BOSS 7.0.8
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EvtBtoXsgammaKagan.cc
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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// Module: EvtBtoXsgammaKagan.cc
9//
10// Description:
11// Routine to perform two-body non-resonant B->Xs,gamma decays.
12// The X_s mass spectrum generated is based on the Kagan-Neubert model.
13// See hep-ph/9805303 for the model details and input parameters.
14//
15// The input parameters are 1:fermi_model, 2:mB, 3:mb, 4:mu, 5:lam1,
16// 6:delta, 7:z, 8:nIntervalS, 9:nIntervalmH. Choosing fermi_model=1
17// uses an exponential shape function, fermi_model=2 uses a gaussian
18// shape function and fermi_model=3 a roman shape function. The complete mass
19// spectrum for a given set of input parameters is calculated from
20// scratch in bins of nIntervalmH. The s22, s27 and s28 coefficients are calculated
21// in bins of nIntervalS. As the program includes lots of integration, the
22// theoretical hadronic mass spectra is computed for the first time
23// the init method is called. Then, all the other times (eg if we want to decay a B0
24// as well as an anti-B0) the vector mass info stored the first time is used again.
25//
26// Modification history:
27//
28// Jane Tinslay, Francesca Di Lodovico March 21, 2001 Module created
29//------------------------------------------------------------------------
30//
31#include "EvtGenBase/EvtPatches.hh"
32
33#include <stdlib.h>
34#include "EvtGenModels/EvtBtoXsgamma.hh"
35#include "EvtGenBase/EvtRandom.hh"
36#include "EvtGenModels/EvtBtoXsgammaKagan.hh"
37#include <string>
38#include "EvtGenBase/EvtConst.hh"
39#include "EvtGenBase/EvtParticle.hh"
40#include "EvtGenBase/EvtGenKine.hh"
41#include "EvtGenBase/EvtPDL.hh"
42#include "EvtGenBase/EvtReport.hh"
43#include "EvtGenModels/EvtItgSimpsonIntegrator.hh"
44#include "EvtGenModels/EvtItgFunction.hh"
45#include "EvtGenModels/EvtItgPtrFunction.hh"
46#include "EvtGenModels/EvtItgTwoCoeffFcn.hh"
47#include "EvtGenModels/EvtItgThreeCoeffFcn.hh"
48#include "EvtGenModels/EvtItgFourCoeffFcn.hh"
49#include "EvtGenModels/EvtItgAbsIntegrator.hh"
50#include "EvtGenModels/EvtBtoXsgammaFermiUtil.hh"
51
52#include <fstream>
53using std::endl;
54using std::fstream;
55
56bool EvtBtoXsgammaKagan::bbprod = false;
57double EvtBtoXsgammaKagan::intervalMH = 0;
58
59EvtBtoXsgammaKagan::~EvtBtoXsgammaKagan(){
60 delete [] massHad;
61 delete [] brHad;
62}
63
64void EvtBtoXsgammaKagan::init(int nArg, double* args){
65
66 if ((nArg) > 12 || (nArg > 1 && nArg <10) || nArg == 11){
67
68 report(ERROR,"EvtGen") << "EvtBtoXsgamma generator model "
69 << "EvtBtoXsgammaKagan expected "
70 << "either 1(default config) or "
71 << "10 (default mass range) or "
72 << "12 (user range) arguments but found: "
73 <<nArg<<endl;
74 report(ERROR,"EvtGen") << "Will terminate execution!"<<endl;
75 ::abort();
76 }
77
78 if(nArg == 1){
79 bbprod = true;
80 getDefaultHadronicMass();
81 }else{
82 bbprod = false;
83 computeHadronicMass(nArg, args);
84 }
85
86 double mHminLimit=0.6373;
87 double mHmaxLimit=4.5;
88
89 if (nArg>10){
90 _mHmin = args[10];
91 _mHmax = args[11];
92 if (_mHmin > _mHmax){
93 report(ERROR,"EvtGen") << "Minimum hadronic mass exceeds maximum "
94 << endl;
95 report(ERROR,"EvtGen") << "Will terminate execution!" << endl;
96 ::abort();
97 }
98 if (_mHmin < mHminLimit){
99 report(ERROR,"EvtGen") << "Minimum hadronic mass below K pi threshold"
100 << endl;
101 report(ERROR,"EvtGen") << "Resetting to K pi threshold" << endl;
102 _mHmin = mHminLimit;
103 }
104 if (_mHmax > mHmaxLimit){
105 report(ERROR,"EvtGen") << "Maximum hadronic mass above 4.5 GeV/c^2"
106 << endl;
107 report(ERROR,"EvtGen") << "Resetting to 4.5 GeV/c^2" << endl;
108 _mHmax = mHmaxLimit;
109 }
110 }else{
111 _mHmin=mHminLimit; // usually just above K pi threshold for Xsd/u
112 _mHmax=mHmaxLimit;
113 }
114
115}
116
117void EvtBtoXsgammaKagan::getDefaultHadronicMass(){
118
119 massHad = new double[81];
120 brHad = new double[81];
