Line data Source code
1 :
2 : //////////////////////////////////////////////////////////////////////
3 : //
4 : // Module: EvtVubBLNP.cc
5 : //
6 : // Description: Modeled on Riccardo Faccini's EvtVubNLO module
7 : //
8 : // tripleDiff from BLNP's notebook (based on BLNP4, hep-ph/0504071)
9 : //
10 : //////////////////////////////////////////////////////////////////
11 :
12 : #include "EvtGenBase/EvtPatches.hh"
13 : #include <stdlib.h>
14 : #include "EvtGenBase/EvtParticle.hh"
15 : #include "EvtGenBase/EvtGenKine.hh"
16 : #include "EvtGenBase/EvtPDL.hh"
17 : #include "EvtGenBase/EvtReport.hh"
18 : #include "EvtGenModels/EvtVubBLNP.hh"
19 : #include <string>
20 : #include "EvtGenBase/EvtVector4R.hh"
21 : #include "EvtGenModels/EvtItgSimpsonIntegrator.hh"
22 : #include "EvtGenModels/EvtItgPtrFunction.hh"
23 : #include "EvtGenBase/EvtRandom.hh"
24 : #include "EvtGenModels/EvtPFermi.hh"
25 :
26 : // For incomplete gamma function
27 : #include "math.h"
28 : #include "signal.h"
29 : #define ITMAX 100
30 : #define EPS 3.0e-7
31 : #define FPMIN 1.0e-30
32 :
33 : using std::cout;
34 : using std::endl;
35 :
36 0 : EvtVubBLNP::~EvtVubBLNP() {
37 0 : }
38 :
39 : std::string EvtVubBLNP::getName(){
40 0 : return "VUB_BLNP";
41 : }
42 :
43 : EvtDecayBase *EvtVubBLNP::clone() {
44 :
45 0 : return new EvtVubBLNP;
46 :
47 0 : }
48 :
49 : void EvtVubBLNP::init() {
50 :
51 : // get parameters (declared in the header file)
52 :
53 : // Input parameters
54 0 : mBB = 5.2792;
55 0 : lambda2 = 0.12;
56 :
57 : // Shape function parameters
58 0 : b = getArg(0);
59 0 : Lambda = getArg(1);
60 0 : Ecut = 1.8;
61 0 : wzero = mBB - 2*Ecut;
62 :
63 : // SF and SSF modes
64 0 : itype = (int)getArg(5);
65 0 : dtype = getArg(5);
66 0 : isubl = (int)getArg(6);
67 :
68 : // flags
69 0 : flag1 = (int)getArg(7);
70 0 : flag2 = (int)getArg(8);
71 0 : flag3 = (int)getArg(9);
72 :
73 : // Quark mass
74 0 : mb = 4.61;
75 :
76 :
77 : // hidden parameter what and SF stuff
78 : const double xlow = 0;
79 0 : const double xhigh = mBB;
80 : const int aSize = 10000;
81 0 : EvtPFermi pFermi(Lambda,b);
82 : // pf is the cumulative distribution normalized to 1.
83 0 : _pf.resize(aSize);
84 0 : for(int i=0;i<aSize;i++){
85 0 : double what = xlow + (double)(i+0.5)/((double)aSize)*(xhigh-xlow);
86 0 : if ( i== 0 )
87 0 : _pf[i] = pFermi.getSFBLNP(what);
88 : else
89 0 : _pf[i] = _pf[i-1] + pFermi.getSFBLNP(what);
90 0 : }
91 0 : for (size_t i=0; i<_pf.size(); i++) {
92 0 : _pf[i]/=_pf[_pf.size()-1];
93 : }
94 :
95 :
96 :
97 : // Matching scales
98 0 : muh = mBB*getArg(2); // 0.5
99 0 : mui = getArg(3); // 1.5
100 0 : mubar = getArg(4); // 1.5
101 :
102 : // Perturbative quantities
103 0 : CF = 4.0/3.0;
104 0 : CA = 3.0;
105 : double nf = 4.0;
106 :
107 0 : beta0 = 11.0/3.0*CA - 2.0/3.0*nf;
108 0 : beta1 = 34.0/3.0*CA*CA - 10.0/3.0*CA*nf - 2.0*CF*nf;
109 0 : beta2 = 2857.0/54.0*CA*CA*CA + (CF*CF - 205.0/18.0*CF*CA - 1415.0/54.0*CA*CA)*nf + (11.0/9.0*CF + 79.0/54.0*CA)*nf*nf;
110 :
111 0 : zeta3 = 1.0 + 1/8.0 + 1/27.0 + 1/64.0;
112 :
113 0 : Gamma0 = 4*CF;
114 0 : Gamma1 = CF*( (268.0/9.0 - 4.0*M_PI*M_PI/3.0)*CA - 40.0/9.0*nf);
115 0 : Gamma2 = 16*CF*( (245.0/24.0 - 67.0/54.0*M_PI*M_PI + + 11.0/180.0*pow(M_PI,4) + 11.0/6.0*zeta3)*CA*CA* + (-209.0/108.0 + 5.0/27.0*M_PI*M_PI - 7.0/3.0*zeta3)*CA*nf + (-55.0/24.0 + 2*zeta3)*CF*nf - nf*nf/27.0);
116 :
117 0 : gp0 = -5.0*CF;
118 0 : gp1 = -8.0*CF*( (3.0/16.0 - M_PI*M_PI/4.0 + 3*zeta3)*CF + (1549.0/432.0 + 7.0/48.0*M_PI*M_PI - 11.0/4.0*zeta3)*CA - (125.0/216.0 + M_PI*M_PI/24.0)*nf );
119 :
120 : // Lbar and mupisq
121 :
122 0 : Lbar = Lambda; // all models
123 0 : mupisq = 3*Lambda*Lambda/b;
124 0 : if (itype == 1) mupisq = 3*Lambda*Lambda/b;
125 0 : if (itype == 2) mupisq = 3*Lambda*Lambda*(Gamma(1+0.5*b)*Gamma(0.5*b)/pow( Gamma(0.5 + 0.5*b), 2) - 1);
126 :
127 : // moment2 for SSFs
128 0 : moment2 = pow(0.3,3);
129 :
130 : // inputs for total rate (T for Total); use BLNP notebook defaults
