Z^0</i>. These decays are
252only introduced after the production process has been considered in full,
253and the subsequent FSR is carried out inside the resonance, with
254preserved resonance mass.
255
256<p/>
257One aspect of FSR for a hard process in hadron collisions is that often
258colour diples are formed between a scattered parton and a beam remnant,
259or rather the hole left behind by an incoming partons. If such holes
260are allowed as dipole ends and take the recoil when the scattered parton
261undergoes a branching then this translates into the need to take some
262amount of remnant energy also in the case of FSR, i.e. the roles of
263ISR and FSR are not completely decoupled. The energy taken away is
264bokkept by increasing the <i>x</i> value assigned to the incoming
265scattering parton, and a reweighting factor
266<i>x_new f(x_new, pT^2) / x_old f(x_old, pT^2)</i> 
267in the emission probability ensures that not unphysically large
268<i>x_new</i> values are reached. Usually such <i>x</i> changes are
269small, and they can be viewed as a higher-order effect beyond the
270accuracy of the leading-log initial-state showers.
271
272<p/>
273This choice is not unique, however. As an alternative, if nothing else
274useful for cross-checks, one could imagine that the FSR is completely
275decoupled from the ISR and beam remnants.
276
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
280If on, the final-state shower is allowed to borrow energy from
281the beam remnants as described above, thereby changing the mass of the
282scattering subsystem. If off, the partons in the scattering subsystem
283are constrained to borrow energy from each other, such that the total
284four-momentum of the system is preserved. This flag has no effect
285on resonance decays, where the shower always preserves the resonance
286mass, cf. the comment above about showers for resonances never being
287interleaved.
288 
289
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
293When beam recoil is allowed there is still some ambiguity how far
294into the beam end of the dipole that emission should be allowed.
295It is dampened in the beam region, but probably not enough.
296When on an additional suppression factor
297<i>4 pT2_hard / (4 pT2_hard + m2)</i> is multiplied on to the
298emission probability. Here <i>pT_hard</i> is the transverse momentum
299of the radiating parton and <i>m</i> the off-shell mass it acquires
300by 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
302at 90 degrees without beam recoil.   
303 
304
305<h3>Global recoil</h3>
306
307The final-state algorithm is based on dipole-style recoils, where
308one single parton takes the full recoil of a branching. This is unlike
309the initial-state algorithm, where the complete already-existing
310final state shares the recoil of each new emission. As an alternative,
311also the final-state algorithm contains an option where the recoil
312is shared between all partons in the final state. Thus the radiation
313pattern is unrelated to colour correlations. This is especially
314convenient for some matching algorithms, like MC@NLO, where a full
315analytic knowledge of the shower radiation pattern is needed to avoid
316doublecountning. (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
318in [<a href="Bibliography.php" target="page">Nor01</a>].)
319
320<p/> 
321Technically, the radiation pattern is most conveniently represented
322in the rest frame of the final state of the hard subprocess. Then, for
323each parton at a time, the rest of the final state can be viewed as
324a single effective parton. This "parton" has a fixed invariant mass
325during the emission process, and takes the recoil without any changed
326direction of motion. The momenta of the individual new recoilers are
327then obtained by a simple common boost of the original ones.
328
329<p/> 
330This alternative approach will miss out on the colour coherence
331phenomena. Specifically, with the whole subcollision mass as "dipole"
332mass, the phase space for subsequent emissions is larger than for
333the normal dipole algorithm. The phase space difference grows as
334more and more gluons are created, and thus leads to a way too steep
335multiplication of soft gluons. Therefore the main application is
336for the first one or few emissions of the shower, where a potential
337overestimate of the emission rate is to be corrected for anyway,
338by matching to the relevant matrix elements. Thereafter, subsequent
339emissions should be handled as before, i.e. with dipoles spanned
340between nearby partons. Furthermore, only the first (hardest)
341subcollision is handled with global recoils, since subsequent MPI's
342would not be subject to matrix element corrections anyway.
343
344<p/> 
345In order for the mid-shower switch from global to local recoils
346to work, colours are traced and bookkept just as for normal showers;
347it is only that this information is not used in those steps where
348a global recoil is requested. (Thus, e.g., a gluon is still bookkept
349as one colour and one anticolour dipole end, with half the charge
350each, but with global recoil those two ends radiate identically.)
351
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
355Alternative approach as above, where all final-state particles share
356the 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
359interaction, and only while the number of particles in the final state
360is at most <code>TimeShower:nMaxGlobalRecoil</code> before the
361branching.
