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da0e9ce3 1//--------------------------------------------------------------------------
2//
3// Environment:
4// This software is part of the EvtGen package developed jointly
5// for the BaBar and CLEO collaborations. If you use all or part
6// of it, please give an appropriate acknowledgement.
7//
8// Copyright Information: See EvtGen/COPYRIGHT
9// Copyright (C) 1998 Caltech, UCSB
10//
11// Module: EvtbTosllAmp.cc
12//
13// Description: Routine to implement semileptonic decays to pseudo-scalar
14// mesons.
15//
16// Modification history:
17//
18// DJL April 17,1998 Module created
19//
20//------------------------------------------------------------------------
21//
22#include "EvtGenBase/EvtPatches.hh"
23#include "EvtGenBase/EvtPatches.hh"
24#include "EvtGenBase/EvtParticle.hh"
25#include "EvtGenBase/EvtGenKine.hh"
26#include "EvtGenBase/EvtPDL.hh"
27#include "EvtGenBase/EvtReport.hh"
28#include "EvtGenBase/EvtVector4C.hh"
29#include "EvtGenBase/EvtTensor4C.hh"
30#include "EvtGenBase/EvtDiracSpinor.hh"
31#include "EvtGenModels/EvtbTosllAmp.hh"
32#include "EvtGenBase/EvtId.hh"
33#include "EvtGenBase/EvtAmp.hh"
34#include "EvtGenBase/EvtScalarParticle.hh"
35#include "EvtGenBase/EvtVectorParticle.hh"
36#include "EvtGenBase/EvtDiLog.hh"
37
38double EvtbTosllAmp::CalcMaxProb( EvtId parent, EvtId meson,
39 EvtId lepton1, EvtId lepton2,
40 EvtbTosllFF *FormFactors,
41 double& poleSize) {
42
43 //This routine takes the arguements parent, meson, and lepton
44 //number, and a form factor model, and returns a maximum
45 //probability for this semileptonic form factor model. A
46 //brute force method is used. The 2D cos theta lepton and
47 //q2 phase space is probed.
48
49 //Start by declaring a particle at rest.
50
51 //It only makes sense to have a scalar parent. For now.
52 //This should be generalized later.
53
54 EvtScalarParticle *scalar_part;
55 EvtParticle *root_part;
56
57 scalar_part=new EvtScalarParticle;
58
59 //cludge to avoid generating random numbers!
60 scalar_part->noLifeTime();
61
62 EvtVector4R p_init;
63
64 p_init.set(EvtPDL::getMass(parent),0.0,0.0,0.0);
65 scalar_part->init(parent,p_init);
66 root_part=(EvtParticle *)scalar_part;
67 root_part->setDiagonalSpinDensity();
68
69 EvtParticle *daughter, *lep1, *lep2;
70
71 EvtAmp amp;
72
73 EvtId listdaug[3];
74 listdaug[0] = meson;
75 listdaug[1] = lepton1;
76 listdaug[2] = lepton2;
77
78 amp.init(parent,3,listdaug);
79
80 root_part->makeDaughters(3,listdaug);
81 daughter=root_part->getDaug(0);
82 lep1=root_part->getDaug(1);
83 lep2=root_part->getDaug(2);
84
85 //cludge to avoid generating random numbers!