121
122 double mass[81] = { 0, 0.0625995, 0.125199, 0.187798, 0.250398, 0.312997, 0.375597, 0.438196, 0.500796, 0.563395, 0.625995, 0.688594, 0.751194, 0.813793, 0.876392, 0.938992, 1.00159, 1.06419, 1.12679, 1.18939, 1.25199, 1.31459, 1.37719, 1.43979, 1.50239, 1.56499, 1.62759, 1.69019, 1.75278, 1.81538, 1.87798, 1.94058, 2.00318, 2.06578, 2.12838, 2.19098, 2.25358, 2.31618, 2.37878, 2.44138, 2.50398, 2.56658, 2.62918, 2.69178, 2.75438, 2.81698, 2.87958, 2.94217, 3.00477, 3.06737, 3.12997, 3.19257, 3.25517, 3.31777, 3.38037, 3.44297, 3.50557, 3.56817, 3.63077, 3.69337, 3.75597, 3.81857, 3.88117, 3.94377, 4.00637, 4.06896, 4.13156, 4.19416, 4.25676, 4.31936, 4.38196, 4.44456, 4.50716, 4.56976, 4.63236, 4.69496, 4.75756, 4.82016, 4.88276, 4.94536, 5.00796};
123
124 double br[81] = { 0, 1.03244e-09, 3.0239e-08, 1.99815e-07, 7.29392e-07, 1.93129e-06, 4.17806e-06, 7.86021e-06, 1.33421e-05, 2.09196e-05, 3.07815e-05, 4.29854e-05, 5.74406e-05, 7.3906e-05, 9.2003e-05, 0.000111223, 0.000130977, 0.000150618, 0.000169483, 0.000186934, 0.000202392, 0.000215366, 0.000225491, 0.000232496, 0.000236274, 0.000236835, 0.000234313, 0.000228942, 0.000221042, 0.000210994, 0.000199215, 0.000186137, 0.000172194, 0.000157775, 0.000143255, 0.000128952, 0.000115133, 0.000102012, 8.97451e-05, 7.84384e-05, 6.81519e-05, 5.89048e-05, 5.06851e-05, 4.34515e-05, 3.71506e-05, 3.1702e-05, 2.70124e-05, 2.30588e-05, 1.96951e-05, 1.68596e-05, 1.44909e-05, 1.25102e-05, 1.08596e-05, 9.48476e-06, 8.34013e-06, 7.38477e-06, 6.58627e-06, 5.91541e-06, 5.35022e-06, 4.87047e-06, 4.46249e-06, 4.11032e-06, 3.80543e-06, 3.54051e-06, 3.30967e-06, 3.10848e-06, 2.93254e-06, 2.78369e-06, 2.65823e-06, 2.55747e-06, 2.51068e-06, 2.57179e-06, 2.74684e-06, 3.02719e-06, 3.41182e-06, 3.91387e-06, 4.56248e-06, 5.40862e-06, 6.53915e-06, 8.10867e-06, 1.04167e-05 };
125
126 for(int i=0; i<81; i++){
127 massHad[i] = mass[i];
128 brHad[i] = br[i];
129 }
130 intervalMH=80;
131}
132
133void EvtBtoXsgammaKagan::computeHadronicMass(int nArg, double* args){
134
135 //Input parameters
136 int fermiFunction = (int)args[1];
137 _mB = args[2];
138 _mb = args[3];
139 _mu = args[4];
140 _lam1 = args[5];
141 _delta = args[6];
142 _z = args[7];
143 _nIntervalS = args[8];
144 _nIntervalmH = args[9];
145 std::vector<double> mHVect(int(_nIntervalmH+1.0));
146 massHad = new double[int(_nIntervalmH+1.0)];
147 brHad = new double[int(_nIntervalmH+1.0)];
148 intervalMH=_nIntervalmH;
149
150 //Going to have to add a new entry into the data file - takes ages...
151 report(WARNING,"EvtGen") << "EvtBtoXsgammaKagan: calculating new hadronic mass spectra. This takes a while..." << endl;
152
153 //Now need to compute the mHVect vector for
154 //the current parameters
155
156 //A few more parameters
157 double _mubar = _mu;
158 _mW = 80.33;
159 _mt = 175.0;
160 _alpha = 1./137.036;
161 _lambdabar = _mB - _mb;
162 _kappabar = 3.382 - 4.14*(sqrt(_z) - 0.29);
163 _fz=Fz(_z);
164 _rer8 = (44./9.) - (8./27.)*pow(EvtConst::pi,2.);
165 _r7 = (-10./3.) - (8./9.)*pow(EvtConst::pi,2.);
166 _rer2 = -4.092 + 12.78*(sqrt(_z) -.29);
167 _gam77 = 32./3.;
168 _gam27 = 416./81.;
169 _gam87 = -32./9.;
170 _lam2 = .12;
171 _beta0 = 23./3.;
172 _beta1 = 116./3.;
173 _alphasmZ = .118;
174 _mZ = 91.187;
175 _ms = _mb/50.;
176
177 double eGammaMin = 0.5*_mB*(1. - _delta);
178 double eGammaMax = 0.5*_mB;
179 double yMin = 2.*eGammaMin/_mB;
180 double yMax = 2.*eGammaMax/_mB;
181 double _CKMrat= 0.976;
182 double Nsl = 1.0;
183
184 //Calculate alpha the various scales
185 _alphasmW = CalcAlphaS(_mW);
186 _alphasmt = CalcAlphaS(_mt);
187 _alphasmu = CalcAlphaS(_mu);
188 _alphasmubar = CalcAlphaS(_mubar);
189
190 //Calculate the Wilson Coefficients and Delta
191 _etamu = _alphasmW/_alphasmu;
192 _kSLemmu = (12./23.)*((1./_etamu) -1.);
193 CalcWilsonCoeffs();
194 CalcDelta();
195
196 //Build s22 and s27 vector - saves time because double
197 //integration is required otherwise
198 std::vector<double> s22Coeffs(int(_nIntervalS+1.0));