131 0 : flagpower = 1;
132 0 : flag2loop = 1;
133 :
134 : // stuff for the integrator
135 0 : maxLoop = 20;
136 : //precision = 1.0e-3;
137 0 : precision = 2.0e-2;
138 :
139 : // vector of global variables, to pass to static functions (which can't access globals);
140 0 : gvars.push_back(0.0); // 0
141 0 : gvars.push_back(0.0); // 1
142 0 : gvars.push_back(mui); // 2
143 0 : gvars.push_back(b); // 3
144 0 : gvars.push_back(Lambda); // 4
145 0 : gvars.push_back(mBB); // 5
146 0 : gvars.push_back(mb); // 6
147 0 : gvars.push_back(wzero); // 7
148 0 : gvars.push_back(beta0); // 8
149 0 : gvars.push_back(beta1); // 9
150 0 : gvars.push_back(beta2); // 10
151 0 : gvars.push_back(dtype); // 11
152 :
153 : // check that there are 3 daughters and 10 arguments
154 0 : checkNDaug(3);
155 0 : checkNArg(10);
156 :
157 0 : }
158 :
159 : void EvtVubBLNP::initProbMax() {
160 0 : noProbMax();
161 0 : }
162 :
163 : void EvtVubBLNP::decay(EvtParticle *Bmeson) {
164 :
165 : int j;
166 :
167 : EvtParticle *xuhad, *lepton, *neutrino;
168 0 : EvtVector4R p4;
169 : double Pp, Pm, Pl, pdf, EX, sh, El, ml, mpi, ratemax;
170 :
171 : double xhigh, xlow, what;
172 :
173 0 : Bmeson->initializePhaseSpace(getNDaug(), getDaugs());
174 :
175 0 : xuhad = Bmeson->getDaug(0);
176 0 : lepton = Bmeson->getDaug(1);
177 0 : neutrino = Bmeson ->getDaug(2);
178 :
179 0 : mBB = Bmeson->mass();
180 0 : ml = lepton->mass();
181 :
182 :
183 :
184 : // get SF value
185 : xlow = 0;
186 0 : xhigh = mBB;
187 : // the case for alphas = 0 is not considered
188 0 : what = 2*xhigh;
189 0 : while( what > xhigh || what < xlow ) {
190 0 : what = findBLNPWhat();
191 0 : what = xlow + what*(xhigh-xlow);
192 : }
193 :
194 :
195 :
196 : bool tryit = true;
197 :
198 0 : while (tryit) {
199 :
200 : // generate pp between 0 and
201 : // Flat(min, max) gives R(max - min) + min, where R = random btwn 0 and 1
202 :
203 0 : Pp = EvtRandom::Flat(0, mBB); // P+ = EX - |PX|
204 0 : Pl = EvtRandom::Flat(0, mBB); // mBB - 2El
205 0 : Pm = EvtRandom::Flat(0, mBB); // P- = EX + |PX|
206 :
207 0 : sh = Pm*Pp;
208 0 : EX = 0.5*(Pm + Pp);
209 0 : El = 0.5*(mBB - Pl);
210 :
211 : // Need maximum rate. Waiting for Mr. Paz to give it to me.
212 : // Meanwhile, use this.
213 : ratemax = 3.0; // From trial and error - most events below 3.0
214 :
215 : // kinematic bounds (Eq. 2)
216 : mpi = 0.14;
217 0 : if ((Pp > 0)&&(Pp <= Pl)&&(Pl <= Pm)&&(Pm < mBB)&&(El > ml)&&(sh > 4*mpi*mpi)) {
218 :
219 : // Probability of pass proportional to PDF
220 0 : pdf = rate3(Pp, Pl, Pm);
221 0 : double testRan = EvtRandom::Flat(0., ratemax);
222 0 : if (pdf >= testRan) tryit = false;
223 0 : }
224 : }
225 : // o.k. we have the three kineamtic variables
226 : // now calculate a flat cos Theta_H [-1,1] distribution of the
227 : // hadron flight direction w.r.t the B flight direction
228 : // because the B is a scalar and should decay isotropic.
229 : // Then chose a flat Phi_H [0,2Pi] w.r.t the B flight direction
230 : // and and a flat Phi_L [0,2Pi] in the W restframe w.r.t the
231 : // W flight direction.
232 :
233 0 : double ctH = EvtRandom::Flat(-1,1);
234 0 : double phH = EvtRandom::Flat(0,2*M_PI);
235 0 : double phL = EvtRandom::Flat(0,2*M_PI);
236 :
237 : // now compute the four vectors in the B Meson restframe
238 :
239 : double ptmp,sttmp;
240 : // calculate the hadron 4 vector in the B Meson restframe
241 :
242 0 : sttmp = sqrt(1-ctH*ctH);
243 0 : ptmp = sqrt(EX*EX-sh);
244 0 : double pHB[4] = {EX,ptmp*sttmp*cos(phH),ptmp*sttmp*sin(phH),ptmp*ctH};
245 0 : p4.set(pHB[0],pHB[1],pHB[2],pHB[3]);
246 0 : xuhad->init( getDaug(0), p4);
247 :
248 :
249 : bool _storeWhat(true);
250 :
251 0 : if (_storeWhat ) {
252 : // cludge to store the hidden parameter what with the decay;
253 : // the lifetime of the Xu is abused for this purpose.
254 : // tau = 1 ps corresponds to ctau = 0.3 mm -> in order to
255 : // stay well below BaBars sensitivity we take what/(10000 GeV).
