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FragmentationFlavZpT.cc
1 // FragmentationFlavZpT.cc is a part of the PYTHIA event generator.
2 // Copyright (C) 2012 Torbjorn Sjostrand.
3 // PYTHIA is licenced under the GNU GPL version 2, see COPYING for details.
4 // Please respect the MCnet Guidelines, see GUIDELINES for details.
5 
6 // Function definitions (not found in the header) for the
7 // StringFlav, StringZ and StringPT classes.
8 
9 #include "FragmentationFlavZpT.h"
10 
11 namespace Pythia8 {
12 
13 //==========================================================================
14 
15 // The StringFlav class.
16 
17 //--------------------------------------------------------------------------
18 
19 // Constants: could be changed here if desired, but normally should not.
20 // These are of technical nature, as described for each.
21 
22 // Offset for different meson multiplet id values.
23 const int StringFlav::mesonMultipletCode[6]
24  = { 1, 3, 10003, 10001, 20003, 5};
25 
26 // Clebsch-Gordan coefficients for baryon octet and decuplet are
27 // fixed once and for all, so only weighted sum needs to be edited.
28 // Order: ud0 + u, ud0 + s, uu1 + u, uu1 + d, ud1 + u, ud1 + s.
29 const double StringFlav::baryonCGOct[6]
30  = { 0.75, 0.5, 0., 0.1667, 0.0833, 0.1667};
31 const double StringFlav::baryonCGDec[6]
32  = { 0., 0., 1., 0.3333, 0.6667, 0.3333};
33 
34 //--------------------------------------------------------------------------
35 
36 // Initialize data members of the flavour generation.
37 
38 void StringFlav::init(Settings& settings, Rndm* rndmPtrIn) {
39 
40  // Save pointer.
41  rndmPtr = rndmPtrIn;
42 
43  // Basic parameters for generation of new flavour.
44  probQQtoQ = settings.parm("StringFlav:probQQtoQ");
45  probStoUD = settings.parm("StringFlav:probStoUD");
46  probSQtoQQ = settings.parm("StringFlav:probSQtoQQ");
47  probQQ1toQQ0 = settings.parm("StringFlav:probQQ1toQQ0");
48 
49  // Parameters derived from above.
50  probQandQQ = 1. + probQQtoQ;
51  probQandS = 2. + probStoUD;
52  probQandSinQQ = 2. + probSQtoQQ * probStoUD;
53  probQQ1corr = 3. * probQQ1toQQ0;
54  probQQ1corrInv = 1. / probQQ1corr;
55  probQQ1norm = probQQ1corr / (1. + probQQ1corr);
56 
57  // Parameters for normal meson production.
58  for (int i = 0; i < 4; ++i) mesonRate[i][0] = 1.;
59  mesonRate[0][1] = settings.parm("StringFlav:mesonUDvector");
60  mesonRate[1][1] = settings.parm("StringFlav:mesonSvector");
61  mesonRate[2][1] = settings.parm("StringFlav:mesonCvector");
62  mesonRate[3][1] = settings.parm("StringFlav:mesonBvector");
63 
64  // Parameters for L=1 excited-meson production.
65  mesonRate[0][2] = settings.parm("StringFlav:mesonUDL1S0J1");
66  mesonRate[1][2] = settings.parm("StringFlav:mesonSL1S0J1");
67  mesonRate[2][2] = settings.parm("StringFlav:mesonCL1S0J1");
68  mesonRate[3][2] = settings.parm("StringFlav:mesonBL1S0J1");
69  mesonRate[0][3] = settings.parm("StringFlav:mesonUDL1S1J0");
70  mesonRate[1][3] = settings.parm("StringFlav:mesonSL1S1J0");
71  mesonRate[2][3] = settings.parm("StringFlav:mesonCL1S1J0");
72  mesonRate[3][3] = settings.parm("StringFlav:mesonBL1S1J0");
73  mesonRate[0][4] = settings.parm("StringFlav:mesonUDL1S1J1");
74  mesonRate[1][4] = settings.parm("StringFlav:mesonSL1S1J1");
75  mesonRate[2][4] = settings.parm("StringFlav:mesonCL1S1J1");
76  mesonRate[3][4] = settings.parm("StringFlav:mesonBL1S1J1");
77  mesonRate[0][5] = settings.parm("StringFlav:mesonUDL1S1J2");
78  mesonRate[1][5] = settings.parm("StringFlav:mesonSL1S1J2");
79  mesonRate[2][5] = settings.parm("StringFlav:mesonCL1S1J2");
80  mesonRate[3][5] = settings.parm("StringFlav:mesonBL1S1J2");
81 
82  // Store sum over multiplets for Monte Carlo generation.
83  for (int i = 0; i < 4; ++i) mesonRateSum[i]
84  = mesonRate[i][0] + mesonRate[i][1] + mesonRate[i][2]
85  + mesonRate[i][3] + mesonRate[i][4] + mesonRate[i][5];
86 
87  // Parameters for uubar - ddbar - ssbar meson mixing.