199 std::vector<double> s27Coeffs(int(_nIntervalS+1.0));
200 std::vector<double> s28Coeffs(int(_nIntervalS+1.0));
201
202 double dy = (yMax - yMin)/_nIntervalS;
203 double yp = yMin;
204
205 std::vector<double> sCoeffs(1);
206 sCoeffs[0] = _z;
207
208 //Define s22 and s27 functions
209 EvtItgPtrFunction *mys22Func = new EvtItgPtrFunction(&s22Func, 0., yMax+0.1, sCoeffs);
210 EvtItgPtrFunction *mys27Func = new EvtItgPtrFunction(&s27Func, 0., yMax+0.1, sCoeffs);
211
212 //Use a simpson integrator
213 EvtItgAbsIntegrator *mys22Simp = new EvtItgSimpsonIntegrator(*mys22Func, 1.0e-4, 20);
214 EvtItgAbsIntegrator *mys27Simp = new EvtItgSimpsonIntegrator(*mys27Func, 1.0e-4, 50);
215
216 int i;
217
218 for (i=0;i<int(_nIntervalS+1.0);i++) {
219
220 s22Coeffs[i] = (16./27.)*mys22Simp->evaluate(1.0e-20,yp);
221 s27Coeffs[i] = (-8./9.)*_z*mys27Simp->evaluate(1.0e-20,yp);
222 s28Coeffs[i] = -s27Coeffs[i]/3.;
223 yp = yp + dy;
224
225 }
226
227 delete mys22Func;
228 delete mys27Func;
229 delete mys22Simp;
230 delete mys27Simp;
231
232 //Define functions and vectors used to calculate mHVect. Each function takes a set
233 //of vectors which are used as the function coefficients
234 std::vector<double> FermiCoeffs(6);
235 std::vector<double> varCoeffs(3);
236 std::vector<double> DeltaCoeffs(1);
237 std::vector<double> s88Coeffs(2);
238 std::vector<double> sInitCoeffs(3);
239
240 varCoeffs[0] = _mB;
241 varCoeffs[1] = _mb;
242 varCoeffs[2] = 0.;
243
244 DeltaCoeffs[0] = _alphasmu;
245
246 s88Coeffs[0] = _mb;
247 s88Coeffs[1] = _ms;
248
249 sInitCoeffs[0] = _nIntervalS;
250 sInitCoeffs[1] = yMin;
251 sInitCoeffs[2] = yMax;
252
253 FermiCoeffs[0]=fermiFunction;
254 FermiCoeffs[1]=0.0;
255 FermiCoeffs[2]=0.0;
256 FermiCoeffs[3]=0.0;
257 FermiCoeffs[4]=0.0;
258 FermiCoeffs[5]=0.0;
259
260 //Coefficients for gamma function
261 std::vector<double> gammaCoeffs(6);
262 gammaCoeffs[0]=76.18009172947146;
263 gammaCoeffs[1]=-86.50532032941677;
264 gammaCoeffs[2]=24.01409824083091;
265 gammaCoeffs[3]=-1.231739572450155;
266 gammaCoeffs[4]=0.1208650973866179e-2;
267 gammaCoeffs[5]=-0.5395239384953e-5;
268
269 //Calculate quantities for the fermi function to be used
270 //Distinguish among the different shape functions
271 if (fermiFunction == 1) {
272
273 FermiCoeffs[1]=_lambdabar;
274 FermiCoeffs[2]=(-3.*pow(_lambdabar,2.)/_lam1) - 1.;
275 FermiCoeffs[3]=_lam1;
276 FermiCoeffs[4]=1.0;
277
278 EvtItgPtrFunction *myNormFunc = new EvtItgPtrFunction(&EvtBtoXsgammaFermiUtil::FermiExpFunc, -_mb, _mB-_mb, FermiCoeffs);
279 EvtItgAbsIntegrator *myNormSimp = new EvtItgSimpsonIntegrator(*myNormFunc, 1.0e-4, 40);
280 FermiCoeffs[4]=myNormSimp->normalisation();
281 delete myNormFunc; myNormFunc=0;
282 delete myNormSimp; myNormSimp=0;
283
284 } else if (fermiFunction == 2) {
285
286 double a = EvtBtoXsgammaFermiUtil::FermiGaussFuncRoot(_lambdabar, _lam1, _mb, gammaCoeffs);
287 FermiCoeffs[1]=_lambdabar;
288 FermiCoeffs[2]=a;
289 FermiCoeffs[3]= EvtBtoXsgammaFermiUtil::Gamma((2.0 + a)/2., gammaCoeffs)/
290 EvtBtoXsgammaFermiUtil::Gamma((1.0 + a)/2., gammaCoeffs);
291 FermiCoeffs[4]=1.0;
292
293 EvtItgPtrFunction *myNormFunc = new EvtItgPtrFunction(&EvtBtoXsgammaFermiUtil::FermiGaussFunc, -_mb, _mB-_mb, FermiCoeffs);
294 EvtItgAbsIntegrator *myNormSimp = new EvtItgSimpsonIntegrator(*myNormFunc, 1.0e-4, 40);
295 FermiCoeffs[4]=myNormSimp->normalisation();
296 delete myNormFunc; myNormFunc=0;
297 delete myNormSimp; myNormSimp=0;
298
299 }
300 else if (fermiFunction == 3) {
301
302 double rho = EvtBtoXsgammaFermiUtil::FermiRomanFuncRoot(_lambdabar, _lam1);
303 FermiCoeffs[1]=_mB;
304 FermiCoeffs[2]=_mb;
305 FermiCoeffs[3]= rho;
306 FermiCoeffs[4]=_lambdabar;
307 FermiCoeffs[5]=1.0;
308
309 EvtItgPtrFunction *myNormFunc = new EvtItgPtrFunction(&EvtBtoXsgammaFermiUtil::FermiRomanFunc, -_mb, _mB-_mb, FermiCoeffs);
310 EvtItgAbsIntegrator *myNormSimp = new EvtItgSimpsonIntegrator(*myNormFunc, 1.0e-4, 40);
311 FermiCoeffs[5]=myNormSimp->normalisation();
312 delete myNormFunc; myNormFunc=0;
313 delete myNormSimp; myNormSimp=0;