256 : // To extract what back from the StdHepTrk its necessary to get
257 : // delta_ctau = Xu->decayVtx()->point().distanceTo(XuDaughter->decayVtx()->point());
258 : //
259 : // what = delta_ctau * 100000 * Mass_Xu/Momentum_Xu
260 : //
261 0 : xuhad->setLifetime(what/10000.);
262 0 : }
263 :
264 :
265 : // calculate the W 4 vector in the B Meson restrframe
266 :
267 : double apWB = ptmp;
268 0 : double pWB[4] = {mBB-EX,-pHB[1],-pHB[2],-pHB[3]};
269 :
270 : // first go in the W restframe and calculate the lepton and
271 : // the neutrino in the W frame
272 :
273 0 : double mW2 = mBB*mBB + sh - 2*mBB*EX;
274 0 : double beta = ptmp/pWB[0];
275 0 : double gamma = pWB[0]/sqrt(mW2);
276 :
277 0 : double pLW[4];
278 :
279 0 : ptmp = (mW2-ml*ml)/2/sqrt(mW2);
280 0 : pLW[0] = sqrt(ml*ml + ptmp*ptmp);
281 :
282 0 : double ctL = (El - gamma*pLW[0])/beta/gamma/ptmp;
283 0 : if ( ctL < -1 ) ctL = -1;
284 0 : if ( ctL > 1 ) ctL = 1;
285 0 : sttmp = sqrt(1-ctL*ctL);
286 :
287 : // eX' = eZ x eW
288 0 : double xW[3] = {-pWB[2],pWB[1],0};
289 : // eZ' = eW
290 0 : double zW[3] = {pWB[1]/apWB,pWB[2]/apWB,pWB[3]/apWB};
291 :
292 0 : double lx = sqrt(xW[0]*xW[0]+xW[1]*xW[1]);
293 0 : for (j=0;j<2;j++)
294 0 : xW[j] /= lx;
295 :
296 : // eY' = eZ' x eX'
297 0 : double yW[3] = {-pWB[1]*pWB[3],-pWB[2]*pWB[3],pWB[1]*pWB[1]+pWB[2]*pWB[2]};
298 0 : double ly = sqrt(yW[0]*yW[0]+yW[1]*yW[1]+yW[2]*yW[2]);
299 0 : for (j=0;j<3;j++)
300 0 : yW[j] /= ly;
301 :
302 : // p_lep = |p_lep| * ( sin(Theta) * cos(Phi) * eX'
303 : // + sin(Theta) * sin(Phi) * eY'
304 : // + cos(Theta) * eZ')
305 0 : for (j=0;j<3;j++)
306 0 : pLW[j+1] = sttmp*cos(phL)*ptmp*xW[j]
307 0 : + sttmp*sin(phL)*ptmp*yW[j]
308 0 : + ctL *ptmp*zW[j];
309 :
310 : double apLW = ptmp;
311 :
312 : // boost them back in the B Meson restframe
313 :
314 0 : double appLB = beta*gamma*pLW[0] + gamma*ctL*apLW;
315 :
316 0 : ptmp = sqrt(El*El-ml*ml);
317 0 : double ctLL = appLB/ptmp;
318 :
319 0 : if ( ctLL > 1 ) ctLL = 1;
320 0 : if ( ctLL < -1 ) ctLL = -1;
321 :
322 0 : double pLB[4] = {El,0,0,0};
323 0 : double pNB[4] = {pWB[0]-El,0,0,0};
324 :
325 0 : for (j=1;j<4;j++) {
326 0 : pLB[j] = pLW[j] + (ctLL*ptmp - ctL*apLW)/apWB*pWB[j];
327 0 : pNB[j] = pWB[j] - pLB[j];
328 : }
329 :
330 0 : p4.set(pLB[0],pLB[1],pLB[2],pLB[3]);
331 0 : lepton->init( getDaug(1), p4);
332 :
333 0 : p4.set(pNB[0],pNB[1],pNB[2],pNB[3]);
334 0 : neutrino->init( getDaug(2), p4);
335 :
336 : return ;
337 :
338 0 : }
339 :
340 : double EvtVubBLNP::rate3(double Pp, double Pl, double Pm) {
341 :
342 : // rate3 in units of GF^2*Vub^2/pi^3
343 :
344 0 : double factor = 1.0/16*(mBB-Pp)*U1lo(muh, mui)*pow( (Pm - Pp)/(mBB - Pp), alo(muh, mui));
345 :
346 0 : double doneJS = DoneJS(Pp, Pm, mui);
347 0 : double done1 = Done1(Pp, Pm, mui);
348 0 : double done2 = Done2(Pp, Pm, mui);
349 0 : double done3 = Done3(Pp, Pm, mui);
350 :
351 : // The EvtSimpsonIntegrator returns zero for bad integrals.
352 : // So if any of the integrals are zero (ie bad), return zero.
353 : // This will cause pdf = 0, so the event will not pass.
354 : // I hope this will not introduce a bias.