88  for (int spin = 0; spin < 6; ++spin) {
89  double theta;
90  if (spin == 0) theta = settings.parm("StringFlav:thetaPS");
91  else if (spin == 1) theta = settings.parm("StringFlav:thetaV");
92  else if (spin == 2) theta = settings.parm("StringFlav:thetaL1S0J1");
93  else if (spin == 3) theta = settings.parm("StringFlav:thetaL1S1J0");
94  else if (spin == 4) theta = settings.parm("StringFlav:thetaL1S1J1");
95  else theta = settings.parm("StringFlav:thetaL1S1J2");
96  double alpha = (spin == 0) ? 90. - (theta + 54.7) : theta + 54.7;
97  alpha *= M_PI / 180.;
98  // Fill in (flavour, spin)-dependent probability of producing
99  // the lightest or the lightest two mesons of the nonet.
100  mesonMix1[0][spin] = 0.5;
101  mesonMix2[0][spin] = 0.5 * (1. + pow2(sin(alpha)));
102  mesonMix1[1][spin] = 0.;
103  mesonMix2[1][spin] = pow2(cos(alpha));
104  }
105 
106  // Additional suppression of eta and etaPrime.
107  etaSup = settings.parm("StringFlav:etaSup");
108  etaPrimeSup = settings.parm("StringFlav:etaPrimeSup");
109 
110  // Sum of baryon octet and decuplet weights.
111  decupletSup = settings.parm("StringFlav:decupletSup");
112  for (int i = 0; i < 6; ++i) baryonCGSum[i]
113  = baryonCGOct[i] + decupletSup * baryonCGDec[i];
114 
115  // Maximum SU(6) weight for ud0, ud1, uu1 types.
116  baryonCGMax[0] = max( baryonCGSum[0], baryonCGSum[1]);
117  baryonCGMax[1] = baryonCGMax[0];
118  baryonCGMax[2] = max( baryonCGSum[2], baryonCGSum[3]);
119  baryonCGMax[3] = baryonCGMax[2];
120  baryonCGMax[4] = max( baryonCGSum[4], baryonCGSum[5]);
121  baryonCGMax[5] = baryonCGMax[4];
122 
123  // Popcorn baryon parameters.
124  popcornRate = settings.parm("StringFlav:popcornRate");
125  popcornSpair = settings.parm("StringFlav:popcornSpair");
126  popcornSmeson = settings.parm("StringFlav:popcornSmeson");
127 
128  // Suppression of leading (= first-rank) baryons.
129  suppressLeadingB = settings.flag("StringFlav:suppressLeadingB");
130  lightLeadingBSup = settings.parm("StringFlav:lightLeadingBSup");
131  heavyLeadingBSup = settings.parm("StringFlav:heavyLeadingBSup");
132 
133  // Begin calculation of derived parameters for baryon production.
134 
135  // Enumerate distinguishable diquark types (in diquark first is popcorn q).
136  enum Diquark {ud0, ud1, uu1, us0, su0, us1, su1, ss1};
137 
138  // Maximum SU(6) weight by diquark type.
139  double barCGMax[8];
140  barCGMax[ud0] = baryonCGMax[0];
141  barCGMax[ud1] = baryonCGMax[4];
142  barCGMax[uu1] = baryonCGMax[2];
143  barCGMax[us0] = baryonCGMax[0];
144  barCGMax[su0] = baryonCGMax[0];
145  barCGMax[us1] = baryonCGMax[4];
146  barCGMax[su1] = baryonCGMax[4];
147  barCGMax[ss1] = baryonCGMax[2];
148 
149  // Diquark SU(6) survival = Sum_quark (quark tunnel weight) * SU(6).
150  double dMB[8];
151  dMB[ud0] = 2. * baryonCGSum[0] + probStoUD * baryonCGSum[1];
152  dMB[ud1] = 2. * baryonCGSum[4] + probStoUD * baryonCGSum[5];
153  dMB[uu1] = baryonCGSum[2] + (1. + probStoUD) * baryonCGSum[3];
154  dMB[us0] = (1. + probStoUD) * baryonCGSum[0] + baryonCGSum[1];
155  dMB[su0] = dMB[us0];
156  dMB[us1] = (1. + probStoUD) * baryonCGSum[4] + baryonCGSum[5];
157  dMB[su1] = dMB[us1];
158  dMB[ss1] = probStoUD * baryonCGSum[2] + 2. * baryonCGSum[3];
159  for (int i = 1; i < 8; ++i) dMB[i] = dMB[i] / dMB[0];
160 
161  // Tunneling factors for diquark production; only half a pair = sqrt.
162  double probStoUDroot = sqrt(probStoUD);
163  double probSQtoQQroot = sqrt(probSQtoQQ);
164  double probQQ1toQQ0root = sqrt(probQQ1toQQ0);
165  double qBB[8];
166  qBB[ud1] = probQQ1toQQ0root;
167  qBB[uu1] = probQQ1toQQ0root;
168  qBB[us0] = probSQtoQQroot;
169  qBB[su0] = probStoUDroot * probSQtoQQroot;
170  qBB[us1] = probQQ1toQQ0root * qBB[us0];
171  qBB[su1] = probQQ1toQQ0root * qBB[su0];
172  qBB[ss1] = probStoUDroot * pow2(probSQtoQQroot) * probQQ1toQQ0root;
173 
174  // spin * (vertex factor) * (half-tunneling factor above).