314
315 }
316
317 //Define functions
318 EvtItgThreeCoeffFcn* myDeltaFermiFunc = new EvtItgThreeCoeffFcn(&DeltaFermiFunc, -_mb, _mB-_mb, FermiCoeffs, varCoeffs, DeltaCoeffs);
319 EvtItgThreeCoeffFcn* mys88FermiFunc = new EvtItgThreeCoeffFcn(&s88FermiFunc, -_mb, _mB-_mb, FermiCoeffs, varCoeffs, s88Coeffs);
320 EvtItgTwoCoeffFcn* mys77FermiFunc = new EvtItgTwoCoeffFcn(&s77FermiFunc, -_mb, _mB-_mb, FermiCoeffs, varCoeffs);
321 EvtItgTwoCoeffFcn* mys78FermiFunc = new EvtItgTwoCoeffFcn(&s78FermiFunc, -_mb, _mB-_mb, FermiCoeffs, varCoeffs);
322 EvtItgFourCoeffFcn* mys22FermiFunc = new EvtItgFourCoeffFcn(&sFermiFunc, -_mb, _mB-_mb, FermiCoeffs, varCoeffs, sInitCoeffs, s22Coeffs);
323 EvtItgFourCoeffFcn* mys27FermiFunc = new EvtItgFourCoeffFcn(&sFermiFunc, -_mb, _mB-_mb, FermiCoeffs, varCoeffs, sInitCoeffs, s27Coeffs);
324 EvtItgFourCoeffFcn* mys28FermiFunc = new EvtItgFourCoeffFcn(&sFermiFunc, -_mb, _mB-_mb, FermiCoeffs, varCoeffs, sInitCoeffs, s28Coeffs);
325
326 //Define integrators
327 EvtItgSimpsonIntegrator* myDeltaFermiSimp =
328 new EvtItgSimpsonIntegrator(*myDeltaFermiFunc, 1.0e-4, 40);
329 EvtItgSimpsonIntegrator* mys77FermiSimp =
330 new EvtItgSimpsonIntegrator(*mys77FermiFunc, 1.0e-4, 40);
331 EvtItgSimpsonIntegrator* mys88FermiSimp =
332 new EvtItgSimpsonIntegrator(*mys88FermiFunc, 1.0e-4, 40);
333 EvtItgSimpsonIntegrator* mys78FermiSimp =
334 new EvtItgSimpsonIntegrator(*mys78FermiFunc, 1.0e-4, 40);
335 EvtItgSimpsonIntegrator* mys22FermiSimp =
336 new EvtItgSimpsonIntegrator(*mys22FermiFunc, 1.0e-4, 40);
337 EvtItgSimpsonIntegrator* mys27FermiSimp =
338 new EvtItgSimpsonIntegrator(*mys27FermiFunc, 1.0e-4, 40);
339 EvtItgSimpsonIntegrator* mys28FermiSimp =
340 new EvtItgSimpsonIntegrator(*mys28FermiFunc, 1.0e-4, 40);
341
342 //Finally calculate mHVect for the range of hadronic masses
343 double mHmin = sqrt(_mB*_mB - 2.*_mB*eGammaMax);
344 double mHmax = sqrt(_mB*_mB - 2.*_mB*eGammaMin);
345 double dmH = (mHmax - mHmin)/_nIntervalmH;
346
347 double mH=mHmin;
348
349 //Calculating the Branching Fractions
350 for (i=0;i<int(_nIntervalmH+1.0);i++) {
351
352 double ymH = 1. - ((mH*mH)/(_mB*_mB));
353
354 //Need to set ymH as one of the input parameters
355 myDeltaFermiFunc->setCoeff(2, 2, ymH);
356 mys77FermiFunc->setCoeff(2, 2, ymH);
357 mys88FermiFunc->setCoeff(2, 2, ymH);
358 mys78FermiFunc->setCoeff(2, 2, ymH);
359 mys22FermiFunc->setCoeff(2, 2, ymH);
360 mys27FermiFunc->setCoeff(2, 2, ymH);
361 mys28FermiFunc->setCoeff(2, 2, ymH);
362
363 //Integrate
364
365 double deltaResult = myDeltaFermiSimp->evaluate((_mB*ymH-_mb),_mB-_mb);
366 double s77Result = mys77FermiSimp->evaluate((_mB*ymH-_mb),_mB-_mb);
367 double s88Result = mys88FermiSimp->evaluate((_mB*ymH-_mb),_mB-_mb);
368 double s78Result = mys78FermiSimp->evaluate((_mB*ymH-_mb),_mB-_mb);
369 double s22Result = mys22FermiSimp->evaluate((_mB*ymH-_mb),_mB-_mb);
370 double s27Result = mys27FermiSimp->evaluate((_mB*ymH-_mb),_mB-_mb);
371
372 double py = (pow(_CKMrat,2.)*(6./_fz)*(_alpha/EvtConst::pi)*(deltaResult*_cDeltatot + (_alphasmu/EvtConst::pi)*(s77Result*pow(_c70mu,2.) + s27Result*_c2mu*(_c70mu - _c80mu/3.) + s78Result*_c70mu*_c80mu + s22Result*_c2mu*_c2mu + s88Result*_c80mu*_c80mu ) ) );
373
374 mHVect[i] = 2.*(mH/(_mB*_mB))*0.105*Nsl*py;
375
376 massHad[i] = mH;
377 brHad[i] = 2.*(mH/(_mB*_mB))*0.105*Nsl*py;
378
379 mH = mH+dmH;
380
381 }
382
383 //Clean up
384 delete myDeltaFermiFunc; myDeltaFermiFunc=0;
385 delete mys88FermiFunc; mys88FermiFunc=0;
386 delete mys77FermiFunc; mys77FermiFunc=0;
387 delete mys78FermiFunc; mys78FermiFunc=0;
388 delete mys22FermiFunc; mys22FermiFunc=0;
389 delete mys27FermiFunc; mys27FermiFunc=0;
390 delete mys28FermiFunc; mys28FermiFunc=0;
391
392 delete myDeltaFermiSimp; myDeltaFermiSimp=0;
393 delete mys77FermiSimp; mys77FermiSimp=0;
394 delete mys88FermiSimp; mys88FermiSimp=0;
395 delete mys78FermiSimp; mys78FermiSimp=0;
396 delete mys22FermiSimp; mys22FermiSimp=0;
397 delete mys27FermiSimp; mys27FermiSimp=0;
398 delete mys28FermiSimp; mys28FermiSimp=0;