362 
363 
364<br/><br/><table><tr><td><strong>TimeShower:nMaxGlobalRecoil </td><td></td><td> <input type="text" name="19" value="2" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>2</strong></code>; <code>minimum = 1</code>)</td></tr></table>
365Represents the maximum number of particles in the final state for which
366the next final-state emission can be performed with the global recoil
367strategy. This number counts all particles, whether they are
368allowed to radiate or not, e.g. also <i>Z^0</i>. Also partons
369created by initial-state radiation emissions counts towards this sum,
370as part of the interleaved evolution. Without interleaved evolution
371this option would not make sense, since then a varying and large
372number of partons could already have been created by the initial-state
373radiation before the first final-state one, and then there is not
374likely to be any matrix elements available for matching.
375 
376
377<p/> 
378The global-recoil machinery does not work well with rescattering in the
379MPI machinery, since then the recoiling system is not uniquely defined.
380<code>MultipartonInteractions:allowRescatter = off</code> by default,
381so this is not a main issue. If both options are switched on,
382rescattering will only be allowed to kick in after the global recoil
383has ceased to be active, i.e. once the <code>nMaxGlobalRecoil</code>
384limit has been exceeded. This should not be a major conflict,
385since rescattering is mainly of interest at later stages of the
386downwards <i>pT</i> evolution.
387
388<p/> 
389Further, it is strongly recommended to set
390<code>TimeShower:MEcorrections = off</code> (not default!), i.e. not
391to correct the emission probability to the internal matrix elements.
392The internal ME options do not cover any cases relevant for a multibody
393recoiler anyway, so no guarantees are given what prescription would
394come to be used. Instead, without ME corrections,  a process-independent
395emission rate is obtained, and  <?php $filepath = $_GET["filepath"];
396echo "<a href='UserHooks.php?filepath=".$filepath."' target='page'>";?>user hooks</a>
397can provide the desired process-specific rejection factors.
398 
399<h3>Radiation off octet onium states</h3>
400
401In the current implementation, charmonium and bottomonium production
402can proceed either through colour singlet or colour octet mechanisms,
403both of them implemented in terms of <i>2 -> 2</i> hard processes
404such as <i>g g -> (onium) g</i>.
405In the former case the state does not radiate and the onium therefore
406is produced in isolation, up to normal underlying-event activity. In
407the latter case the situation is not so clear, but it is sensible to
408assume that a shower can evolve. (Assuming, of course, that the
409transverse momentum of the onium state is sufficiently high that 
410radiation is of relevance.)
411
412<p/> 
413There could be two parts to such a shower. Firstly a gluon (or even a
414quark, though less likely) produced in a hard <i>2 -> 2</i> process
415can undergo showering into many gluons, whereof one branches into the
416heavy-quark pair. Secondly, once the pair has been produced, each quark
417can radiate further gluons. This latter kind of emission could easily
418break up a semibound quark pair, but might also create a new semibound
419state where before an unbound pair existed, and to some approximation
420these two effects should balance in the onium production rate.
421The showering "off an onium state" as implemented here therefore should
422not be viewed as an accurate description of the emission history
423step by step, but rather as an effective approach to ensure that the
424octet onium produced "in the hard process" is embedded in a realistic
425amount of jet activity.
426Of course both the isolated singlet and embedded octet are likely to
427be extremes, but hopefully the mix of the two will strike a reasonable
428balance. However, it is possible that some part of the octet production
429occurs in channels where it should not be accompanied by (hard) radiation.
430Therefore reducing the fraction of octet onium states allowed to radiate
431is a valid variation to explore uncertainties.
432
433<p/>
434If an octet onium state is chosen to radiate, the simulation of branchings
435is based on the assumption that the full radiation is provided by an
436incoherent sum of radiation off the quark and off the antiquark of the
437onium 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
439a simplification of a more complex picture, averaging over factors pulling
440in different directions. Firstly, radiation off a gluon ought
441to be enhanced by a factor 9/4 relative to a quark rather than the 2
442now 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
444following the harder gluon in a <i>g -> g g</i> branching. This could
445give us a bias towards producing too hard onia. A soft gluon would have
446little phase space to branch into a heavy-quark pair however, so the
447bias may not be as big as it would seem at first glance. Thirdly,
448once the gluon has branched into a quark pair, each quark carries roughly
449only half of the onium energy. The maximum energy per emitted gluon should
450then be roughly half the onium energy rather than the full, as it is now.
451Thereby the energy of radiated gluons is exaggerated, i.e. onia become too
452soft. So the second and the third points tend to cancel each other.
453
454<p/>
455Finally, note that the lower cutoff scale of the shower evolution depends
456on the onium mass rather than on the quark mass, as it should be. Gluons
457below the octet-onium scale should only be part of the octet-to-singlet
458transition.
459
460<br/><br/><table><tr><td><strong>TimeShower:octetOniumFraction </td><td></td><td> <input type="text" name="20" value="1." size="20"/>  &nbsp;&nbsp;(<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)</td></tr></table>
461Allow colour-octet charmonium and bottomonium states to radiate gluons.