175  double qBM[8];
176  qBM[ud1] = 3. * qBB[ud1];
177  qBM[uu1] = 6. * qBB[uu1];
178  qBM[us0] = probStoUD * qBB[us0];
179  qBM[su0] = qBB[su0];
180  qBM[us1] = probStoUD * 3. * qBB[us1];
181  qBM[su1] = 3. * qBB[su1];
182  qBM[ss1] = probStoUD * 6. * qBB[ss1];
183 
184  // Combine above two into total diquark weight for q -> B Bbar.
185  for (int i = 1; i < 8; ++i) qBB[i] = qBB[i] * qBM[i];
186 
187  // Suppression from having strange popcorn meson.
188  qBM[us0] *= popcornSmeson;
189  qBM[us1] *= popcornSmeson;
190  qBM[ss1] *= popcornSmeson;
191 
192  // Suppression for a heavy quark of a diquark to fit into a baryon
193  // on the other side of popcorn meson: (0) s/u for q -> B M;
194  // (1) s/u for rank 0 diquark su -> M B; (2) ditto for s -> c/b.
195  double uNorm = 1. + qBM[ud1] + qBM[uu1] + qBM[us0] + qBM[us1];
196  scbBM[0] = (2. * (qBM[su0] + qBM[su1]) + qBM[ss1]) / uNorm;
197  scbBM[1] = scbBM[0] * popcornSpair * qBM[su0] / qBM[us0];
198  scbBM[2] = (1. + qBM[ud1]) * (2. + qBM[us0]) / uNorm;
199 
200  // Include maximum of Clebsch-Gordan coefficients.
201  for (int i = 1; i < 8; ++i) dMB[i] *= qBM[i];
202  for (int i = 1; i < 8; ++i) qBM[i] *= barCGMax[i] / barCGMax[0];
203  for (int i = 1; i < 8; ++i) qBB[i] *= barCGMax[i] / barCGMax[0];
204 
205  // Popcorn fraction for normal diquark production.
206  double qNorm = uNorm * popcornRate / 3.;
207  double sNorm = scbBM[0] * popcornSpair;
208  popFrac = qNorm * (1. + qBM[ud1] + qBM[uu1] + qBM[us0] + qBM[us1]
209  + sNorm * (qBM[su0] + qBM[su1] + 0.5 * qBM[ss1])) / (1. + qBB[ud1]
210  + qBB[uu1] + 2. * (qBB[us0] + qBB[us1]) + 0.5 * qBB[ss1]);
211 
212  // Popcorn fraction for rank 0 diquarks, depending on number of s quarks.
213  popS[0] = qNorm * qBM[ud1] / qBB[ud1];
214  popS[1] = qNorm * 0.5 * (qBM[us1] / qBB[us1]
215  + sNorm * qBM[su1] / qBB[su1]);
216  popS[2] = qNorm * sNorm * qBM[ss1] / qBB[ss1];
217 
218  // Recombine diquark weights to flavour and spin ratios. Second index:
219  // 0 = s/u popcorn quark ratio.
220  // 1, 2 = s/u ratio for vertex quark if popcorn quark is u/d or s.
221  // 3 = q/q' vertex quark ratio if popcorn quark is light and = q.
222  // 4, 5, 6 = (spin 1)/(spin 0) ratio for su, us and ud.
223 
224  // Case 0: q -> B B.
225  dWT[0][0] = (2. * (qBB[su0] + qBB[su1]) + qBB[ss1])
226  / (1. + qBB[ud1] + qBB[uu1] + qBB[us0] + qBB[us1]);
227  dWT[0][1] = 2. * (qBB[us0] + qBB[us1]) / (1. + qBB[ud1] + qBB[uu1]);
228  dWT[0][2] = qBB[ss1] / (qBB[su0] + qBB[su1]);
229  dWT[0][3] = qBB[uu1] / (1. + qBB[ud1] + qBB[uu1]);
230  dWT[0][4] = qBB[su1] / qBB[su0];
231  dWT[0][5] = qBB[us1] / qBB[us0];
232  dWT[0][6] = qBB[ud1];
233 
234  // Case 1: q -> B M B.
235  dWT[1][0] = (2. * (qBM[su0] + qBM[su1]) + qBM[ss1])
236  / (1. + qBM[ud1] + qBM[uu1] + qBM[us0] + qBM[us1]);
237  dWT[1][1] = 2. * (qBM[us0] + qBM[us1]) / (1. + qBM[ud1] + qBM[uu1]);
238  dWT[1][2] = qBM[ss1] / (qBM[su0] + qBM[su1]);
239  dWT[1][3] = qBM[uu1] / (1. + qBM[ud1] + qBM[uu1]);
240  dWT[1][4] = qBM[su1] / qBM[su0];
241  dWT[1][5] = qBM[us1] / qBM[us0];
242  dWT[1][6] = qBM[ud1];
243 
244  // Case 2: qq -> M B; diquark inside chain.