355 0 : if (doneJS*done1*done2*done3 == 0.0) {
356 : //cout << "Integral failed: (Pp, Pm, Pl) = (" << Pp << ", " << Pm << ", " << Pl << ")" << endl;
357 0 : return 0.0;
358 : }
359 : // if (doneJS*done1*done2*done3 != 0.0) {
360 : // cout << "Integral OK: (Pp, Pm, Pl) = (" << Pp << ", " << Pm << ", " << Pl << ")" << endl;
361 : //}
362 :
363 0 : double f1 = F1(Pp, Pm, muh, mui, mubar, doneJS, done1);
364 0 : double f2 = F2(Pp, Pm, muh, mui, mubar, done3);
365 0 : double f3 = F3(Pp, Pm, muh, mui, mubar, done2);
366 0 : double answer = factor*( (mBB + Pl - Pp - Pm)*(Pm - Pl)*f1 + 2*(Pl - Pp)*(Pm - Pl)*f2 + (mBB - Pm)*(Pm - Pp)*f3 );
367 : return answer;
368 :
369 0 : }
370 :
371 : double EvtVubBLNP::F1(double Pp, double Pm, double muh, double mui, double mubar, double doneJS, double done1) {
372 :
373 0 : std::vector<double> vars(12);
374 0 : vars[0] = Pp;
375 0 : vars[1] = Pm;
376 0 : for (int j=2;j<12;j++) {vars[j] = gvars[j];}
377 :
378 0 : double y = (Pm - Pp)/(mBB - Pp);
379 0 : double ah = CF*alphas(muh, vars)/4/M_PI;
380 0 : double ai = CF*alphas(mui, vars)/4/M_PI;
381 0 : double abar = CF*alphas(mubar, vars)/4/M_PI;
382 0 : double lambda1 = -mupisq;
383 :
384 0 : double t1 = -4*ai/(Pp - Lbar)*(2*log((Pp - Lbar)/mui) + 1);
385 0 : double t2 = 1 + dU1nlo(muh, mui) + anlo(muh, mui)*log(y);
386 0 : double t3 = -4.0*pow(log(y*mb/muh),2) + 10.0*log(y*mb/muh) - 4.0*log(y) - 2.0*log(y)/(1-y) - 4.0*PolyLog(2, 1-y) - M_PI*M_PI/6.0 - 12.0;
387 0 : double t4 = 2*pow( log(y*mb*Pp/(mui*mui)), 2) - 3*log(y*mb*Pp/(mui*mui)) + 7 - M_PI*M_PI;
388 :
389 0 : double t5 = -wS(Pp) + 2*t(Pp) + (1.0/y - 1.0)*(u(Pp) - v(Pp));
390 0 : double t6 = -(lambda1 + 3.0*lambda2)/3.0 + 1.0/pow(y,2)*(4.0/3.0*lambda1 - 2.0*lambda2);
391 :
392 0 : double shapePp = Shat(Pp, vars);
393 :
394 0 : double answer = (t2 + ah*t3 + ai*t4)*shapePp + ai*doneJS + 1/(mBB - Pp)*(flag2*abar*done1 + flag1*t5) + 1/pow(mBB - Pp, 2)*flag3*shapePp*t6;
395 0 : if (Pp > Lbar + mui/exp(0.5)) answer = answer + t1;
396 : return answer;
397 :
398 0 : }
399 :
400 : double EvtVubBLNP::F2(double Pp, double Pm, double muh, double /*mui*/, double mubar, double done3) {
401 :
402 0 : std::vector<double> vars(12);
403 0 : vars[0] = Pp;
404 0 : vars[1] = Pm;
405 0 : for (int j=2;j<12;j++) {vars[j] = gvars[j];}
406 :
407 0 : double y = (Pm - Pp)/(mBB - Pp);
408 0 : double lambda1 = -mupisq;
409 0 : double ah = CF*alphas(muh, vars)/4/M_PI;
410 0 : double abar = CF*alphas(mubar, vars)/4/M_PI;
411 :
412 0 : double t6 = -wS(Pp) - 2*t(Pp) + 1.0/y*(t(Pp) + v(Pp));
413 0 : double t7 = 1/pow(y,2)*(2.0/3.0*lambda1 + 4.0*lambda2) - 1/y*(2.0/3.0*lambda1 + 3.0/2.0*lambda2);
414 :
415 0 : double shapePp = Shat(Pp, vars);
416 :
417 0 : double answer = ah*log(y)/(1-y)*shapePp + 1/(mBB - Pp)*(flag2*abar*0.5*done3 + flag1/y*t6) + 1.0/pow(mBB - Pp,2)*flag3*shapePp*t7;
418 : return answer;
419 :
420 0 : }
421 :
422 : double EvtVubBLNP::F3(double Pp, double Pm, double /*muh*/, double /*mui*/, double mubar, double done2) {
423 :
424 0 : std::vector<double> vars(12);
425 0 : vars[0] = Pp;
426 0 : vars[1] = Pm;
427 0 : for (int j=2;j<12;j++) {vars[j] = gvars[j];}
428 :
429 0 : double y = (Pm - Pp)/(mBB - Pp);
430 0 : double lambda1 = -mupisq;
431 0 : double abar = CF*alphas(mubar, vars)/4/M_PI;
432 :
433 0 : double t7 = 1.0/pow(y,2)*(-2.0/3.0*lambda1 + lambda2);
434 :
435 0 : double shapePp = Shat(Pp, vars);
436 :
437 0 : double answer = 1.0/(Pm - Pp)*flag2*0.5*y*abar*done2 + 1.0/pow(mBB-Pp,2)*flag3*shapePp*t7;
438 : return answer;
439 :
440 0 : }
441 :
442 : double EvtVubBLNP::DoneJS(double Pp, double Pm, double /*mui*/) {
443 :
444 0 : std::vector<double> vars(12);
445 0 : vars[0] = Pp;
446 0 : vars[1] = Pm;
447 0 : for (int j=2;j<12;j++) {vars[j] = gvars[j];}
448 :
449 0 : double lowerlim = 0.001*Pp;
450 0 : double upperlim = (1.0-0.001)*Pp;
451 :
452 0 : EvtItgPtrFunction *func = new EvtItgPtrFunction(&IntJS, lowerlim, upperlim, vars);
453 0 : EvtItgSimpsonIntegrator *integ = new EvtItgSimpsonIntegrator(*func, precision, maxLoop);
454 0 : double myintegral = integ->evaluate(lowerlim, upperlim);
455 0 : delete integ;
456 0 : delete func;
457 : return myintegral;
458 :
459 0 : }
460 :