399
400}
401
402double EvtBtoXsgammaKagan::GetMass( int Xscode ){
403
404// Get hadronic mass for the event according to the hadronic mass spectra computed in computeHadronicMass
405 double mass=0.0;
406 // double min=0.6373; // usually just above K pi threshold for Xsd/u
407 double min=_mHmin;
408 if(bbprod)min=1.1;
409 // double max=4.5;
410 double max=_mHmax;
411 double xbox(0), ybox(0);
412 double boxheight(0);
413 double trueHeight(0);
414 double boxwidth=max-min;
415
416 for (int i=0;i<int(intervalMH+1.0);i++) {
417 if(brHad[i]>boxheight)boxheight=brHad[i];
418 }
419 while ((mass > max) || (mass < min)){
420 xbox = EvtRandom::Flat(boxwidth)+min;
421 ybox=EvtRandom::Flat(boxheight);
422 trueHeight=0.0;
423 for (int i=0;i<int(intervalMH+1.0);i++) {
424 if(massHad[i]>=xbox&& trueHeight==0.0){
425 trueHeight=(brHad[i]+brHad[i+1])/2.;
426 }
427 }
428 if (ybox>trueHeight) {
429 mass=0.0;
430 } else {
431 mass=xbox;
432 }
433 }
434
435 return mass;
436}
437
438double EvtBtoXsgammaKagan::CalcAlphaS(double scale) {
439
440 double v = 1. -_beta0*(_alphasmZ/(2.*EvtConst::pi))*(log(_mZ/scale));
441 return (_alphasmZ/v)*(1. - ((_beta1/_beta0)*(_alphasmZ/(4.*EvtConst::pi))*(log(v)/v)));
442
443}
444
445void EvtBtoXsgammaKagan::CalcWilsonCoeffs( ){
446
447 double mtatmw=_mt*pow((_alphasmW/_alphasmt),(12./23.))*(1 + (12./23.)*((253./18.) - (116./23.))*((_alphasmW - _alphasmt)/(4.0*EvtConst::pi)) - (4./3.)*(_alphasmt/EvtConst::pi));
448 double xt=pow(mtatmw,2.)/pow(_mW,2.);
449
450
451
452 /////LO
453 _c2mu = .5*pow(_etamu,(-12./23.)) + .5*pow(_etamu,(6./23.));
454
455 double c7mWsm = ((3.*pow(xt,3.) - 2.*pow(xt,2.))/(4.*pow((xt - 1.),4.)))*log(xt)
456 + ((-8.*pow(xt,3.) - 5.*pow(xt,2.) + 7.*xt)/(24.*pow((xt - 1.),3.) )) ;
457
458 double c8mWsm = ((-3.*pow(xt,2.))/(4.*pow((xt - 1.),4.)))*log(xt)
459 + ((- pow(xt,3.) + 5.*pow(xt,2.) + 2.*xt)/(8.*pow((xt - 1.),3.)));
460
461 double c7constmu = (626126./272277.)*pow(_etamu,(14./23.))
462 - (56281./51730.)*pow(_etamu,(16./23.)) - (3./7.)*pow(_etamu,(6./23.))
463 - (1./14.)*pow(_etamu,(-12./23.)) - .6494*pow(_etamu,.4086) - .038*pow(_etamu,-.423)
464 - .0186*pow(_etamu,-.8994) - .0057*pow(_etamu,.1456);
465
466 _c70mu = c7mWsm*pow(_etamu,(16./23.)) + (8./3.)*(pow(_etamu,(14./23.))
467 -pow(_etamu,(16./23.)))*c8mWsm + c7constmu;
468
469 double c8constmu = (313063./363036.)*pow(_etamu,(14./23.))
470 -.9135*pow(_etamu,.4086) + .0873*pow(_etamu,-.423) - .0571*pow(_etamu,-.8994)
471 + .0209*pow(_etamu,.1456);
472
473 _c80mu = c8mWsm*pow(_etamu,(14./23.)) + c8constmu;
474
475 //Compute the dilogarithm (PolyLog(2,x)) with the Simpson integrator
476 //The dilogarithm is defined as: Li_2(x)=Int_0^x(-log(1.-z)/z)
477 //however, Mathematica implements it as Sum[z^k/k^2,{k,1,Infinity}], so, althought the two
478 //results are similar and both implemented in the program, we prefer to use the
479 //one closer to the Mathematica implementation as identical to what used by the theorists.
480
481 // EvtItgFunction *myDiLogFunc = new EvtItgFunction(&diLogFunc, 0., 1.-1./xt);
482 //EvtItgAbsIntegrator *myDiLogSimp = new EvtItgSimpsonIntegrator(*myDiLogFunc, 1.0e-4, 50);
483 //double li2 = myDiLogSimp->evaluate(1.0e-20,1.-1./xt);
484
485 double li2=diLogMathematica(1.-1./xt);
486
487double c7mWsm1 = ( (-16. *pow(xt,4.) -122. *pow(xt,3.) + 80. *pow(xt,2.) -8. *xt)/
488(9. *pow((xt -1.),4.)) * li2 +
489(6. *pow(xt,4.) + 46. *pow(xt,3.) -28. *pow(xt,2.))/(3. *pow((xt-1.),5.)) *pow(log(xt),2.)
490+ (-102. *pow(xt,5.) -588. *pow(xt,4.) -2262. *pow(xt,3.) + 3244. *pow(xt,2.) -1364. *xt
491+ 208.)/(81. *pow((xt-1),5.)) *log(xt)
492+ (1646. *pow(xt,4.) + 12205. *pow(xt,3.) -10740. *pow(xt,2.) + 2509. *xt -436.)/
493(486. *pow((xt-1),4.)) );
494
495double c8mWsm1 = ((-4. *pow(xt,4.) + 40. *pow(xt,3.) + 41. *pow(xt,2.) + xt)/
496(6. *pow((xt-1.),4.)) * li2
497+ (-17. *pow(xt,3.) -31. *pow(xt,2.))/(2. *pow((xt-1.),5.) ) *pow(log(xt),2.)
498+ (-210. *pow(xt,5.) + 1086. *pow(xt,4.) + 4893. *pow(xt,3.) + 2857. *pow(xt,2.)