245  dWT[2][0] = (2. * (dMB[su0] + dMB[su1]) + dMB[ss1])
246  / (1. + dMB[ud1] + dMB[uu1] + dMB[us0] + dMB[us1]);
247  dWT[2][1] = 2. * (dMB[us0] + dMB[us1]) / (1. + dMB[ud1] + dMB[uu1]);
248  dWT[2][2] = dMB[ss1] / (dMB[su0] + dMB[su1]);
249  dWT[2][3] = dMB[uu1] / (1. + dMB[ud1] + dMB[uu1]);
250  dWT[2][4] = dMB[su1] / dMB[su0];
251  dWT[2][5] = dMB[us1] / dMB[us0];
252  dWT[2][6] = dMB[ud1];
253 
254 }
255 
256 //--------------------------------------------------------------------------
257 
258 // Pick a new flavour (including diquarks) given an incoming one.
259 
260 FlavContainer StringFlav::pick(FlavContainer& flavOld) {
261 
262  // Initial values for new flavour.
263  FlavContainer flavNew;
264  flavNew.rank = flavOld.rank + 1;
265 
266  // For original diquark assign popcorn quark and whether popcorn meson.
267  int idOld = abs(flavOld.id);
268  if (flavOld.rank == 0 && idOld > 1000) assignPopQ(flavOld);
269 
270  // Diquark exists, to be forced into baryon now.
271  bool doOldBaryon = (idOld > 1000 && flavOld.nPop == 0);
272  // Diquark exists, but do meson now.
273  bool doPopcornMeson = flavOld.nPop > 0;
274  // Newly created diquark gives baryon now, antibaryon later.
275  bool doNewBaryon = false;
276 
277  // Choose whether to generate a new meson or a new baryon.
278  if (!doOldBaryon && !doPopcornMeson && probQandQQ * rndmPtr->flat() > 1.) {
279  doNewBaryon = true;
280  if ((1. + popFrac) * rndmPtr->flat() > 1.) flavNew.nPop = 1;
281  }
282 
283  // Optional suppression of first-rank baryon.
284  if (flavOld.rank == 0 && doNewBaryon && suppressLeadingB) {
285  double leadingBSup = (idOld < 4) ? lightLeadingBSup : heavyLeadingBSup;
286  if (rndmPtr->flat() > leadingBSup) {
287  doNewBaryon = false;
288  flavNew.nPop = 0;
289  }
290  }
291 
292  // Single quark for new meson or for baryon where diquark already exists.
293  if (!doPopcornMeson && !doNewBaryon) {
294  flavNew.id = pickLightQ();
295  if ( (flavOld.id > 0 && flavOld.id < 9) || flavOld.id < -1000 )
296  flavNew.id = -flavNew.id;
297 
298  // Done for simple-quark case.
299  return flavNew;
300  }
301 
302  // Case: 0 = q -> B B, 1 = q -> B M B, 2 = qq -> M B.
303  int iCase = flavNew.nPop;
304  if (flavOld.nPop == 1) iCase = 2;
305 
306  // Flavour of popcorn quark (= q shared between B and Bbar).
307  if (doNewBaryon) {
308  double sPopWT = dWT[iCase][0];
309  if (iCase == 1) sPopWT *= scbBM[0] * popcornSpair;
310  double rndmFlav = (2. + sPopWT) * rndmPtr->flat();
311  flavNew.idPop = 1;
312  if (rndmFlav > 1.) flavNew.idPop = 2;
313  if (rndmFlav > 2.) flavNew.idPop = 3;
314  } else flavNew.idPop = flavOld.idPop;
315 
316  // Flavour of vertex quark.
317  double sVtxWT = dWT[iCase][1];
318  if (flavNew.idPop >= 3) sVtxWT = dWT[iCase][2];
319  if (flavNew.idPop > 3) sVtxWT *= 0.5 * (1. + 1./dWT[iCase][4]);
320  double rndmFlav = (2. + sVtxWT) * rndmPtr->flat();
321  flavNew.idVtx = 1;
322  if (rndmFlav > 1.) flavNew.idVtx = 2;
323  if (rndmFlav > 2.) flavNew.idVtx = 3;
324 
325  // Special case for light flavours, possibly identical.
326  if (flavNew.idPop < 3 && flavNew.idVtx < 3) {
327  flavNew.idVtx = flavNew.idPop;
328  if (rndmPtr->flat() > dWT[iCase][3]) flavNew.idVtx = 3 - flavNew.idPop;
329  }
330 
331  // Pick 2 * spin + 1.
332  int spin = 3;
333  if (flavNew.idVtx != flavNew.idPop) {
334  double spinWT = dWT[iCase][6];
335  if (flavNew.idVtx == 3) spinWT = dWT[iCase][5];
336  if (flavNew.idPop >= 3) spinWT = dWT[iCase][4];
337  if ((1. + spinWT) * rndmPtr->flat() < 1.) spin = 1;
338  }
339 
340  // Form outgoing diquark. Done.
