EvtGen 2.2.0
Monte Carlo generator of particle decays, in particular the weak decays of heavy flavour particles such as B mesons.
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EvtbTosllWilsCoeffNLO.cpp
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1
2/***********************************************************************
3* Copyright 1998-2020 CERN for the benefit of the EvtGen authors *
4* *
5* This file is part of EvtGen. *
6* *
7* EvtGen is free software: you can redistribute it and/or modify *
8* it under the terms of the GNU General Public License as published by *
9* the Free Software Foundation, either version 3 of the License, or *
10* (at your option) any later version. *
11* *
12* EvtGen is distributed in the hope that it will be useful, *
13* but WITHOUT ANY WARRANTY; without even the implied warranty of *
14* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
15* GNU General Public License for more details. *
16* *
17* You should have received a copy of the GNU General Public License *
18* along with EvtGen. If not, see <https://www.gnu.org/licenses/>. *
19***********************************************************************/
20
21#include "EvtGenModels/EvtbTosllWilsCoeffNLO.hh"
22
23#include "EvtGenBase/EvtDiLog.hh"
24#include "EvtGenBase/EvtId.hh"
25#include "EvtGenBase/EvtReport.hh"
26#include "EvtGenBase/EvtTensor4C.hh"
27#include "EvtGenBase/EvtVector4C.hh"
28
29#include <cstdlib>
30
31// **************************************************************
32// * *
33// * The strong running coupling constant from PDG *
34// * *
35// * mu - the scale parameter ( in GeV ); *
36// * Nf - number of "effective" flavours ( Nf=5 for b-quark); *
37// * the colors number = 3; *
38// * ias - the number for alpha_s(M_Z) choice: *
39// * = 0 PDG 1sigma minimal alpha_s(M_Z); *
40// * = 1 PDG average value alpha_s(M_Z); *
41// * = 2 PDG 1sigma maximal alpha_s(M_Z). *
42// * *
43// **************************************************************
44double EvtbTosllWilsCoeffNLO::As( double mu, int Nf, int ias )
45{
46 double as, ll;
47 double b0, b1, b2; /* terms in the series of the beta-function */
48 double alpha_strong[] = { 0.1156, 0.1176, 0.1196 }; /* at M_Z scale */
49 double MZ = 91.19; /* in GeV */
50
51 b0 = 11. - 2. * ( (double)Nf ) / 3.;
52 b1 = 51. - 19. * ( (double)Nf ) / 3.;
53 b2 = 2857. - 5033. * ( (double)Nf ) / 9. +
54 325. * pow( ( (double)Nf ), 2. ) / 27.;
55
56 // RG Equation solution
57 alpha_strong[ias] = alpha_strong[ias] / ( 4.0 * EvtConst::pi );
58 ll = 0.0 - log( MZ / mu ) +
59 ( b0 * b2 - b1 * b1 ) * alpha_strong[ias] / ( 2.0 * pow( b0, 3.0 ) );
60 ll = ll + 1.0 / ( 2.0 * b0 * alpha_strong[ias] );
61 ll = ll + b1 * log( alpha_strong[ias] ) / ( 2.0 * b0 * b0 );
62
63 // Running coupling constant from M_Z to mu
64 as = pow( ( log( log( 2.0 * ll ) ) - 0.5 ), 2.0 ) +
65 b2 * b0 / ( 8.0 * b1 * b1 ) - 5.0 / 4.0;
66 as = as * pow( ( b1 / ( b0 * b0 * ll ) ), 2.0 );
67 as = 1.0 - b1 * log( 2.0 * ll ) / ( b0 * b0 * ll ) - as;
68 as = 2.0 * EvtConst::pi * as / ( b0 * ll );
69
70 if ( as <= 0.0 ) {
71 EvtGenReport( EVTGEN_ERROR, "EvtGen" )
72 << "The function EvtbTosllWilsCoeffNLO::As"
73 << "\n Unexpected value of the running coupling constant!"