86 daughter->noLifeTime();
87 lep1->noLifeTime();
88 lep2->noLifeTime();
89
90
91 //Initial particle is unpolarized, well it is a scalar so it is
92 //trivial
93 EvtSpinDensity rho;
94 rho.setDiag(root_part->getSpinStates());
95
96 double mass[3];
97
98 double m = root_part->mass();
99
100 EvtVector4R p4meson, p4lepton1, p4lepton2, p4w;
101 double q2max;
102
103 double q2, elepton, plepton;
104 int i,j;
105 double erho,prho,costl;
106
107 double maxfoundprob = 0.0;
108 double prob = -10.0;
109 int massiter;
110
111 double maxpole=0;
112
113 for (massiter=0;massiter<3;massiter++){
114
115 mass[0] = EvtPDL::getMeanMass(meson);
116 mass[1] = EvtPDL::getMeanMass(lepton1);
117 mass[2] = EvtPDL::getMeanMass(lepton2);
118 if ( massiter==1 ) {
119 mass[0] = EvtPDL::getMinMass(meson);
120 }
121 if ( massiter==2 ) {
122 mass[0] = EvtPDL::getMaxMass(meson);
123 if ( (mass[0]+mass[1]+mass[2])>m) mass[0]=m-mass[1]-mass[2]-0.00001;
124 }
125
126 q2max = (m-mass[0])*(m-mass[0]);
127
128 //loop over q2
129 //cout << "m " << m << "mass[0] " << mass[0] << " q2max "<< q2max << endl;
130 for (i=0;i<25;i++) {
131 //want to avoid picking up the tail of the photon propagator
132 q2 = ((i+1.5)*q2max)/26.0;
133
134 if (i==0) q2=4*(mass[1]*mass[1]);
135
136 erho = ( m*m + mass[0]*mass[0] - q2 )/(2.0*m);
137
138 prho = sqrt(erho*erho-mass[0]*mass[0]);
139
140 p4meson.set(erho,0.0,0.0,-1.0*prho);
141 p4w.set(m-erho,0.0,0.0,prho);
142
143 //This is in the W rest frame
144 elepton = (q2+mass[1]*mass[1])/(2.0*sqrt(q2));
145 plepton = sqrt(elepton*elepton-mass[1]*mass[1]);
146
147 double probctl[3];
148
149 for (j=0;j<3;j++) {
150
151 costl = 0.99*(j - 1.0);
152
153 //These are in the W rest frame. Need to boost out into
154 //the B frame.
155 p4lepton1.set(elepton,0.0,
156 plepton*sqrt(1.0-costl*costl),plepton*costl);
157 p4lepton2.set(elepton,0.0,
158 -1.0*plepton*sqrt(1.0-costl*costl),-1.0*plepton*costl);
159
160 EvtVector4R boost((m-erho),0.0,0.0,1.0*prho);
161 p4lepton1=boostTo(p4lepton1,boost);
162 p4lepton2=boostTo(p4lepton2,boost);
163
164 //Now initialize the daughters...
165
166 daughter->init(meson,p4meson);
167 lep1->init(lepton1,p4lepton1);
168 lep2->init(lepton2,p4lepton2);
169
170 CalcAmp(root_part,amp,FormFactors);
171
172 //Now find the probability at this q2 and cos theta lepton point
173 //and compare to maxfoundprob.
174
175 //Do a little magic to get the probability!!
176
177 //cout <<"amp:"<<amp.getSpinDensity()<<endl;
178
179 prob = rho.normalizedProb(amp.getSpinDensity());
180
181 //cout << "prob:"<<q2<<" "<<costl<<" "<<prob<<endl;
182
183 probctl[j]=prob;
184 }
185
186 //probclt contains prob at ctl=-1,0,1.
187 //prob=a+b*ctl+c*ctl^2
188
189 double a=probctl[1];
190 double b=0.5*(probctl[2]-probctl[0]);
191 double c=0.5*(probctl[2]+probctl[0])-probctl[1];
192
193 prob=probctl[0];
194 if (probctl[1]>prob) prob=probctl[1];
195 if (probctl[2]>prob) prob=probctl[2];
196
197 if (fabs(c)>1e-20){
198 double ctlx=-0.5*b/c;
199 if (fabs(ctlx)<1.0){
200 double probtmp=a+b*ctlx+c*ctlx*ctlx;
201 if (probtmp>prob) prob=probtmp;
202 }
203
204 }
205
206 //report(DEBUG,"EvtGen") << "prob,probctl:"<<prob<<" "
207 // << probctl[0]<<" "
208 // << probctl[1]<<" "
209 // << probctl[2]<<endl;
210
211 if (i==0) {
212 maxpole=prob;
213 continue;
214 }
215
216 if ( prob > maxfoundprob ) {
217 maxfoundprob = prob;
218 }
219
220 //cout << "q2,maxfoundprob:"<<q2<<" "<<maxfoundprob<<endl;
221
222 }
223 if ( EvtPDL::getWidth(meson) <= 0.0 ) {
224 //if the particle is narrow dont bother with changing the mass.