341  flavNew.id = 1000 * max(flavNew.idVtx, flavNew.idPop)
342  + 100 * min(flavNew.idVtx, flavNew.idPop) + spin;
343  if ( (flavOld.id < 0 && flavOld.id > -9) || flavOld.id > 1000 )
344  flavNew.id = -flavNew.id;
345  return flavNew;
346 
347 }
348 
349 //--------------------------------------------------------------------------
350 
351 // Combine two flavours (including diquarks) to produce a hadron.
352 // The weighting of the combination may fail, giving output 0.
353 
354 int StringFlav::combine(FlavContainer& flav1, FlavContainer& flav2) {
355 
356  // Recognize largest and smallest flavour.
357  int id1Abs = abs(flav1.id);
358  int id2Abs = abs(flav2.id);
359  int idMax = max(id1Abs, id2Abs);
360  int idMin = min(id1Abs, id2Abs);
361 
362  // Construct a meson.
363  if (idMax < 9 || idMin > 1000) {
364 
365  // Popcorn meson: use only vertex quarks. Fail if none.
366  if (idMin > 1000) {
367  id1Abs = flav1.idVtx;
368  id2Abs = flav2.idVtx;
369  idMax = max(id1Abs, id2Abs);
370  idMin = min(id1Abs, id2Abs);
371  if (idMin == 0) return 0;
372  }
373 
374  // Pick spin state and preliminary code.
375  int flav = (idMax < 3) ? 0 : idMax - 2;
376  double rndmSpin = mesonRateSum[flav] * rndmPtr->flat();
377  int spin = -1;
378  do rndmSpin -= mesonRate[flav][++spin];
379  while (rndmSpin > 0.);
380  int idMeson = 100 * idMax + 10 * idMin + mesonMultipletCode[spin];
381 
382  // For nondiagonal mesons distinguish particle/antiparticle.
383  if (idMax != idMin) {
384  int sign = (idMax%2 == 0) ? 1 : -1;
385  if ( (idMax == id1Abs && flav1.id < 0)
386  || (idMax == id2Abs && flav2.id < 0) ) sign = -sign;
387  idMeson *= sign;
388 
389  // For light diagonal mesons include uubar - ddbar - ssbar mixing.
390  } else if (flav < 2) {
391  double rMix = rndmPtr->flat();
392  if (rMix < mesonMix1[flav][spin]) idMeson = 110;
393  else if (rMix < mesonMix2[flav][spin]) idMeson = 220;
394  else idMeson = 330;
395  idMeson += mesonMultipletCode[spin];
396 
397  // Additional suppression of eta and eta' may give failure.
398  if (idMeson == 221 && etaSup < rndmPtr->flat()) return 0;
399  if (idMeson == 331 && etaPrimeSup < rndmPtr->flat()) return 0;
400  }
401 
402  // Finished for mesons.
403  return idMeson;
404  }
405 
406  // SU(6) factors for baryon production may give failure.
407  int idQQ1 = idMax / 1000;
408  int idQQ2 = (idMax / 100) % 10;
409  int spinQQ = idMax % 10;
410  int spinFlav = spinQQ - 1;
411  if (spinFlav == 2 && idQQ1 != idQQ2) spinFlav = 4;
412  if (idMin != idQQ1 && idMin != idQQ2) spinFlav++;
413  if (baryonCGSum[spinFlav] < rndmPtr->flat() * baryonCGMax[spinFlav])
414  return 0;
415 
416  // Order quarks to form baryon. Pick spin.
417  int idOrd1 = max( idMin, max( idQQ1, idQQ2) );
418  int idOrd3 = min( idMin, min( idQQ1, idQQ2) );
419  int idOrd2 = idMin + idQQ1 + idQQ2 - idOrd1 - idOrd3;
420  int spinBar = (baryonCGSum[spinFlav] * rndmPtr->flat()
421  < baryonCGOct[spinFlav]) ? 2 : 4;
422 
423  // Distinguish Lambda- and Sigma-like.
424  bool LambdaLike = false;
425  if (spinBar == 2 && idOrd1 > idOrd2 && idOrd2 > idOrd3) {
426  LambdaLike = (spinQQ == 1);
427  if (idOrd1 != idMin && spinQQ == 1) LambdaLike = (rndmPtr->flat() < 0.25);
428  else if (idOrd1 != idMin) LambdaLike = (rndmPtr->flat() < 0.75);
429  }
430 
431  // Form baryon code and return with sign.
432  int idBaryon = (LambdaLike)
433  ? 1000 * idOrd1 + 100 * idOrd3 + 10 * idOrd2 + spinBar
434  : 1000 * idOrd1 + 100 * idOrd2 + 10 * idOrd3 + spinBar;
435  return (flav1.id > 0) ? idBaryon : -idBaryon;
436 
437 }
438 
439 //--------------------------------------------------------------------------
440 
441 // Assign popcorn quark inside an original (= rank 0) diquark.