4620 means that no octet-onium states radiate, 1 that all do, with possibility
463to interpolate between these two extremes.
464 
465
466<br/><br/><table><tr><td><strong>TimeShower:octetOniumColFac </td><td></td><td> <input type="text" name="21" value="2." size="20"/>  &nbsp;&nbsp;(<code>default = <strong>2.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 4.</code>)</td></tr></table>
467The colour factor used used in the splitting kernel for those octet onium
468states that are allowed to radiate, normalized to the <i>q -> q g</i>
469splitting kernel. Thus the default corresponds to twice the radiation
470off a quark. The physically preferred range would be between 1 and 9/4.
471 
472
473<h3>Further variables</h3>
474
475There are several possibilities you can use to switch on or off selected
476branching types in the shower, or in other respects simplify the shower.
477These should normally not be touched. Their main function is for
478cross-checks.
479
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
483Allow a QCD shower, i.e. branchings <i>q -> q g</i>, <i>g -> g g</i>
484and <i>g -> q qbar</i>; on/off = true/false.
485 
486
487<br/><br/><table><tr><td><strong>TimeShower:nGluonToQuark </td><td></td><td> <input type="text" name="23" value="5" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)</td></tr></table>
488Number 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.
491 
492
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
496Allow quarks to radiate photons, i.e. branchings <i>q -> q gamma</i>;
497on/off = true/false.
498 
499
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
503Allow leptons to radiate photons, i.e. branchings <i>l -> l gamma</i>; 
504on/off = true/false.
505 
506
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
510Allow photons to branch into lepton or quark pairs, i.e. branchings
511<i>gamma -> l+ l-</i> and <i>gamma -> q qbar</i>;
512on/off = true/false.
513 
514
515<br/><br/><table><tr><td><strong>TimeShower:nGammaToQuark </td><td></td><td> <input type="text" name="27" value="5" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)</td></tr></table>
516Number 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.
519 
520
521<br/><br/><table><tr><td><strong>TimeShower:nGammaToLepton </td><td></td><td> <input type="text" name="28" value="3" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)</td></tr></table>
522Number 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>.
526 
527
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
531Use of matrix element corrections where available; on/off = true/false.
532 
533
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
537Use of matrix element corrections also after the first emission,
538for dipole ends of the same system that did not yet radiate.
539Only has a meaning if <code>MEcorrections</code> above is
540switched on.
541 
542
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
546Azimuthal asymmetry induced by gluon polarization; on/off = true/false.
547 
548
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 &nbsp;&nbsp;(<code>default = <strong>on</strong></code>)<br/>
552In the decays of coloured resonances, say <i>t -> b W</i>, it is not
553possible to set up dipoles with matched colours. Originally the
554<i>b</i> radiator therefore has <i>W</i> as recoiler, and that
555choice is unique. Once a gluon has been radiated, however, it is
556possible either to have the unmatched colour (inherited by the gluon)
557still recoiling against the <i>W</i> (<code>off</code>), or else
558let it recoil against the <i>b</i> also for this dipole
559(<code>on</code>). Before version 8.160 the former was the only
560possibility, which could give unphysical radiation patterns. It is
561kept as an option to check backwards compatibility. The same issue
562exists for QED radiation, but obviously is less significant. Consider
563the example <i>W -> e nu</i>, where originally the <i>nu</i>
564takes the recoil. In the old (<code>off</code>) scheme the <i>nu</i>
565would remain recoiler, while in the new (<code>on</code>) instead
566each newly emitted photon becomes the new recoiler.
567 
568
569<input type="hidden" name="saved" value="1"/>
570
571<?php
572echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
573
574<table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
575</form>
576
577<?php
578
579if($_POST["saved"] == 1)
580{
581$filepath = $_POST["filepath"];
582$handle = fopen($filepath, 'a');
583
584if($_POST["1"] != "1")
585{
586$data = "TimeShower:pTmaxMatch = ".$_POST["1"]."\n";
587fwrite($handle,$data);
588}
589if($_POST["2"] != "1.0")
590{
591$data = "TimeShower:pTmaxFudge = ".$_POST["2"]."\n";
592fwrite($handle,$data);
593}
594if($_POST["3"] != "1.0")
595{
596$data = "TimeShower:pTmaxFudgeMPI = ".$_POST["3"]."\n";
597fwrite($handle,$data);
598}
599if($_POST["4"] != "0")
600{
601$data = "TimeShower:pTdampMatch = ".$_POST["4"]."\n";
602fwrite($handle,$data);
603}
604if($_POST["5"] != "1.0")
605{
606$data = "TimeShower:pTdampFudge = ".$_POST["5"]."\n";
607fwrite($handle,$data);
608}
609if($_POST["6"] != "0.1383")
610{
611$data = "TimeShower:alphaSvalue = ".$_POST["6"]."\n";
612fwrite($handle,$data);
613}
614if($_POST["7"] != "1")
615{
616$data = "TimeShower:alphaSorder = ".$_POST["7"]."\n";
617fwrite($handle,$data);
618}
619if($_POST["8"] != "1")
620{
621$data = "TimeShower:alphaEMorder = ".$_POST["8"]."\n";
622fwrite($handle,$data);
623}
624if($_POST["9"] != "1.")