225 massiter = 4;
226 }
227
228 }
229
230 root_part->deleteTree();
231
232 poleSize=0.04*(maxpole/maxfoundprob)*4*(mass[1]*mass[1]);
233
234 //poleSize=0.002;
235
236 //cout <<"maxfoundprob,maxpole,poleSize:"<<maxfoundprob<<" "
237 // <<maxpole<<" "<<poleSize<<endl;
238
239 maxfoundprob *=1.15;
240
241 return maxfoundprob;
242
243}
244
245
246EvtComplex EvtbTosllAmp::GetC7Eff(double q2, bool nnlo)
247{
248
249 if (!nnlo) return -0.313;
250 double mbeff = 4.8;
251 double shat = q2/mbeff/mbeff;
252 double logshat;
253 logshat = log(shat);
254
255 double muscale;
256 muscale = 2.5;
257 double alphas;
258 alphas = 0.267;
259 double A7;
260 A7 = -0.353 + 0.023;
261 double A8;
262 A8 = -0.164;
da0e9ce3 263 double C1;
264 C1 = -0.697;
265 double C2;
266 C2 = 1.046;
da0e9ce3 267
268 double Lmu;
269 Lmu = log(muscale/mbeff);
270
271 EvtComplex uniti(0.0,1.0);
272
273 EvtComplex c7eff;
274 if (shat > 0.25)
275 {
276 c7eff = A7;
277 return c7eff;
278 }
279
da0e9ce3 280 // change energy scale to 5.0 for full NNLO calculation below shat = 0.25
281 muscale = 5.0;
282 alphas = 0.215;
283 A7 = -0.312 + 0.008;
284 A8 = -0.148;
da0e9ce3 285 C1 = -0.487;
286 C2 = 1.024;
da0e9ce3 287 Lmu = log(muscale/mbeff);
288
289 EvtComplex F71;
290 EvtComplex f71;
291 EvtComplex k7100(-0.68192,-0.074998);
292 EvtComplex k7101(0.0,0.0);
293 EvtComplex k7110(-0.23935,-0.12289);
294 EvtComplex k7111(0.0027424,0.019676);
295 EvtComplex k7120(-0.0018555,-0.175);
296 EvtComplex k7121(0.022864,0.011456);
297 EvtComplex k7130(0.28248,-0.12783);
298 EvtComplex k7131(0.029027,-0.0082265);
299 f71 = k7100 + k7101*logshat + shat*(k7110 + k7111*logshat) +
300 shat*shat*(k7120 + k7121*logshat) +
301 shat*shat*shat*(k7130 + k7131*logshat);
302 F71 = (-208.0/243.0)*Lmu + f71;
303
304 EvtComplex F72;
305 EvtComplex f72;
306 EvtComplex k7200(4.0915,0.44999);
307 EvtComplex k7201(0.0,0.0);
308 EvtComplex k7210(1.4361,0.73732);
309 EvtComplex k7211(-0.016454,-0.11806);
310 EvtComplex k7220(0.011133,1.05);
311 EvtComplex k7221(-0.13718,-0.068733);
312 EvtComplex k7230(-1.6949,0.76698);
313 EvtComplex k7231(-0.17416,0.049359);
314 f72 = k7200 + k7201*logshat + shat*(k7210 + k7211*logshat) +
315 shat*shat*(k7220 + k7221*logshat) +
316 shat*shat*shat*(k7230 + k7231*logshat);
317 F72 = (416.0/81.0)*Lmu + f72;
318
319 EvtComplex F78;
320 F78 = (-32.0/9.0)*Lmu + 8.0*EvtConst::pi*EvtConst::pi/27.0 + (-44.0/9.0)
321 + (-8.0*EvtConst::pi/9.0)*uniti +
322 (4.0/3.0*EvtConst::pi*EvtConst::pi - 40.0/3.0)*shat +
323 (32.0*EvtConst::pi*EvtConst::pi/9.0 - 316.0/9.0)*shat*shat +
324 (200.0*EvtConst::pi*EvtConst::pi/27.0 - 658.0/9.0)*shat*shat*shat +
325 (-8.0*logshat/9.0)*(shat + shat*shat + shat*shat*shat);