74 << "\n alpha_s(" << mu << ") = " << as << ";"
75 << "\n Nf =" << Nf << ", ias = " << ias << ";"
76 << "\n ln(mu/lambda_QCD) = " << ll << ";" << std::endl;
77 ::abort();
78 }
79
80 return as;
81}
82
83// ************************************************************
84// * *
85// * Spencer function *
86// * in serial representation *
87// * ( w <= 1.0 ) *
88// * *
89// * *
90// ************************************************************
91double EvtbTosllWilsCoeffNLO::Li2( double w )
92{
93 double Lii = 0.0;
94 double k = 1.0;
95
96 while ( k <= 20.0 ) {
97 Lii = Lii + pow( w, k ) / pow( k, 2.0 );
98 k++;
99 };
100
101 /* printf("\n Spencer function value: Lii(%f)=%f \n\n",w,Lii); */
102
103 return Lii;
104}
105
106/* Coefficient C1(mu) *
107 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
108double EvtbTosllWilsCoeffNLO::C1( double mu, double Mw, int Nf, int ias )
109{
110 double CC1;
111 double eta;
112 double asW; /* the strong coupling constant at the scale Mw */
113 double asmu; /* the strong coupling constant at the scale mu */
114 int i;
115
116 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
117 0.4086, -0.4230, -0.8994, 0.1456 };
118 double k1[] = { 0.0, 0.0, 0.5, -0.5, 0.0, 0.0, 0.0, 0.0 };
119
120 asW = As( Mw, Nf, ias );
121 asmu = As( mu, Nf, ias );
122 eta = asW / asmu;
123
124 CC1 = 0.0;
125 i = 0;
126 while ( i < 8 ) {
127 CC1 = CC1 + k1[i] * pow( eta, a[i] );
128 i++;
129 };
130
131 return CC1;
132}
133
134/* Coefficient C2(mu) *
135 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
136double EvtbTosllWilsCoeffNLO::C2( double mu, double Mw, int Nf, int ias )
137{
138 double CC2;
139 double eta;
140 double asW; /* the strong coupling constant at the scale Mw */
141 double asmu; /* the strong coupling constant at the scale mu */
142 int i;
143
144 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
145 0.4086, -0.4230, -0.8994, 0.1456 };
146 double k2[] = { 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0 };
147
148 asW = As( Mw, Nf, ias );
149 asmu = As( mu, Nf, ias );
150 eta = asW / asmu;
151
152 CC2 = 0.0;
153 i = 0;
154 while ( i < 8 ) {
155 CC2 = CC2 + k2[i] * pow( eta, a[i] );
156 i++;
157 };
158
159 return CC2;
160}
161
162/* Coefficient C3(mu) *
163 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
164double EvtbTosllWilsCoeffNLO::C3( double mu, double Mw, int Nf, int ias )
165{
166 double CC3;
167 double eta;
168 double asW; /* the strong coupling constant at the scale Mw */
169 double asmu; /* the strong coupling constant at the scale mu */
170 int i;
171
172 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
173 0.4086, -0.4230, -0.8994, 0.1456 };
174 double k3[] = { 0.0, 0.0, -1.0 / 14.0, 1.0 / 6.0,
175 0.0510, -0.1403, -0.0113, 0.0054 };
176
177 asW = As( Mw, Nf, ias );
178 asmu = As( mu, Nf, ias );
179 eta = asW / asmu;
180
181 CC3 = 0.0;
182 i = 0;
183 while ( i < 8 ) {
184 CC3 = CC3 + k3[i] * pow( eta, a[i] );
185 i++;
186 };
187
188 return CC3;
189}
190
191/* Coefficient C4(mu) *
192 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
193double EvtbTosllWilsCoeffNLO::C4( double mu, double Mw, int Nf, int ias )
194{
195 double CC4;
196 double eta;
197 double asW; /* the strong coupling constant at the scale Mw */
198 double asmu; /* the strong coupling constant at the scale mu */
199 int i;
200
201 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
202 0.4086, -0.4230, -0.8994, 0.1456 };
203 double k4[] = { 0.0, 0.0, -1.0 / 14.0, -1.0 / 6.0,
204 0.0984, 0.1214, 0.0156, 0.0026 };
205
206 asW = As( Mw, Nf, ias );
207 asmu = As( mu, Nf, ias );
208 eta = asW / asmu;
209
210 CC4 = 0.0;
211 i = 0;
212 while ( i < 8 ) {
213 CC4 = CC4 + k4[i] * pow( eta, a[i] );