442 
443 void StringFlav::assignPopQ(FlavContainer& flav) {
444 
445  // Safety check that intended to do something.
446  int idAbs = abs(flav.id);
447  if (flav.rank > 0 || idAbs < 1000) return;
448 
449  // Make choice of popcorn quark.
450  int id1 = (idAbs/1000)%10;
451  int id2 = (idAbs/100)%10;
452  double pop2WT = 1.;
453  if (id1 == 3) pop2WT = scbBM[1];
454  else if (id1 > 3) pop2WT = scbBM[2];
455  if (id2 == 3) pop2WT /= scbBM[1];
456  else if (id2 > 3) pop2WT /= scbBM[2];
457  // Agrees with Patrik code, but opposite to intention??
458  flav.idPop = ((1. + pop2WT) * rndmPtr->flat() > 1.) ? id2 : id1;
459  flav.idVtx = id1 + id2 - flav.idPop;
460 
461  // Also determine if to produce popcorn meson.
462  flav.nPop = 0;
463  double popWT = popS[0];
464  if (id1 == 3) popWT = popS[1];
465  if (id2 == 3) popWT = popS[2];
466  if (idAbs%10 == 1) popWT *= sqrt(probQQ1toQQ0);
467  if ((1. + popWT) * rndmPtr->flat() > 1.) flav.nPop = 1;
468 
469 }
470 
471 //--------------------------------------------------------------------------
472 
473 // Combine two quarks to produce a diquark.
474 // Normally according to production composition, but nonvanishing idHad
475 // means diquark from known hadron content, so use SU(6) wave fucntion.
476 
477 int StringFlav::makeDiquark(int id1, int id2, int idHad) {
478 
479  // Initial values.
480  int idMin = min( abs(id1), abs(id2));
481  int idMax = max( abs(id1), abs(id2));
482  int spin = 1;
483 
484  // Select spin of diquark formed from two valence quarks in proton.
485  // (More hadron cases??)
486  if (abs(idHad) == 2212) {
487  if (idMin == 1 && idMax == 2 && rndmPtr->flat() < 0.75) spin = 0;
488 
489  // Else select spin of diquark according to production composition.
490  } else {
491  if (idMin != idMax && rndmPtr->flat() > probQQ1norm) spin = 0;
492  }
493 
494  // Combined diquark code.
495  int idNewAbs = 1000 * idMax + 100 * idMin + 2 * spin + 1;
496  return (id1 > 0) ? idNewAbs : -idNewAbs;
497 
498 }
499 
500 //==========================================================================
501 
502 // The StringZ class.
503 
504 //--------------------------------------------------------------------------
505 
506 // Constants: could be changed here if desired, but normally should not.
507 // These are of technical nature, as described for each.
508 
509 // When a or c are close to special cases, default to these.
510 const double StringZ::CFROMUNITY = 0.01;
511 const double StringZ::AFROMZERO = 0.02;
512 const double StringZ::AFROMC = 0.01;
513 
514 // Do not take exponent of too large or small number.
515 const double StringZ::EXPMAX = 50.;
516 
517 //--------------------------------------------------------------------------
518 
519 // Initialize data members of the string z selection.
520 
521 void StringZ::init(Settings& settings, ParticleData& particleData,
522  Rndm* rndmPtrIn) {
523 
524  // Save pointer.
525  rndmPtr = rndmPtrIn;
526 
527  // c and b quark masses.
528  mc2 = pow2( particleData.m0(4));
529  mb2 = pow2( particleData.m0(5));
530 
531  // Paramaters of Lund/Bowler symmetric fragmentation function.
532  aLund = settings.parm("StringZ:aLund");
533  bLund = settings.parm("StringZ:bLund");
534  aExtraDiquark = settings.parm("StringZ:aExtraDiquark");
535  rFactC = settings.parm("StringZ:rFactC");
536  rFactB = settings.parm("StringZ:rFactB");
537  rFactH = settings.parm("StringZ:rFactH");
538 
539  // Flags and parameters of Peterson/SLAC fragmentation function.
540  usePetersonC = settings.flag("StringZ:usePetersonC");
541  usePetersonB = settings.flag("StringZ:usePetersonB");
542  usePetersonH = settings.flag("StringZ:usePetersonH");
543  epsilonC = settings.parm("StringZ:epsilonC");
544  epsilonB = settings.parm("StringZ:epsilonB");
545  epsilonH = settings.parm("StringZ:epsilonH");
546 
547  // Parameters for joining procedure.
548  stopM = settings.parm("StringFragmentation:stopMass");
549  stopNF = settings.parm("StringFragmentation:stopNewFlav");
550  stopS = settings.parm("StringFragmentation:stopSmear");
551 
552 }
553 
554 //--------------------------------------------------------------------------
555 
556 // Generate the fraction z that the next hadron will take,
557 // using either Lund/Bowler or, for heavy, Peterson/SLAC functions.
558 // Note: for a heavy new coloured particle we assume pT negligible.