499-1994. *xt + 280.)/(216. *pow((xt-1),5.)) *log(xt)
500+ (737. *pow(xt,4.) -14102. *pow(xt,3.) -28209. *pow(xt,2.) + 610. *xt -508.)/
501(1296. *pow((xt-1),4.)) );
502
503double E1 = (xt *(18. -11. *xt -pow(xt,2.))/(12.*pow( (1. -xt),3.))
504+ pow(xt,2.)* (15. -16. *xt + 4. *pow(xt,2.))/(6. *pow((1. -xt),4.)) *log(xt)
505-2./3. *log(xt) );
506
507double e1 = 4661194./816831.;
508double e2 = -8516./2217. ;
509double e3 = 0.;
510double e4 = 0.;
511double e5 = -1.9043;
512double e6 = -.1008;
513double e7 = .1216;
514double e8 = .0183;
515
516double f1 = -17.3023;
517double f2 = 8.5027;
518double f3 = 4.5508;
519double f4 = .7519;
520double f5 = 2.004;
521double f6 = .7476;
522double f7 = -.5385;
523double f8 = .0914;
524
525double g1 = 14.8088;
526double g2 = -10.809;
527double g3 = -.874;
528double g4 = .4218;
529double g5 = -2.9347;
530double g6 = .3971;
531double g7 = .1600;
532double g8 = .0225;
533
534
535double c71constmu = ((e1 *_etamu *E1 + f1 + g1 *_etamu) *pow(_etamu,(14./23.))
536+ (e2 *_etamu *E1 + f2 + g2 *_etamu) *pow(_etamu,(16./23.))
537+ (e3 *_etamu *E1 + f3 + g3 *_etamu) *pow(_etamu,(6./23.))
538+ (e4 *_etamu *E1 + f4 + g4 *_etamu) *pow(_etamu,(-12./23.))
539+ (e5 *_etamu *E1 + f5 + g5 *_etamu) *pow(_etamu,.4086)
540+ (e6 *_etamu *E1 + f6 + g6 *_etamu) *pow(_etamu,(-.423))
541+ (e7 *_etamu *E1 + f7 + g7 *_etamu) *pow(_etamu,(-.8994))
542+ (e8 *_etamu *E1 + f8 + g8 *_etamu) *pow(_etamu,.1456 ));
543
544double c71pmu = ( ((297664./14283. *pow(_etamu,(16./23.))
545-7164416./357075. *pow(_etamu,(14./23.))
546+ 256868./14283. *pow(_etamu,(37./23.)) - 6698884./357075. *pow(_etamu,(39./23.)))
547*(c8mWsm))
548+ 37208./4761. *(pow(_etamu,(39./23.)) - pow(_etamu,(16./23.))) *(c7mWsm)
549+ c71constmu );
550
551_c71mu = (_alphasmW/_alphasmu *(pow(_etamu,(16./23.))* c7mWsm1 + 8./3. *(pow(_etamu,(14./23.))
552- pow(_etamu,(16./23.)) ) *c8mWsm1 ) + c71pmu);
553
554_c7emmu = ((32./75. *pow(_etamu,(-9./23.)) - 40./69. *pow(_etamu,(-7./23.)) +
555 88./575. *pow(_etamu,(16./23.))) *c7mWsm + (-32./575. *pow(_etamu,(-9./23.)) +
556 32./1449. *pow(_etamu,(-7./23.)) + 640./1449.*pow(_etamu,(14./23.)) -
557 704./1725.*pow(_etamu,(16./23.)) ) *c8mWsm
558 - 190./8073.*pow(_etamu,(-35./23.)) - 359./3105. *pow(_etamu,(-17./23.)) +
559 4276./121095. *pow(_etamu,(-12./23.)) + 350531./1009125.*pow(_etamu,(-9./23.))
560 + 2./4347. *pow(_etamu,(-7./23.)) - 5956./15525. *pow(_etamu,(6./23.)) +
561 38380./169533. *pow(_etamu,(14./23.)) - 748./8625. *pow(_etamu,(16./23.)));
562
563// Wilson coefficients values as according to Kagan's program
564// _c2mu=1.10566;
565//_c70mu=-0.314292;
566// _c80mu=-0.148954;
567// _c71mu=0.480964;
568// _c7emmu=0.0323219;
569
570}
571
572void EvtBtoXsgammaKagan::CalcDelta() {
573
574 double cDelta77 = (1. + (_alphasmu/(2.*EvtConst::pi)) *(_r7 - (16./3.) + _gam77*log(_mb/_mu)) + ( (pow((1. - _z),4.)/_fz) - 1.)*(6.*_lam2/pow(_mb,2.)) + (_alphasmubar/(2.*EvtConst::pi))*_kappabar )*pow(_c70mu,2.);
575
576 double cDelta27 = ((_alphasmu/(2.*EvtConst::pi))*(_rer2 + _gam27*log(_mb/_mu)) - (_lam2/(9.*_z*pow(_mb,2.))))*_c2mu*_c70mu;
577
578 double cDelta78 = (_alphasmu/(2.*EvtConst::pi))*(_rer8 + _gam87*log(_mb/_mu))*_c70mu*_c80mu;
579
580 _cDeltatot = cDelta77 + cDelta27 + cDelta78 + (_alphasmu/(2.*EvtConst::pi))*_c71mu*_c70mu + (_alpha/_alphasmu)*(2.*_c7emmu*_c70mu - _kSLemmu*pow(_c70mu,2.));
581
582}
583
584double EvtBtoXsgammaKagan::Delta(double y, double alphasMu) {
585
586 //Fix for singularity at endpoint
587 if (y >= 1.0) y = 0.9999999999;
588
589 return ( - 4.*(alphasMu/(3.*EvtConst::pi*(1. - y)))*(log(1. - y) + 7./4.)*
590 exp(-2.*(alphasMu/(3.*EvtConst::pi))*(pow(log(1. - y),2) + (7./2.)*log(1. - y))));
591
592}
593
594double EvtBtoXsgammaKagan::s77(double y) {
595
596 //Fix for singularity at endpoint
597 if (y >= 1.0) y = 0.9999999999;
598
599 return ((1./3.)*(7. + y - 2.*pow(y,2) - 2.*(1. + y)*log(1. - y)));
600}
601
602double EvtBtoXsgammaKagan::s88(double y, double mb, double ms) {
603
604 //Fix for singularity at endpoint
605 if (y >= 1.0) y = 0.9999999999;
606
607 return ((1./27.)*((2.*(2. - 2.*y + pow(y,2))/y)*(log(1. - y) + 2.*log(mb/ms))
608 - 2.*pow(y,2) - y - 8.*((1. - y)/y)));
609}
610
611double EvtBtoXsgammaKagan::s78(double y) {
612
613 //Fix for singularity at endpoint
614 if (y >= 1.0) y = 0.9999999999;
615
616 return ((8./9.)*(((1. - y)/y)*log(1. - y) + 1. + (pow(y,2)/4.)));
617}
618
619double EvtBtoXsgammaKagan::ReG(double y) {
620
621 if (y < 4.) return -2.*pow(atan(sqrt(y/(4. - y))),2.);
622 else {
623 return 2.*(pow(log((sqrt(y) + sqrt(y - 4.))/2.),2.)) - (1./2.)*pow(EvtConst::pi,2.);