326
327 c7eff = A7 - alphas/(4.0*EvtConst::pi)*(C1*F71 + C2*F72 + A8*F78);
328
329 return c7eff;
330}
331
332
333EvtComplex EvtbTosllAmp::GetC9Eff(double q2, bool nnlo, bool btod)
334{
335
336 if (!nnlo) return 4.344;
337 double mbeff = 4.8;
338 double shat = q2/mbeff/mbeff;
339 double logshat;
340 logshat = log(shat);
341 double mchat = 0.29;
342
343
344 double muscale;
345 muscale = 2.5;
346 double alphas;
347 alphas = 0.267;
da0e9ce3 348 double A8;
349 A8 = -0.164;
350 double A9;
351 A9 = 4.287 + (-0.218);
da0e9ce3 352 double C1;
353 C1 = -0.697;
354 double C2;
355 C2 = 1.046;
356 double T9;
357 T9 = 0.114 + 0.280;
358 double U9;
359 U9 = 0.045 + 0.023;
360 double W9;
361 W9 = 0.044 + 0.016;
362
363 double Lmu;
364 Lmu = log(muscale/mbeff);
365
366
367 EvtComplex uniti(0.0,1.0);
368
369 EvtComplex hc;
370 double xarg;
371 xarg = 4.0*mchat/shat;
372 hc = -4.0/9.0*log(mchat*mchat) + 8.0/27.0 + 4.0*xarg/9.0;
373
374if (xarg < 1.0)
375 {
376 hc = hc - 2.0/9.0*(2.0 + xarg)*sqrt(fabs(1.0 - xarg))*
377 (log(fabs((sqrt(1.0 - xarg)+1.0)/(sqrt(1.0 - xarg) - 1.0))) -
378 uniti*EvtConst::pi);
379 }
380 else
381 {
382 hc = hc - 2.0/9.0*(2.0 + xarg)*sqrt(fabs(1.0 - xarg))*
383 2.0*atan(1.0/sqrt(xarg - 1.0));
384 }
385
386 EvtComplex h1;
387 xarg = 4.0/shat;
388 h1 = 8.0/27.0 + 4.0*xarg/9.0;
389 if (xarg < 1.0)
390 {
391 h1 = h1 - 2.0/9.0*(2.0 + xarg)*sqrt(fabs(1.0 - xarg))*
392 (log(fabs((sqrt(1.0 - xarg)+1.0)/(sqrt(1.0 - xarg) - 1.0))) -
393 uniti*EvtConst::pi);
394 }
395 else
396 {
397 h1 = h1 - 2.0/9.0*(2.0 + xarg)*sqrt(fabs(1.0 - xarg))*
398 2.0*atan(1.0/sqrt(xarg - 1.0));
399 }
400
401
402 EvtComplex h0;
403 h0 = 8.0/27.0 - 4.0*log(2.0)/9.0 + 4.0*uniti*EvtConst::pi/9.0;
404
405
406 // X=V_{ud}^* V_ub / V_{td}^* V_tb * (4/3 C_1 +C_2) * (h(\hat m_c^2, hat s)-
407 // h(\hat m_u^2, hat s))
408 EvtComplex Vudstar(1.0 - 0.2279*0.2279/2.0, 0.0);
409 EvtComplex Vub((0.118+0.273)/2.0, -1.0*(0.305+0.393)/2.0);
410 EvtComplex Vtdstar(1.0 - (0.118+0.273)/2.0,(0.305+0.393)/2.0);
411 EvtComplex Vtb(1.0,0.0);
412
413 EvtComplex Xd;
414 Xd = (Vudstar * Vub / Vtdstar * Vtb) * (4.0/3.0*C1 + C2) * (hc - h0);
415
416
417 EvtComplex c9eff=4.344;
418 if (shat > 0.25)
419 {
420 c9eff = A9 + T9*hc + U9*h1 + W9*h0;
421 if (btod)
422 {
423 c9eff += Xd;
424 }
425
426 return c9eff;
427 }
428
429 // change energy scale to 5.0 for full NNLO calculation below shat = 0.25
430 muscale = 5.0;
431 alphas = 0.215;
432 A9 = 4.174 + (-0.035);
433 C1 = -0.487;
434 C2 = 1.024;
435 A8 = -0.148;
436 T9 = 0.374 + 0.252;
437 U9 = 0.033 + 0.015;
438 W9 = 0.032 + 0.012;
439 Lmu = log(muscale/mbeff);
440
441 EvtComplex F91;
442 EvtComplex f91;