461 : double EvtVubBLNP::Done1(double Pp, double Pm, double /*mui*/) {
462 :
463 0 : std::vector<double> vars(12);
464 0 : vars[0] = Pp;
465 0 : vars[1] = Pm;
466 0 : for (int j=2;j<12;j++) {vars[j] = gvars[j];}
467 :
468 0 : double lowerlim = 0.001*Pp;
469 0 : double upperlim = (1.0-0.001)*Pp;
470 :
471 0 : EvtItgPtrFunction *func = new EvtItgPtrFunction(&Int1, lowerlim, upperlim, vars);
472 0 : EvtItgSimpsonIntegrator *integ = new EvtItgSimpsonIntegrator(*func, precision, maxLoop);
473 0 : double myintegral = integ->evaluate(lowerlim, upperlim);
474 0 : delete integ;
475 0 : delete func;
476 : return myintegral;
477 :
478 0 : }
479 :
480 : double EvtVubBLNP::Done2(double Pp, double Pm, double /*mui*/) {
481 :
482 0 : std::vector<double> vars(12);
483 0 : vars[0] = Pp;
484 0 : vars[1] = Pm;
485 0 : for (int j=2;j<12;j++) {vars[j] = gvars[j];}
486 :
487 0 : double lowerlim = 0.001*Pp;
488 0 : double upperlim = (1.0-0.001)*Pp;
489 :
490 0 : EvtItgPtrFunction *func = new EvtItgPtrFunction(&Int2, lowerlim, upperlim, vars);
491 0 : EvtItgSimpsonIntegrator *integ = new EvtItgSimpsonIntegrator(*func, precision, maxLoop);
492 0 : double myintegral = integ->evaluate(lowerlim, upperlim);
493 0 : delete integ;
494 0 : delete func;
495 : return myintegral;
496 :
497 0 : }
498 :
499 : double EvtVubBLNP::Done3(double Pp, double Pm, double /*mui*/) {
500 :
501 0 : std::vector<double> vars(12);
502 0 : vars[0] = Pp;
503 0 : vars[1] = Pm;
504 0 : for (int j=2;j<12;j++) {vars[j] = gvars[j];}
505 :
506 0 : double lowerlim = 0.001*Pp;
507 0 : double upperlim = (1.0-0.001)*Pp;
508 :
509 0 : EvtItgPtrFunction *func = new EvtItgPtrFunction(&Int3, lowerlim, upperlim, vars);
510 0 : EvtItgSimpsonIntegrator *integ = new EvtItgSimpsonIntegrator(*func, precision, maxLoop);
511 0 : double myintegral = integ->evaluate(lowerlim, upperlim);
512 0 : delete integ;
513 0 : delete func;
514 : return myintegral;
515 :
516 0 : }
517 :
518 : double EvtVubBLNP::Int1(double what, const std::vector<double> &vars) {
519 0 : return Shat(what, vars)*g1(what, vars);
520 : }
521 :
522 : double EvtVubBLNP::Int2(double what, const std::vector<double> &vars) {
523 0 : return Shat(what, vars)*g2(what, vars);
524 : }
525 :
526 : double EvtVubBLNP::Int3(double what, const std::vector<double> &vars) {
527 0 : return Shat(what, vars)*g3(what, vars);
528 : }
529 :
530 : double EvtVubBLNP::IntJS(double what, const std::vector<double> &vars) {
531 :
532 0 : double Pp = vars[0];
533 0 : double Pm = vars[1];
534 0 : double mui = vars[2];
535 0 : double mBB = vars[5];
536 0 : double mb = vars[6];
537 0 : double y = (Pm - Pp)/(mBB - Pp);
538 :
539 0 : return 1/(Pp-what)*(Shat(what, vars) - Shat(Pp, vars))*(4*log(y*mb*(Pp-what)/(mui*mui)) - 3);
540 : }
541 :
542 : double EvtVubBLNP::g1(double w, const std::vector<double> &vars) {
543 :
544 0 : double Pp = vars[0];
545 0 : double Pm = vars[1];
546 0 : double mBB = vars[5];
547 0 : double y = (Pm - Pp)/(mBB - Pp);
548 0 : double x = (Pp - w)/(mBB - Pp);
549 :
550 0 : double q1 = (1+x)*(1+x)*y*(x+y);
551 0 : double q2 = y*(-9 + 10*y) + x*x*(-12.0 + 13.0*y) + 2*x*(-8.0 + 6*y + 3*y*y);
552 0 : double q3 = 4/x*log(y + y/x);
553 0 : double q4 = 3.0*pow(x,4)*(-2.0 + y) - 2*pow(y,3) - 4*pow(x,3)*(2.0+y) - 2*x*y*y*(4+y) - x*x*y*(12 + 4*y + y*y);
554 0 : double q5 = log(1 + y/x);
555 :
556 0 : double answer = q2/q1 - q3 - 2*q4*q5/(q1*y*x);
557 0 : return answer;
558 :
559 : }
560 :
561 : double EvtVubBLNP::g2(double w, const std::vector<double> &vars) {
562 :
563 0 : double Pp = vars[0];
564 0 : double Pm = vars[1];
565 0 : double mBB = vars[5];
566 0 : double y = (Pm - Pp)/(mBB - Pp);
567 0 : double x = (Pp - w)/(mBB - Pp);
568 :
569 0 : double q1 = (1+x)*(1+x)*pow(y,3)*(x+y);
570 0 : double q2 = 10.0*pow(x,4) + y*y + 3.0*pow(x,2)*y*(10.0+y) + pow(x,3)*(12.0+19.0*y) + x*y*(8.0 + 4.0*y + y*y);
571 0 : double q3 = 5*pow(x,4) + 2.0*y*y + 6.0*pow(x,3)*(1.0+2.0*y) + 4.0*x*y*(1+2.0*y) + x*x*y*(18.0+5.0*y);
572 0 : double q4 = log(1 + y/x);
573 :
574 0 : double answer = 2.0/q1*( y*q2 - 2*x*q3*q4);
575 0 : return answer;
576 :
577 : }
578 :
579 : double EvtVubBLNP::g3(double w, const std::vector<double> &vars) {
580 :
581 0 : double Pp = vars[0];
582 0 : double Pm = vars[1];