559 
560 double StringZ::zFrag( int idOld, int idNew, double mT2) {
561 
562  // Find if old or new flavours correspond to diquarks.
563  int idOldAbs = abs(idOld);
564  int idNewAbs = abs(idNew);
565  bool isOldDiquark = (idOldAbs > 1000 && idOldAbs < 10000);
566  bool isNewDiquark = (idNewAbs > 1000 && idNewAbs < 10000);
567 
568  // Find heaviest quark in fragmenting parton/diquark.
569  int idFrag = idOldAbs;
570  if (isOldDiquark) idFrag = max( idOldAbs / 1000, (idOldAbs / 100) % 10);
571 
572  // Use Peterson where explicitly requested for heavy flavours.
573  if (idFrag == 4 && usePetersonC) return zPeterson( epsilonC);
574  if (idFrag == 5 && usePetersonB) return zPeterson( epsilonB);
575  if (idFrag > 5 && usePetersonH) {
576  double epsilon = epsilonH * mb2 / mT2;
577  return zPeterson( epsilon);
578  }
579 
580  // Shape parameters of Lund symmetric fragmentation function.
581  double aShape = aLund;
582  if (isOldDiquark) aShape += aExtraDiquark;
583  double bShape = bLund * mT2;
584  double cShape = 1.;
585  if (isOldDiquark) cShape -= aExtraDiquark;
586  if (isNewDiquark) cShape += aExtraDiquark;
587  if (idFrag == 4) cShape += rFactC * bLund * mc2;
588  if (idFrag == 5) cShape += rFactB * bLund * mb2;
589  if (idFrag > 5) cShape += rFactH * bLund * mT2;
590  return zLund( aShape, bShape, cShape);
591 
592 }
593 
594 //--------------------------------------------------------------------------
595 
596 // Generate a random z according to the Lund/Bowler symmetric
597 // fragmentation function f(z) = (1 -z)^a * exp(-b/z) / z^c.
598 // Normalized so that f(z_max) = 1 it can also be written as
599 // f(z) = exp( a * ln( (1 - z) / (1 - z_max) ) + b * (1/z_max - 1/z)
600 // + c * ln(z_max/z) ).
601 
602 double StringZ::zLund( double a, double b, double c) {
603 
604  // Special cases for c = 1, a = 0 and a = c.
605  bool cIsUnity = (abs( c - 1.) < CFROMUNITY);
606  bool aIsZero = (a < AFROMZERO);
607  bool aIsC = (abs(a - c) < AFROMC);
608 
609  // Determine position of maximum.
610  double zMax;
611  if (aIsZero) zMax = (c > b) ? b / c : 1.;
612  else if (aIsC) zMax = b / (b + c);
613  else { zMax = 0.5 * (b + c - sqrt( pow2(b - c) + 4. * a * b)) / (c - a);
614  if (zMax > 0.9999 && b > 100.) zMax = min(zMax, 1. - a / b); }
615 
616  // Subdivide z range if distribution very peaked near either endpoint.
617  bool peakedNearZero = (zMax < 0.1);
618  bool peakedNearUnity = (zMax > 0.85 && b > 1.);
619 
620  // Find integral of trial function everywhere bigger than f.
621  // (Dummy start values.)
622  double fIntLow = 1.;
623  double fIntHigh = 1.;
624  double fInt = 2.;
625  double zDiv = 0.5;
626  double zDivC = 0.5;
627  // When z_max is small use that f(z)
628  // < 1 for z < z_div = 2.75 * z_max,
629  // < (z_div/z)^c for z > z_div (=> logarithm for c = 1, else power).
630  if (peakedNearZero) {
631  zDiv = 2.75 * zMax;
632  fIntLow = zDiv;
633  if (cIsUnity) fIntHigh = -zDiv * log(zDiv);
634  else { zDivC = pow( zDiv, 1. - c);
635  fIntHigh = zDiv * (1. - 1./zDivC) / (c - 1.);}
636  fInt = fIntLow + fIntHigh;
637  // When z_max large use that f(z)
638  // < exp( b * (z - z_div) ) for z < z_div with z_div messy expression,
639  // < 1 for z > z_div.
640  // To simplify expressions the integral is extended to z = -infinity.
641  } else if (peakedNearUnity) {
642  double rcb = sqrt(4. + pow2(c / b));
643  zDiv = rcb - 1./zMax - (c / b) * log( zMax * 0.5 * (rcb + c / b) );
644  if (!aIsZero) zDiv += (a/b) * log(1. - zMax);
645  zDiv = min( zMax, max(0., zDiv));
646  fIntLow = 1. / b;
647  fIntHigh = 1. - zDiv;
648  fInt = fIntLow + fIntHigh;
649  }
650 
651  // Choice of z, preweighted for peaks at low or high z. (Dummy start values.)
652  double z = 0.5;
653  double fPrel = 1.;
654  double fVal = 1.;
655  do {
656  // Choice of z flat good enough for distribution peaked in the middle;
657  // if not this z can be reused as a random number in general.
658  z = rndmPtr->flat();
659  fPrel = 1.;
660  // When z_max small use flat below z_div and 1/z^c above z_div.