214 i++;
215 };
216
217 return CC4;
218}
219
220/* Coefficient C5(mu) *
221 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
222double EvtbTosllWilsCoeffNLO::C5( double mu, double Mw, int Nf, int ias )
223{
224 double CC5;
225 double eta;
226 double asW; /* the strong coupling constant at the scale Mw */
227 double asmu; /* the strong coupling constant at the scale mu */
228 int i;
229
230 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
231 0.4086, -0.4230, -0.8994, 0.1456 };
232 double k5[] = { 0.0, 0.0, 0.0, 0.0, -0.0397, 0.0117, -0.0025, 0.0304 };
233
234 asW = As( Mw, Nf, ias );
235 asmu = As( mu, Nf, ias );
236 eta = asW / asmu;
237
238 CC5 = 0.0;
239 i = 0;
240 while ( i < 8 ) {
241 CC5 = CC5 + k5[i] * pow( eta, a[i] );
242 i++;
243 };
244
245 return CC5;
246}
247
248/* Coefficient C6(mu) *
249 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
250double EvtbTosllWilsCoeffNLO::C6( double mu, double Mw, int Nf, int ias )
251{
252 double CC6;
253 double eta;
254 double asW; /* the strong coupling constant at the scale Mw */
255 double asmu; /* the strong coupling constant at the scale mu */
256 int i;
257
258 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
259 0.4086, -0.4230, -0.8994, 0.1456 };
260 double k6[] = { 0.0, 0.0, 0.0, 0.0, 0.0335, 0.0239, -0.0462, -0.0112 };
261
262 asW = As( Mw, Nf, ias );
263 asmu = As( mu, Nf, ias );
264 eta = asW / asmu;
265
266 CC6 = 0.0;
267 i = 0;
268 while ( i < 8 ) {
269 CC6 = CC6 + k6[i] * pow( eta, a[i] );
270 i++;
271 };
272
273 return CC6;
274}
275
276/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
277double EvtbTosllWilsCoeffNLO::A( double z )
278{
279 double AA;
280
281 AA = z * ( 8.0 * pow( z, 2.0 ) + 5.0 * z - 7.0 ) /
282 ( 12.0 * pow( ( z - 1.0 ), 3.0 ) );
283 AA = AA + pow( z, 2.0 ) * ( 2.0 - 3.0 * z ) * log( z ) /
284 ( 2.0 * pow( ( z - 1.0 ), 4.0 ) );
285
286 return AA;
287}
288
289/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
290double EvtbTosllWilsCoeffNLO::B( double z )
291{
292 double BB;
293
294 BB = z / ( 4.0 * ( 1.0 - z ) ) +
295 z * log( z ) / ( 4.0 * pow( ( 1.0 - z ), 2.0 ) );
296
297 return BB;
298}
299
300/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
301double EvtbTosllWilsCoeffNLO::C_Bur( double z )
302{
303 double CC;
304
305 CC = z * ( z - 6.0 ) / ( 8.0 * ( z - 1.0 ) );
306 CC = CC +
307 z * ( 3.0 * z + 2.0 ) * log( z ) / ( 8.0 * pow( ( z - 1.0 ), 2.0 ) );
308
309 return CC;
310}
311
312/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
313double EvtbTosllWilsCoeffNLO::D_Bur( double z )
314{
315 double DD;
316
317 DD = ( 25.0 * pow( z, 2.0 ) - 19.0 * pow( z, 3.0 ) ) /
318 ( 36.0 * pow( ( z - 1.0 ), 3.0 ) );
319 DD = DD + pow( z, 2.0 ) * ( 5.0 * pow( z, 2.0 ) - 2.0 * z - 6.0 ) *
320 log( z ) / ( 18.0 * pow( ( z - 1.0 ), 4.0 ) );
321 DD = DD - ( 4.0 / 9.0 ) * log( z );
322
323 return DD;
324}
325
326/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
327double EvtbTosllWilsCoeffNLO::E( double z )
328{
329 double EE;
330
331 EE = z * ( 18.0 - 11.0 * z - z * z ) / ( 12.0 * pow( ( 1.0 - z ), 3.0 ) );
332 EE = EE + pow( z, 2.0 ) * ( 15.0 - 16.0 * z + 4.0 * z * z ) * log( z ) /
333 ( 6.0 * pow( ( 1.0 - z ), 4.0 ) );
334 EE = EE - ( 2.0 / 3.0 ) * log( z );
335
336 return EE;
337}
338
339/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
340double EvtbTosllWilsCoeffNLO::F_Bur( double z )
341{
342 double FF;
343
344 FF = z * ( pow( z, 2.0 ) - 5.0 * z - 2.0 ) /
345 ( 4.0 * pow( ( z - 1.0 ), 3.0 ) );
346 FF = FF + 3.0 * pow( z, 2.0 ) * log( z ) / ( 2.0 * pow( ( z - 1.0 ), 4.0 ) );
347
348 return FF;
349}
350
351/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
352double EvtbTosllWilsCoeffNLO::Y( double z )