624 }
625
626}
627
628double EvtBtoXsgammaKagan::ImG(double y) {
629
630 if (y < 4.) return 0.0;
631 else {
632 return (-2.*EvtConst::pi*log((sqrt(y) + sqrt(y - 4.))/2.));
633 }
634}
635
636double EvtBtoXsgammaKagan::s22Func(double y, const std::vector<double> &coeffs) {
637
638 //coeffs[0]=z
639 return (1. - y)*((pow(coeffs[0],2.)/pow(y,2.))*(pow(ReG(y/coeffs[0]),2.) + pow(ImG(y/coeffs[0]),2.)) + (coeffs[0]/y)*ReG(y/coeffs[0]) + (1./4.));
640
641}
642
643double EvtBtoXsgammaKagan::s27Func(double y, const std::vector<double> &coeffs) {
644
645 //coeffs[0] = z
646 return (ReG(y/coeffs[0]) + y/(2.*coeffs[0]));
647
648}
649
650double EvtBtoXsgammaKagan::DeltaFermiFunc(double y, const std::vector<double> &coeffs1,
651 const std::vector<double> &coeffs2, const std::vector<double> &coeffs3) {
652
653 //coeffs1=fermi function coeffs, coeffs2[0]=mB, coeffs2[1]=mb,
654 //coeffs2[2]=ymH, coeffs3[0]=DeltaCoeff (alphasmu)
655
656 return FermiFunc(y,coeffs1)*(coeffs2[0]/(coeffs2[1]+y))*
657 Delta((coeffs2[0]*coeffs2[2])/(coeffs2[1]+y),coeffs3[0]);
658
659}
660
661double EvtBtoXsgammaKagan::s77FermiFunc(double y, const std::vector<double> &coeffs1,
662 const std::vector<double> &coeffs2) {
663
664 //coeffs1=fermi function coeffs, coeffs2[0]=mB, coeffs2[1]=mb,
665 //coeffs2[2]=ymH
666 return FermiFunc(y,coeffs1)*(coeffs2[0]/(coeffs2[1]+y))*
667 s77((coeffs2[0]*coeffs2[2])/(coeffs2[1]+y));
668
669}
670
671double EvtBtoXsgammaKagan::s88FermiFunc(double y, const std::vector<double> &coeffs1,
672 const std::vector<double> &coeffs2, const std::vector<double> &coeffs3) {
673
674 //coeffs1=fermi function coeffs, coeffs2[0]=mB, coeffs2[1]=mb,
675 //coeffs2[2]=ymH, coeffs3=s88 coeffs
676 return FermiFunc(y,coeffs1)*(coeffs2[0]/(coeffs2[1]+y))*
677 s88((coeffs2[0]*coeffs2[2])/(coeffs2[1]+y),coeffs3[0], coeffs3[1]);
678
679}
680
681double EvtBtoXsgammaKagan::s78FermiFunc(double y, const std::vector<double> &coeffs1,
682 const std::vector<double> &coeffs2) {
683
684 //coeffs1=fermi function coeffs, coeffs2[0]=mB, coeffs2[1]=mb,
685 //coeffs2[2]=ymH
686 return FermiFunc(y,coeffs1)*(coeffs2[0]/(coeffs2[1]+y))*
687 s78((coeffs2[0]*coeffs2[2])/(coeffs2[1]+y));
688
689}
690
691double EvtBtoXsgammaKagan::sFermiFunc(double y, const std::vector<double> &coeffs1,
692 const std::vector<double> &coeffs2, const std::vector<double> &coeffs3,
693 const std::vector<double> &coeffs4) {
694
695 //coeffs1=fermi function coeffs, coeffs2[0]=mB, coeffs2[1]=mb,
696 //coeffs2[2]=ymH, coeffs3[0]=nIntervals in s22 or s27 array, coeffs3[1]=yMin,
697 //coeffs3[2]=yMax, coeffs4=s22 or s27 array
698 return FermiFunc(y,coeffs1)*(coeffs2[0]/(coeffs2[1]+y))*
699 GetArrayVal(coeffs2[0]*coeffs2[2]/(coeffs2[1]+y), coeffs3[0], coeffs3[1], coeffs3[2], coeffs4);
700
701}
702
703double EvtBtoXsgammaKagan::Fz(double z) {
704
705 return (1. -8.*z + 8.*pow(z,3.) - pow(z,4.) - 12.*pow(z,2.)*log(z));
706}
707
708double EvtBtoXsgammaKagan::GetArrayVal(double xp, double nInterval, double xMin, double xMax, std::vector<double> array) {
709
710 double dx = (xMax - xMin)/nInterval;
711 int bin1 = int(((xp-xMin)/(xMax - xMin))*nInterval);
712
713 double x1 = double(bin1)*dx + xMin;
714
715 if (xp == x1) return array[bin1];
716
717 int bin2(0);
718 if (xp > x1) {
719 bin2 = bin1 + 1;
720 }
721 else if (xp < x1) {
722 bin2 = bin1 - 1;
723 }
724
725 if (bin1 <= 0) {
726 bin1=0;
727 bin2 = 1;
728 }
729
730 //If xp is in the last bin, always interpolate between the last two bins
731 if (bin1 == (int)nInterval){
732 bin2 = (int)nInterval;
733 bin1 = (int)nInterval - 1;
734 x1 = double(bin1)*dx + xMin;
735 }
736
737 double x2 = double(bin2)*dx + xMin;
738 double y1 = array[bin1];
739
740 double y2 = array[bin2];
741 double m = (y2 - y1)/(x2 - x1);
742 double c = y1 - m*x1;
743 double result = m*xp + c;
744
745 return result;
746
747}
748
749double EvtBtoXsgammaKagan::FermiFunc(double y, const std::vector<double> &coeffs) {
750
751 //Fermi shape functions :1=exponential, 2=gaussian, 3=roman
752 if (int(coeffs[0]) == 1) return EvtBtoXsgammaFermiUtil::FermiExpFunc(y, coeffs);
753 if (int(coeffs[0]) == 2) return EvtBtoXsgammaFermiUtil::FermiGaussFunc(y, coeffs);
754 if (int(coeffs[0]) == 3) return EvtBtoXsgammaFermiUtil::FermiRomanFunc(y, coeffs);
755 return 1.;
756
757}
758
759double EvtBtoXsgammaKagan::diLogFunc(double y) {
760
761 return -log(fabs(1. - y))/y;
762
763}
764
765
766double EvtBtoXsgammaKagan::diLogMathematica(double y) {
767
768 double li2(0);
769 for(int i=1; i<1000; i++){ //the value 1000 should actually be Infinite...