661  if (peakedNearZero) {
662  if (fInt * rndmPtr->flat() < fIntLow) z = zDiv * z;
663  else if (cIsUnity) {z = pow( zDiv, z); fPrel = zDiv / z;}
664  else { z = pow( zDivC + (1. - zDivC) * z, 1. / (1. - c) );
665  fPrel = pow( zDiv / z, c); }
666  // When z_max large use exp( b * (z -z_div) ) below z_div
667  // and flat above it.
668  } else if (peakedNearUnity) {
669  if (fInt * rndmPtr->flat() < fIntLow) {
670  z = zDiv + log(z) / b;
671  fPrel = exp( b * (z - zDiv) );
672  } else z = zDiv + (1. - zDiv) * z;
673  }
674 
675  // Evaluate actual f(z) (if in physical range) and correct.
676  if (z > 0 && z < 1) {
677  double fExp = b * (1. / zMax - 1. / z)+ c * log(zMax / z);
678  if (!aIsZero) fExp += a * log( (1. - z) / (1. - zMax) );
679  fVal = exp( max( -EXPMAX, min( EXPMAX, fExp) ) ) ;
680  } else fVal = 0.;
681  } while (fVal < rndmPtr->flat() * fPrel);
682 
683  // Done.
684  return z;
685 
686 }
687 
688 //--------------------------------------------------------------------------
689 
690 // Generate a random z according to the Peterson/SLAC formula
691 // f(z) = 1 / ( z * (1 - 1/z - epsilon/(1-z))^2 )
692 // = z * (1-z)^2 / ((1-z)^2 + epsilon * z)^2.
693 
694 double StringZ::zPeterson( double epsilon) {
695 
696  double z, fVal;
697 
698  // For large epsilon pick z flat and reject,
699  // knowing that 4 * epsilon * f(z) < 1 everywhere.
700  if (epsilon > 0.01) {
701  do {
702  z = rndmPtr->flat();
703  fVal = 4. * epsilon * z * pow2(1. - z)
704  / pow2( pow2(1. - z) + epsilon * z);
705  } while (fVal < rndmPtr->flat());
706  return z;
707  }
708 
709  // Else split range, using that 4 * epsilon * f(z)
710  // < 4 * epsilon / (1 - z)^2 for 0 < z < 1 - 2 * sqrt(epsilon)
711  // < 1 for 1 - 2 * sqrt(epsilon) < z < 1
712  double epsRoot = sqrt(epsilon);
713  double epsComb = 0.5 / epsRoot - 1.;
714  double fIntLow = 4. * epsilon * epsComb;
715  double fInt = fIntLow + 2. * epsRoot;
716  do {
717  if (rndmPtr->flat() * fInt < fIntLow) {
718  z = 1. - 1. / (1. + rndmPtr->flat() * epsComb);
719  fVal = z * pow2( pow2(1. - z) / (pow2(1. - z) + epsilon * z) );
720  } else {
721  z = 1. - 2. * epsRoot * rndmPtr->flat();
722  fVal = 4. * epsilon * z * pow2(1. - z)
723  / pow2( pow2(1. - z) + epsilon * z);
724  }
725  } while (fVal < rndmPtr->flat());
726  return z;
727 
728 }
729 
730 //==========================================================================
731 
732 // The StringPT class.
733 
734 //--------------------------------------------------------------------------
735 
736 // Constants: could be changed here if desired, but normally should not.
737 // These are of technical nature, as described for each.
738 
739 // To avoid division by zero one must have sigma > 0.
740 const double StringPT::SIGMAMIN = 0.2;
741 
742 //--------------------------------------------------------------------------
743 
744 // Initialize data members of the string pT selection.
745 
746 void StringPT::init(Settings& settings, ParticleData& , Rndm* rndmPtrIn) {
747 
748  // Save pointer.
749  rndmPtr = rndmPtrIn;
750 
751  // Parameters of the pT width and enhancement.
752  double sigma = settings.parm("StringPT:sigma");
753  sigmaQ = sigma / sqrt(2.);
754  enhancedFraction = settings.parm("StringPT:enhancedFraction");
755  enhancedWidth = settings.parm("StringPT:enhancedWidth");
756 
757  // Parameter for pT suppression in MiniStringFragmentation.
758  sigma2Had = 2. * pow2( max( SIGMAMIN, sigma) );
759 
760 }
761 
762 //--------------------------------------------------------------------------
763 
764 // Generate Gaussian pT such that <p_x^2> = <p_x^2> = sigma^2 = width^2/2,
765 // but with small fraction multiplied up to a broader spectrum.
766 
767 pair<double, double> StringPT::pxy() {
768 
769  double sigma = sigmaQ;
770  if (rndmPtr->flat() < enhancedFraction) sigma *= enhancedWidth;
771  pair<double, double> gauss2 = rndmPtr->gauss2();
772  return pair<double, double>(sigma * gauss2.first, sigma * gauss2.second);
773 
774 }
775 
776 //==========================================================================
777 
778 } // end namespace Pythia8
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