583 0 : double mBB = vars[5];
584 0 : double y = (Pm - Pp)/(mBB - Pp);
585 0 : double x = (Pp - w)/(mBB - Pp);
586 :
587 0 : double q1 = (1+x)*(1+x)*pow(y,3)*(x+y);
588 0 : double q2 = 2.0*pow(y,3)*(-11.0+2.0*y) - 10.0*pow(x,4)*(6 - 6*y + y*y) + x*y*y*(-94.0 + 29.0*y + 2.0*y*y) + 2.0*x*x*y*(-72.0 +18.0*y + 13.0*y*y) - x*x*x*(72.0 + 42.0*y - 70.0*y*y + 3.0*y*y*y);
589 0 : double q3 = -6.0*x*(-5.0+y)*pow(y,3) + 4*pow(y,4) + 5*pow(x,5)*(6-6*y + y*y) - 4*x*x*y*y*(-20.0 + 6*y + y*y) + pow(x,3)*y*(90.0 - 10.0*y - 28.0*y*y + y*y*y) + pow(x,4)*(36.0 + 36.0*y - 50.0*y*y + 4*y*y*y);
590 0 : double q4 = log(1 + y/x);
591 :
592 0 : double answer = q2/q1 + 2/q1/y*q3*q4;
593 0 : return answer;
594 :
595 : }
596 :
597 :
598 : double EvtVubBLNP::Shat(double w, const std::vector<double> &vars) {
599 :
600 0 : double mui = vars[2];
601 0 : double b = vars[3];
602 0 : double Lambda = vars[4];
603 0 : double wzero = vars[7];
604 0 : int itype = (int)vars[11];
605 :
606 : double norm = 0.0;
607 : double shape = 0.0;
608 :
609 0 : if (itype == 1) {
610 :
611 0 : double Lambar = (Lambda/b)*(Gamma(1+b)-Gamma(1+b,b*wzero/Lambda))/(Gamma(b) - Gamma(b, b*wzero/Lambda));
612 0 : double muf = wzero - Lambar;
613 0 : double mupisq = 3*pow(Lambda,2)/pow(b,2)*(Gamma(2+b) - Gamma(2+b, b*wzero/Lambda))/(Gamma(b) - Gamma(b, b*wzero/Lambda)) - 3*Lambar*Lambar;
614 0 : norm = Mzero(muf, mui, mupisq, vars)*Gamma(b)/(Gamma(b) - Gamma(b, b*wzero/Lambda));
615 0 : shape = pow(b,b)/Lambda/Gamma(b)*pow(w/Lambda, b-1)*exp(-b*w/Lambda);
616 0 : }
617 :
618 0 : if (itype == 2) {
619 0 : double dcoef = pow( Gamma(0.5*(1+b))/Gamma(0.5*b), 2);
620 0 : double t1 = wzero*wzero*dcoef/(Lambda*Lambda);
621 0 : double Lambar = Lambda*(Gamma(0.5*(1+b)) - Gamma(0.5*(1+b),t1))/pow(dcoef, 0.5)/(Gamma(0.5*b) - Gamma(0.5*b, t1));
622 0 : double muf = wzero - Lambar;
623 0 : double mupisq = 3*Lambda*Lambda*( Gamma(1+0.5*b) - Gamma(1+0.5*b, t1))/dcoef/(Gamma(0.5*b) - Gamma(0.5*b, t1)) - 3*Lambar*Lambar;
624 0 : norm = Mzero(muf, mui, mupisq, vars)*Gamma(0.5*b)/(Gamma(0.5*b) - Gamma(0.5*b, wzero*wzero*dcoef/(Lambda*Lambda)));
625 0 : shape = 2*pow(dcoef, 0.5*b)/Lambda/Gamma(0.5*b)*pow(w/Lambda, b-1)*exp(-dcoef*w*w/(Lambda*Lambda));
626 0 : }
627 :
628 0 : double answer = norm*shape;
629 0 : return answer;
630 : }
631 :
632 : double EvtVubBLNP::Mzero(double muf, double mu, double mupisq, const std::vector<double> &vars) {
633 :
634 : double CF = 4.0/3.0;
635 0 : double amu = CF*alphas(mu, vars)/M_PI;
636 0 : double answer = 1 - amu*( pow(log(muf/mu), 2) + log(muf/mu) + M_PI*M_PI/24.0) + amu*(log(muf/mu) - 0.5)*mupisq/(3*muf*muf);
637 0 : return answer;
638 :
639 : }
640 :
641 : double EvtVubBLNP::wS(double w) {
642 :
643 0 : double answer = (Lbar - w)*Shat(w, gvars);
644 0 : return answer;
645 : }
646 :
647 : double EvtVubBLNP::t(double w) {
648 :
649 0 : double t1 = -3*lambda2/mupisq*(Lbar - w)*Shat(w, gvars);
650 0 : double myf = myfunction(w, Lbar, moment2);
651 0 : double myBIK = myfunctionBIK(w, Lbar, moment2);
652 : double answer = t1;
653 :
654 0 : if (isubl == 1) answer = t1;
655 0 : if (isubl == 3) answer = t1 - myf;
656 0 : if (isubl == 4) answer = t1 + myf;
657 0 : if (isubl == 5) answer = t1 - myBIK;
658 0 : if (isubl == 6) answer = t1 + myBIK;
659 :
660 0 : return answer;
661 : }
662 :
663 : double EvtVubBLNP::u(double w) {
664 :
665 0 : double u1 = -2*(Lbar - w)*Shat(w, gvars);
666 0 : double myf = myfunction(w, Lbar, moment2);
667 0 : double myBIK = myfunctionBIK(w, Lbar, moment2);
668 : double answer = u1;
669 :
670 0 : if (isubl == 1) answer = u1;
671 0 : if (isubl == 3) answer = u1 + myf;
672 0 : if (isubl == 4) answer = u1 - myf;
673 0 : if (isubl == 5) answer = u1 + myBIK;
674 0 : if (isubl == 6) answer = u1 - myBIK;
675 :
676 0 : return answer;
677 : }
678 :
679 : double EvtVubBLNP::v(double w) {
680 :
681 0 : double v1 = 3*lambda2/mupisq*(Lbar - w)*Shat(w, gvars);
682 0 : double myf = myfunction(w, Lbar, moment2);
683 0 : double myBIK = myfunctionBIK(w, Lbar, moment2);
684 : double answer = v1;
685 :
686 0 : if (isubl == 1) answer = v1;
687 0 : if (isubl == 3) answer = v1 - myf;
688 0 : if (isubl == 4) answer = v1 + myf;
689 0 : if (isubl == 5) answer = v1 - myBIK;