443 EvtComplex k9100(-11.973,0.16371);
444 EvtComplex k9101(-0.081271,-0.059691);
445 EvtComplex k9110(-28.432,-0.25044);
446 EvtComplex k9111(-0.040243,0.016442);
447 EvtComplex k9120(-57.114,-0.86486);
448 EvtComplex k9121(-0.035191,0.027909);
449 EvtComplex k9130(-128.8,-2.5243);
450 EvtComplex k9131(-0.017587,0.050639);
451 f91 = k9100 + k9101*logshat + shat*(k9110 + k9111*logshat) +
452 shat*shat*(k9120 + k9121*logshat) +
453 shat*shat*shat*(k9130 + k9131*logshat);
454 F91 = (-1424.0/729.0 + 16.0*uniti*EvtConst::pi/243.0
455 + 64.0/27.0*log(mchat))*Lmu - 16.0*Lmu*logshat/243.0 +
456 (16.0/1215.0 - 32.0/135.0/mchat/mchat)*Lmu*shat +
457 (4.0/2835.0 - 8.0/315.0/mchat/mchat/mchat/mchat)*Lmu*shat*shat +
458 (16.0/76545.0 - 32.0/8505.0/mchat/mchat/mchat/mchat/mchat/mchat)*
459 Lmu*shat*shat*shat -256.0*Lmu*Lmu/243.0 + f91;
460
461 EvtComplex F92;
462 EvtComplex f92;
463 EvtComplex k9200(6.6338,-0.98225);
464 EvtComplex k9201(0.48763,0.35815);
465 EvtComplex k9210(3.3585,1.5026);
466 EvtComplex k9211(0.24146,-0.098649);
467 EvtComplex k9220(-1.1906,5.1892);
468 EvtComplex k9221(0.21115,-0.16745);
469 EvtComplex k9230(-17.12,15.146);
470 EvtComplex k9231(0.10552,-0.30383);
471 f92 = k9200 + k9201*logshat + shat*(k9210 + k9211*logshat) +
472 shat*shat*(k9220 + k9221*logshat) +
473 shat*shat*shat*(k9230 + k9231*logshat);
474 F92 = (256.0/243.0 - 32.0*uniti*EvtConst::pi/81.0
475 - 128.0/9.0*log(mchat))*Lmu + 32.0*Lmu*logshat/81.0 +
476 (-32.0/405.0 + 64.0/45.0/mchat/mchat)*Lmu*shat +
477 (-8.0/945.0 + 16.0/105.0/mchat/mchat/mchat/mchat)*Lmu*shat*shat +
478 (-32.0/25515.0 + 64.0/2835.0/mchat/mchat/mchat/mchat/mchat/mchat)*
479 Lmu*shat*shat*shat + 512.0*Lmu*Lmu/81.0 + f92;
480
481 EvtComplex F98;
482 F98 = 104.0/9.0 - 32.0*EvtConst::pi*EvtConst::pi/27.0 +
483 (1184.0/27.0 - 40.0*EvtConst::pi*EvtConst::pi/9.0)*shat +
484 (14212.0/135.0 - 32.0*EvtConst::pi*EvtConst::pi/3.0)*shat*shat +
485 (193444.0/945.0 - 560.0*EvtConst::pi*EvtConst::pi/27.0)*shat*shat*shat +
486 16.0*logshat/9.0*(1.0 + shat + shat*shat + shat*shat*shat);
487
488 Xd = (Vudstar * Vub / Vtdstar * Vtb) * (4.0/3.0*C1 + C2) * (hc - h0);
489
490 c9eff = A9 + T9*hc + U9*h1 + W9*h0 -
491 alphas/(4.0*EvtConst::pi)*(C1*F91 + C2*F92 + A8*F98);
492 if (btod)
493 {
494 c9eff += Xd;
495 }
496
497 return c9eff;
498}
499
500EvtComplex EvtbTosllAmp::GetC10Eff(double /*q2*/, bool nnlo)
501{
502
503 if (!nnlo) return -4.669;
504 double A10;
505 A10 = -4.592 + 0.379;
506
507 EvtComplex c10eff;
508 c10eff = A10;
509
510 return c10eff;
511}
512
513double EvtbTosllAmp::dGdsProb(double mb, double ms, double ml,
514 double s)
515{
516 // Compute the decay probability density function given a value of s