625{
626$data = "TimeShower:renormMultFac = ".$_POST["9"]."\n";
627fwrite($handle,$data);
628}
629if($_POST["10"] != "1.")
630{
631$data = "TimeShower:factorMultFac = ".$_POST["10"]."\n";
632fwrite($handle,$data);
633}
634if($_POST["11"] != "0.4")
635{
636$data = "TimeShower:pTmin = ".$_POST["11"]."\n";
637fwrite($handle,$data);
638}
639if($_POST["12"] != "0.4")
640{
641$data = "TimeShower:pTminChgQ = ".$_POST["12"]."\n";
642fwrite($handle,$data);
643}
644if($_POST["13"] != "0.0005")
645{
646$data = "TimeShower:pTminChgL = ".$_POST["13"]."\n";
647fwrite($handle,$data);
648}
649if($_POST["14"] != "10.0")
650{
651$data = "TimeShower:mMaxGamma = ".$_POST["14"]."\n";
652fwrite($handle,$data);
653}
654if($_POST["15"] != "on")
655{
656$data = "TimeShower:interleave = ".$_POST["15"]."\n";
657fwrite($handle,$data);
658}
659if($_POST["16"] != "on")
660{
661$data = "TimeShower:allowBeamRecoil = ".$_POST["16"]."\n";
662fwrite($handle,$data);
663}
664if($_POST["17"] != "on")
665{
666$data = "TimeShower:dampenBeamRecoil = ".$_POST["17"]."\n";
667fwrite($handle,$data);
668}
669if($_POST["18"] != "off")
670{
671$data = "TimeShower:globalRecoil = ".$_POST["18"]."\n";
672fwrite($handle,$data);
673}
674if($_POST["19"] != "2")
675{
676$data = "TimeShower:nMaxGlobalRecoil = ".$_POST["19"]."\n";
677fwrite($handle,$data);
678}
679if($_POST["20"] != "1.")
680{
681$data = "TimeShower:octetOniumFraction = ".$_POST["20"]."\n";
682fwrite($handle,$data);
683}
684if($_POST["21"] != "2.")
685{
686$data = "TimeShower:octetOniumColFac = ".$_POST["21"]."\n";
687fwrite($handle,$data);
688}
689if($_POST["22"] != "on")
690{
691$data = "TimeShower:QCDshower = ".$_POST["22"]."\n";
692fwrite($handle,$data);
693}
694if($_POST["23"] != "5")
695{
696$data = "TimeShower:nGluonToQuark = ".$_POST["23"]."\n";
697fwrite($handle,$data);
698}
699if($_POST["24"] != "on")
700{
701$data = "TimeShower:QEDshowerByQ = ".$_POST["24"]."\n";
702fwrite($handle,$data);
703}
704if($_POST["25"] != "on")
705{
706$data = "TimeShower:QEDshowerByL = ".$_POST["25"]."\n";
707fwrite($handle,$data);
708}
709if($_POST["26"] != "on")
710{
711$data = "TimeShower:QEDshowerByGamma = ".$_POST["26"]."\n";
712fwrite($handle,$data);
713}
714if($_POST["27"] != "5")
715{
716$data = "TimeShower:nGammaToQuark = ".$_POST["27"]."\n";
717fwrite($handle,$data);
718}
719if($_POST["28"] != "3")
720{
721$data = "TimeShower:nGammaToLepton = ".$_POST["28"]."\n";
722fwrite($handle,$data);
723}
724if($_POST["29"] != "on")
725{
726$data = "TimeShower:MEcorrections = ".$_POST["29"]."\n";
727fwrite($handle,$data);
728}
729if($_POST["30"] != "on")
730{
731$data = "TimeShower:MEafterFirst = ".$_POST["30"]."\n";
732fwrite($handle,$data);
733}
734if($_POST["31"] != "on")
735{
736$data = "TimeShower:phiPolAsym = ".$_POST["31"]."\n";
737fwrite($handle,$data);
738}
739if($_POST["32"] != "on")
740{
741$data = "TimeShower:recoilToColoured = ".$_POST["32"]."\n";
742fwrite($handle,$data);
743}
744fclose($handle);
745}
746
747?>
748</body>
749</html>
750
751<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
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