690 0 : if (isubl == 6) answer = v1 + myBIK;
691 :
692 0 : return answer;
693 : }
694 :
695 : double EvtVubBLNP::myfunction(double w, double Lbar, double mom2) {
696 :
697 : double bval = 5.0;
698 0 : double x = w/Lbar;
699 0 : double factor = 0.5*mom2*pow(bval/Lbar, 3);
700 0 : double answer = factor*exp(-bval*x)*(1 - 2*bval*x + 0.5*bval*bval*x*x);
701 0 : return answer;
702 :
703 : }
704 :
705 : double EvtVubBLNP::myfunctionBIK(double w, double Lbar, double /*mom2*/) {
706 :
707 : double aval = 10.0;
708 0 : double normBIK = (4 - M_PI)*M_PI*M_PI/8/(2-M_PI)/aval + 1;
709 0 : double z = 3*M_PI*w/8/Lbar;
710 0 : double q = M_PI*M_PI*2*pow(M_PI*aval, 0.5)*exp(-aval*z*z)/(4*M_PI - 8)*(1 - 2*pow(aval/M_PI, 0.5)*z) + 8/pow(1+z*z, 4)*(z*log(z) + 0.5*z*(1+z*z) - M_PI/4*(1-z*z));
711 0 : double answer = q/normBIK;
712 0 : return answer;
713 :
714 : }
715 :
716 : double EvtVubBLNP::dU1nlo(double muh, double mui) {
717 :
718 0 : double ai = alphas(mui, gvars);
719 0 : double ah = alphas(muh, gvars);
720 :
721 0 : double q1 = (ah - ai)/(4*M_PI*beta0);
722 0 : double q2 = log(mb/muh)*Gamma1 + gp1;
723 0 : double q3 = 4*beta1*(log(mb/muh)*Gamma0 + gp0) + Gamma2*(1-ai/ah);
724 0 : double q4 = beta1*beta1*Gamma0*(-1.0 + ai/ah)/(4*pow(beta0,3));
725 0 : double q5 = -beta2*Gamma0*(1.0 + ai/ah) + beta1*Gamma1*(3 - ai/ah);
726 0 : double q6 = beta1*beta1*Gamma0*(ah - ai)/beta0 - beta2*Gamma0*ah + beta1*Gamma1*ai;
727 :
728 0 : double answer = q1*(q2 - q3/4/beta0 + q4 + q5/(4*beta0*beta0)) + 1/(8*M_PI*beta0*beta0*beta0)*log(ai/ah)*q6;
729 0 : return answer;
730 : }
731 :
732 : double EvtVubBLNP::U1lo(double muh, double mui) {
733 : double epsilon = 0.0;
734 0 : double answer = pow(mb/muh, -2*aGamma(muh, mui, epsilon))*exp(2*Sfun(muh, mui, epsilon) - 2*agp(muh, mui, epsilon));
735 0 : return answer;
736 : }
737 :
738 : double EvtVubBLNP::Sfun(double mu1, double mu2, double epsilon) {
739 0 : double a1 = alphas(mu1, gvars)/4/M_PI;
740 0 : double a2 = alphas(mu2, gvars)/alphas(mu1, gvars);
741 :
742 0 : double answer = S0(a1,a2) + S1(a1,a2) + epsilon*S2(a1,a2);
743 0 : return answer;
744 :
745 : }
746 :
747 : double EvtVubBLNP::S0(double a1, double r) {
748 0 : double answer = -Gamma0/(4.0*beta0*beta0*a1)*(-1.0 + 1.0/r + log(r));
749 0 : return answer;
750 : }
751 :
752 : double EvtVubBLNP::S1(double /*a1*/, double r) {
753 0 : double answer = Gamma0/(4*beta0*beta0)*(0.5*log(r)*log(r)*beta1/beta0 + (Gamma1/Gamma0 - beta1/beta0)*(1 - r + log(r)));
754 0 : return answer;
755 : }
756 :
757 : double EvtVubBLNP::S2(double a1, double r) {
758 :
759 0 : double w1 = pow(beta1,2)/pow(beta0,2) - beta2/beta0 - beta1*Gamma1/(beta0*Gamma0) + Gamma2/Gamma0;
760 : double w2 = pow(beta1,2)/pow(beta0,2) - beta2/beta0;
761 0 : double w3 = beta1*Gamma1/(beta0*Gamma0) - beta2/beta0;
762 0 : double w4 = a1*Gamma0/(4*beta0*beta0);
763 :
764 0 : double answer = w4*(-0.5*pow(1-r,2)*w1 + w2*(1-r)*log(r) + w3*(1-r+r*log(r)));
765 0 : return answer;
766 : }
767 :
768 : double EvtVubBLNP::aGamma(double mu1, double mu2, double epsilon) {
769 0 : double a1 = alphas(mu1, gvars);
770 0 : double a2 = alphas(mu2, gvars);
771 0 : double answer = Gamma0/(2*beta0)*log(a2/a1) + epsilon*(a2-a1)/(8.0*M_PI)*(Gamma1/beta0 - beta1*Gamma0/(beta0*beta0));
772 0 : return answer;
773 : }
774 :
775 : double EvtVubBLNP::agp(double mu1, double mu2, double epsilon) {
776 0 : double a1 = alphas(mu1, gvars);
777 0 : double a2 = alphas(mu2, gvars);
778 0 : double answer = gp0/(2*beta0)*log(a2/a1) + epsilon*(a2-a1)/(8.0*M_PI)*(gp1/beta0 - beta1*gp0/(beta0*beta0));
779 0 : return answer;
780 : }
781 :
782 0 : double EvtVubBLNP::alo(double muh, double mui) { return -2.0*aGamma(muh, mui, 0);}
783 :
784 : double EvtVubBLNP::anlo(double muh, double mui) { // d/depsilon of aGamma
785 :
786 0 : double ah = alphas(muh, gvars);
787 0 : double ai = alphas(mui, gvars);
788 0 : double answer = (ah-ai)/(8.0*M_PI)*(Gamma1/beta0 - beta1*Gamma0/(beta0*beta0));
789 0 : return answer;
790 : }
791 :
792 : double EvtVubBLNP::alphas(double mu, const std::vector<double> &vars) {
793 :
794 : // Note: Lambda4 and Lambda5 depend on mbMS = 4.25
795 : // So if you change mbMS, then you will have to recalculate them.