517 // according to Ali's paper
518
519
520 double delta, lambda, prob;
521 double f1, f2, f3, f4;
522 double msh, mlh, sh;
523
524 mlh = ml / mb;
525 msh = ms / mb;
526 sh = s / (mb*mb);
527
528 EvtComplex c9eff = EvtbTosllAmp::GetC9Eff(sh*mb);
529 EvtComplex c7eff = EvtbTosllAmp::GetC7Eff(sh*mb);
530 EvtComplex c10eff = EvtbTosllAmp::GetC10Eff(sh*mb);
531
532 double alphas = 0.119/
533 (1 + 0.119*log(pow(4.8,2)/pow(91.1867,2))*23.0/12.0/EvtConst::pi);
534 double omega9 = -2.0/9.0*EvtConst::pi*EvtConst::pi - 4.0/3.0*EvtDiLog::DiLog(sh)
535 - 2.0/3.0*log(sh)*log(1.0-sh)
536 - (5.0+4.0*sh)/(3.0*(1.0+2.0*sh)) * log(1.0-sh)
537 - 2.0*sh*(1.0+sh)*(1.0-2.0*sh)
538 /(3.0*pow(1.0-sh,2)*(1.0+2.0*sh)) * log(sh)
539 + (5.0+9.0*sh-6.0*sh*sh)/(6.0*(1.0-sh)*(1.0+2.0*sh));
540 double eta9 = 1.0 + alphas*omega9/EvtConst::pi;
541 double omega7 = -8.0/3.0*log(4.8/mb)
542 -4.0/3.0*EvtDiLog::DiLog(sh)
543 -2.0/9.0*EvtConst::pi*EvtConst::pi
544 -2.0/3.0*log(sh)*log(1.0-sh)
545 -log(1-sh)*(8.0+sh)/(2.0+sh)/3.0
546 -2.0/3.0*sh*(2.0 - 2.0*sh - sh*sh)*log(sh)/pow((1.0 - sh),2)/(2.0 + sh)
547 -(16.0 - 11.0*sh - 17.0*sh*sh)/18.0/(2.0 + sh)/(1.0 - sh);
548 double eta7 = 1.0 + alphas*omega7/EvtConst::pi;
549
550 double omega79 = -4.0/3.0*log(4.8/mb)
551 -4.0/3.0*EvtDiLog::DiLog(sh)
552 -2.0/9.0*EvtConst::pi*EvtConst::pi
553 -2.0/3.0*log(sh)*log(1.0-sh)
554 -1.0/9.0*(2.0+7.0*sh)*log(1.0 - sh)/sh
555 -2.0/9.0*sh*(3.0 - 2.0*sh)*log(sh)/pow((1.0 - sh),2)
556 +1.0/18.0*(5.0 - 9.0*sh)/(1.0 - sh);
557 double eta79 = 1.0 + alphas*omega79/EvtConst::pi;
558
559 double c7c9 = abs(c7eff)*real(c9eff);
560 c7c9 *= pow(eta79,2);
561 double c7c7 = pow(abs(c7eff),2);
562 c7c7 *= pow(eta7,2);
563
564 double c9c9plusc10c10 = pow(abs(c9eff),2) + pow(abs(c10eff),2);
565 c9c9plusc10c10 *= pow(eta9,2);
566 double c9c9minusc10c10 = pow(abs(c9eff),2) - pow(abs(c10eff),2);
567 c9c9minusc10c10 *= pow(eta9,2);
568
569 lambda = 1.0 + sh*sh + pow(msh,4) - 2.0*(sh + sh*msh*msh + msh*msh);
570
571 f1 = pow(1.0-msh*msh,2) - sh*(1.0 + msh*msh);
572 f2 = 2.0*(1.0 + msh*msh) * pow(1.0-msh*msh,2)
573 - sh*(1.0 + 14.0*msh*msh + pow(msh,4)) - sh*sh*(1.0 + msh*msh);
574 f3 = pow(1.0-msh*msh,2) + sh*(1.0 + msh*msh) - 2.0*sh*sh
575 + lambda*2.0*mlh*mlh/sh;
576 f4 = 1.0 - sh + msh*msh;
577
578 delta = ( 12.0*c7c9*f1 + 4.0*c7c7*f2/sh ) * (1.0 + 2.0*mlh*mlh/sh)
579 + c9c9plusc10c10*f3
580 + 6.0*mlh*mlh*c9c9minusc10c10*f4;
581
582 prob = sqrt(lambda*(1.0 - 4.0*mlh*mlh/sh)) * delta;
583
584 return prob;
585}
586
587double EvtbTosllAmp::dGdsdupProb(double mb, double ms, double ml,
588 double s, double u)
589{
590 // Compute the decay probability density function given a value of s and u