770 li2+=pow(y,i)/(i*i);
771 }
772 return li2;
773}
mass
double mass
Definition: CosmicGenerator.cxx:138
f1
TFile * f1
Definition: DataBase/tau_mode.c:4
g1
TF1 * g1
Definition: DataBase/tau_mode.c:66
e1
Double_t e1
Definition: DataBase/tau_mode.c:7
e2
Double_t e2
Definition: DataBase/tau_mode.c:7
exp
EvtComplex exp(const EvtComplex &c)
Definition: EvtComplex.hh:252
report
ostream & report(Severity severity, const char *facility)
Definition: EvtReport.cc:36
ERROR
@ ERROR
Definition: EvtReport.hh:49
WARNING
@ WARNING
Definition: EvtReport.hh:50
v
**********Class see also m_nmax DOUBLE PRECISION m_amel DOUBLE PRECISION m_x2 DOUBLE PRECISION m_alfinv DOUBLE PRECISION m_Xenph INTEGER m_KeyWtm INTEGER m_idyfs DOUBLE PRECISION m_zini DOUBLE PRECISION m_q2 DOUBLE PRECISION m_Wt_KF DOUBLE PRECISION m_WtCut INTEGER m_KFfin *COMMON c_KarLud $ !Input CMS energy[GeV] $ !CMS energy after beam spread beam strahlung[GeV] $ !Beam energy spread[GeV] $ !z boost due to beam spread $ !electron beam mass *ff pair spectrum $ !minimum v
Definition: KarLud.h:35
EvtBtoXsgammaFermiUtil::FermiGaussFunc
static double FermiGaussFunc(double, std::vector< double > const &coeffs)
Definition: EvtBtoXsgammaFermiUtil.cc:48
EvtBtoXsgammaFermiUtil::FermiRomanFunc
static double FermiRomanFunc(double, std::vector< double > const &coeffs)
Definition: EvtBtoXsgammaFermiUtil.cc:187
EvtBtoXsgammaFermiUtil::FermiRomanFuncRoot
static double FermiRomanFuncRoot(double, double)
Definition: EvtBtoXsgammaFermiUtil.cc:163
EvtBtoXsgammaFermiUtil::FermiGaussFuncRoot
static double FermiGaussFuncRoot(double, double, double, std::vector< double > &coeffs)
Definition: EvtBtoXsgammaFermiUtil.cc:55
EvtBtoXsgammaFermiUtil::FermiExpFunc
static double FermiExpFunc(double var, const std::vector< double > &coeffs)
Definition: EvtBtoXsgammaFermiUtil.cc:40
EvtBtoXsgammaFermiUtil::Gamma
static double Gamma(double, const std::vector< double > &coeffs)
Definition: EvtBtoXsgammaFermiUtil.cc:100
EvtBtoXsgammaKagan::init
void init(int, double *)
Definition: EvtBtoXsgammaKagan.cc:64
EvtBtoXsgammaKagan::CalcAlphaS
double CalcAlphaS(double)
Definition: EvtBtoXsgammaKagan.cc:438
EvtBtoXsgammaKagan::computeHadronicMass
void computeHadronicMass(int, double *)
Definition: EvtBtoXsgammaKagan.cc:133
EvtBtoXsgammaKagan::GetMass
double GetMass(int code)
Definition: EvtBtoXsgammaKagan.cc:402
EvtConst::pi
static const double pi
Definition: EvtConst.hh:28
EvtItgAbsIntegrator::evaluate
double evaluate(double lower, double upper) const
Definition: EvtItgAbsIntegrator.cc:52
EvtItgAbsIntegrator::normalisation
double normalisation() const
Definition: EvtItgAbsIntegrator.cc:47
EvtItgFourCoeffFcn::setCoeff
virtual void setCoeff(int, int, double)
Definition: EvtItgFourCoeffFcn.cc:48
EvtItgThreeCoeffFcn::setCoeff
virtual void setCoeff(int, int, double)
Definition: EvtItgThreeCoeffFcn.cc:50
EvtItgTwoCoeffFcn::setCoeff
virtual void setCoeff(int, int, double)
Definition: EvtItgTwoCoeffFcn.cc:47
EvtRandom::Flat
static double Flat()
Definition: EvtRandom.cc:74
y
double y[1000]
Definition: draw_charge_space_coarse_II.cxx:8