796 :
797 0 : double beta0 = vars[8];
798 0 : double beta1 = vars[9];
799 0 : double beta2 = vars[10];
800 :
801 : double Lambda4 = 0.298791;
802 0 : double lg = 2*log(mu/Lambda4);
803 0 : double answer = 4*M_PI/(beta0*lg)*( 1 - beta1*log(lg)/(beta0*beta0*lg) + beta1*beta1/(beta0*beta0*beta0*beta0*lg*lg)*( (log(lg) - 0.5)*(log(lg) - 0.5) - 5.0/4.0 + beta2*beta0/(beta1*beta1)));
804 0 : return answer;
805 :
806 : }
807 :
808 : double EvtVubBLNP::PolyLog(double v, double z) {
809 :
810 0 : if (z >= 1) cout << "Error in EvtVubBLNP: 2nd argument to PolyLog is >= 1." << endl;
811 :
812 : double sum = 0.0;
813 0 : for (int k=1; k<101; k++) {
814 0 : sum = sum + pow(z,k)/pow(k,v);
815 : }
816 0 : return sum;
817 : }
818 :
819 : double EvtVubBLNP::Gamma(double z)
820 : {
821 0 : if (z<=0) return 0;
822 :
823 0 : double v = lgamma(z);
824 0 : return exp(v);
825 0 : }
826 :
827 : double EvtVubBLNP::Gamma(double a, double x)
828 : {
829 : double LogGamma;
830 : /* if (x<0.0 || a<= 0.0) raise(SIGFPE);*/
831 0 : if(x<0.0) x=0.0;
832 0 : if(a<=0.0)a=1.e-50;
833 0 : LogGamma = lgamma(a);
834 0 : if (x < (a+1.0))
835 0 : return gamser(a,x,LogGamma);
836 : else
837 0 : return 1.0-gammcf(a,x,LogGamma);
838 0 : }
839 :
840 : /* ------------------Incomplete gamma function-----------------*/
841 : /* ------------------via its series representation-------------*/
842 :
843 : double EvtVubBLNP::gamser(double a, double x, double LogGamma)
844 : {
845 : double n;
846 : double ap,del,sum;
847 :
848 : ap=a;
849 0 : del=sum=1.0/a;
850 0 : for (n=1;n<ITMAX;n++) {
851 0 : ++ap;
852 0 : del *= x/ap;
853 0 : sum += del;
854 0 : if (fabs(del) < fabs(sum)*EPS) return sum*exp(-x + a*log(x) - LogGamma);
855 : }
856 0 : raise(SIGFPE);
857 :
858 0 : return 0.0;
859 0 : }
860 :
861 : /* ------------------Incomplete gamma function complement------*/
862 : /* ------------------via its continued fraction representation-*/
863 :
864 : double EvtVubBLNP::gammcf(double a, double x, double LogGamma) {
865 :
866 : double an,b,c,d,del,h;
867 : int i;
868 :
869 0 : b = x + 1.0 -a;
870 : c = 1.0/FPMIN;
871 0 : d = 1.0/b;
872 : h = d;
873 0 : for (i=1;i<ITMAX;i++) {
874 0 : an = -i*(i-a);
875 0 : b+=2.0;
876 0 : d=an*d+b;
877 0 : if (fabs(d) < FPMIN) d = FPMIN;
878 0 : c = b+an/c;
879 0 : if (fabs(c) < FPMIN) c = FPMIN;
880 0 : d = 1.0/d;
881 0 : del=d*c;
882 0 : h *= del;
883 0 : if (fabs(del-1.0) < EPS) return exp(-x+a*log(x)-LogGamma)*h;
884 : }
885 0 : raise(SIGFPE);
886 :
887 0 : return 0.0;
888 :
889 0 : }
890 :
891 :
892 : double EvtVubBLNP::findBLNPWhat() {
893 :
894 0 : double ranNum=EvtRandom::Flat();
895 0 : double oOverBins= 1.0/(float(_pf.size()));
896 : int nBinsBelow = 0; // largest k such that I[k] is known to be <= rand
897 0 : int nBinsAbove = _pf.size(); // largest k such that I[k] is known to be > rand
898 : int middle;
899 :
900 0 : while (nBinsAbove > nBinsBelow+1) {
901 0 : middle = (nBinsAbove + nBinsBelow+1)>>1;
902 0 : if (ranNum >= _pf[middle]) {
903 : nBinsBelow = middle;
904 0 : } else {
905 : nBinsAbove = middle;
906 : }
907 : }
908 :
909 0 : double bSize = _pf[nBinsAbove] - _pf[nBinsBelow];
910 : // binMeasure is always aProbFunc[nBinsBelow],
911 :
912 0 : if ( bSize == 0 ) {
913 : // rand lies right in a bin of measure 0. Simply return the center
914 : // of the range of that bin. (Any value between k/N and (k+1)/N is
915 : // equally good, in this rare case.)
916 0 : return (nBinsBelow + .5) * oOverBins;
917 : }
918 :
919 0 : double bFract = (ranNum - _pf[nBinsBelow]) / bSize;
920 :
921 0 : return (nBinsBelow + bFract) * oOverBins;
922 :
923 0 : }
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