591 // according to Ali's paper
592
593 double prob;
594 double f1sp, f2sp, f3sp;
595
596 double sh = s / (mb*mb);
597
598 EvtComplex c9eff = EvtbTosllAmp::GetC9Eff(sh*mb);
599 EvtComplex c7eff = EvtbTosllAmp::GetC7Eff(sh*mb);
600 EvtComplex c10eff = EvtbTosllAmp::GetC10Eff(sh*mb);
601
602 double alphas = 0.119/
603 (1 + 0.119*log(pow(4.8,2)/pow(91.1867,2))*23.0/12.0/EvtConst::pi);
604 double omega9 = - 2.0/9.0*EvtConst::pi*EvtConst::pi - 4.0/3.0*EvtDiLog::DiLog(sh)
605 - 2.0/3.0*log(sh)*log(1.0-sh)
606 - (5.0+4.0*sh)/(3.0*(1.0+2.0*sh)) * log(1.0-sh)
607 - 2.0*sh*(1.0+sh)*(1.0-2.0*sh)
608 /(3.0*pow(1.0-sh,2)*(1.0+2.0*sh)) * log(sh)
609 + (5.0+9.0*sh-6.0*sh*sh)/(6.0*(1.0-sh)*(1.0+2.0*sh));
610 double eta9 = 1.0 + alphas*omega9/EvtConst::pi;
611 double omega7 = -8.0/3.0*log(4.8/mb)
612 -4.0/3.0*EvtDiLog::DiLog(sh)
613 -2.0/9.0*EvtConst::pi*EvtConst::pi
614 -2.0/3.0*log(sh)*log(1.0-sh)
615 -log(1-sh)*(8.0+sh)/(2.0+sh)/3.0
616 -2.0/3.0*sh*(2.0 - 2.0*sh - sh*sh)*log(sh)/pow((1.0 - sh),2)/(2.0 + sh)
617 -(16.0 - 11.0*sh - 17.0*sh*sh)/18.0/(2.0 + sh)/(1.0 - sh);
618 double eta7 = 1.0 + alphas*omega7/EvtConst::pi;
619
620 double omega79 = -4.0/3.0*log(4.8/mb)
621 -4.0/3.0*EvtDiLog::DiLog(sh)
622 -2.0/9.0*EvtConst::pi*EvtConst::pi
623 -2.0/3.0*log(sh)*log(1.0-sh)
624 -1.0/9.0*(2.0+7.0*sh)*log(1.0 - sh)/sh
625 -2.0/9.0*sh*(3.0 - 2.0*sh)*log(sh)/pow((1.0 - sh),2)
626 +1.0/18.0*(5.0 - 9.0*sh)/(1.0 - sh);
627 double eta79 = 1.0 + alphas*omega79/EvtConst::pi;
628
629 double c7c9 = abs(c7eff)*real(c9eff);
630 c7c9 *= pow(eta79,2);
631 double c7c7 = pow(abs(c7eff),2);
632 c7c7 *= pow(eta7,2);
633
634 double c9c9plusc10c10 = pow(abs(c9eff),2) + pow(abs(c10eff),2);
635 c9c9plusc10c10 *= pow(eta9,2);
636 double c9c9minusc10c10 = pow(abs(c9eff),2) - pow(abs(c10eff),2);
637 c9c9minusc10c10 *= pow(eta9,2);
638 double c7c10 = abs(c7eff)*real(c10eff);
639 c7c10 *= eta7; c7c10 *= eta9;
640 double c9c10 = real(c9eff)*real(c10eff);
641 c9c10 *= pow(eta9,2);
642
643 f1sp = ( pow(mb*mb-ms*ms,2) - s*s) * c9c9plusc10c10
644 + 4.0*( pow(mb,4) - ms*ms*mb*mb - pow(ms,4)*(1.0 - ms*ms/(mb*mb))
645 - 8.0*s*ms*ms - s*s*(1.0 + ms*ms/(mb*mb) ))*mb*mb*c7c7/s
646 // kludged mass term
647 *(1.0 + 2.0*ml*ml/s)
648 - 8.0*(s*(mb*mb + ms*ms) - pow(mb*mb-ms*ms,2)) * c7c9
649 // kludged mass term
650 *(1.0 + 2.0*ml*ml/s);
651
652 f2sp = 4.0*s*c9c10 + 8.0*(mb*mb + ms*ms)*c7c10;
653 f3sp = - (c9c9plusc10c10)
654 + 4.0*(1.0 + pow(ms/mb,4)) * mb*mb*c7c7/s
655 // kludged mass term
656 *(1.0 + 2.0*ml*ml/s);
657
658 prob = (f1sp + f2sp*u + f3sp*u*u)/ pow(mb,3);
659
660 return prob;
661}
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