353{
354 double YY;
355
356 YY = C_Bur( z ) - B( z );
357
358 return YY;
359}
360
361/* by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
362double EvtbTosllWilsCoeffNLO::Z( double z )
363{
364 double ZZ;
365
366 ZZ = C_Bur( z ) + 0.25 * D_Bur( z );
367
368 return ZZ;
369}
370
371/* Coefficient C7gamma(mu) in the SM *
372 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
373double EvtbTosllWilsCoeffNLO::C7gamma( double mu, double Mw, double mt, int Nf,
374 int ias )
375{
376 double C7, C70, C80, sum;
377 double AA, FF;
378 double x, eta;
379 double asW, asmu;
380 int i;
381
382 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
383 0.4086, -0.4230, -0.8994, 0.1456 };
384 double h[] = { 2.2996, -1.0880, -3.0 / 7.0, -1.0 / 14.0,
385 -0.6494, -0.0380, -0.0186, -0.0057 };
386
387 x = pow( mt / Mw, 2.0 );
388 asW = As( Mw, Nf, ias );
389 asmu = As( mu, Nf, ias );
390 eta = asW / asmu;
391
392 AA = A( x );
393 FF = F_Bur( x );
394
395 C70 = -0.5 * AA;
396 C80 = -0.5 * FF;
397
398 C7 = pow( eta, ( 16.0 / 23.0 ) ) * C70;
399 C7 = C7 + ( 8.0 / 3.0 ) *
400 ( pow( eta, ( 14.0 / 23.0 ) ) - pow( eta, ( 16.0 / 23.0 ) ) ) *
401 C80;
402
403 sum = 0.0;
404 i = 0;
405 while ( i < 8 ) {
406 sum = sum + h[i] * pow( eta, a[i] );
407 i++;
408 };
409 C7 = C7 + sum;
410
411 return C7;
412}
413
414/* Coefficient P_E *
415 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186; *
416 * see formula (2.12). */
417double EvtbTosllWilsCoeffNLO::Pe( double eta )
418{
419 double sum;
420 double Pee;
421 int i;
422
423 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
424 0.4086, -0.4230, -0.8994, 0.1456 };
425 double q[] = { 0.0, 0.0, 0.0, 0.0, 0.0318, 0.0918, -0.2700, 0.0059 };
426
427 sum = 0.0;
428 i = 0;
429 while ( i < 8 ) {
430 sum = sum + q[i] * pow( eta, ( a[i] + 1.0 ) );
431 i++;
432 };
433 Pee = 0.1405 + sum;
434
435 return Pee;
436}
437
438/* Coefficient P^{NDR}_0 *
439 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186; *
440 * see formula (2.11). */
441double EvtbTosllWilsCoeffNLO::P0ndr( double asW, double eta )
442{
443 double P00ndr;
444 double sum;
445 int i;
446
447 double a[] = { 14.0 / 23.0, 16.0 / 23.0, 6.0 / 23.0, -12.0 / 23.0,
448 0.4086, -0.4230, -0.8994, 0.1456 };
449 double p[] = { 0.0, 0.0, -80.0 / 203.0, 8.0 / 33.0,
450 0.0433, 0.1384, 0.1648, -0.0073 };
451 double r[] = { 0.0, 0.0, 0.8966, -0.1960,
452 -0.2011, 0.1328, -0.0292, -0.1858 };
453 double s[] = { 0.0, 0.0, -0.2009, -0.3579,
454 0.0490, -0.3616, -0.3554, 0.0072 };
455
456 sum = 0.0;
457 i = 0;
458 while ( i < 8 ) {
459 sum = sum + p[i] * pow( eta, ( a[i] + 1.0 ) );
460 i++;
461 };
462 P00ndr = EvtConst::pi * ( -0.1875 + sum ) / asW;
463 P00ndr = P00ndr + 1.2468;
464 sum = 0.0;
465 i = 0;
466 while ( i < 8 ) {
467 sum = sum + ( r[i] + s[i] * eta ) * pow( eta, a[i] );
468 i++;
469 };
470 P00ndr = P00ndr + sum;
471
472 return P00ndr;
473}
474
475/* Coefficient C_{9V} (in the NDR schime) *
476 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186 *
477 * accordint to the equation (2.10). */
478double EvtbTosllWilsCoeffNLO::C9v( double mu, double Mw, double mt, int Nf,
479 int ias )
480{
481 double C9;
482 double x, eta;
483 double asW, asmu;
484 double sin2W = 0.224; /* the square of the weak angle */
485
486 x = pow( mt / Mw, 2.0 );
487 asW = As( Mw, Nf, ias );
488 asmu = As( mu, Nf, ias );
489 eta = asW / asmu;
490
491 /* C9 */
492 C9 = P0ndr( asW, eta ) + ( Y( x ) / sin2W ) - 4.0 * Z( x ) +
493 Pe( eta ) * E( x );
494
495 return C9;
496}
497
498/* Coefficient C_{10A} *
499 * by A.J.Buras and M.Munz, Phys.Rev. D52, 186; *
500 * see formula (2.8). */
501double EvtbTosllWilsCoeffNLO::C10a( double mt, double Mw )
502{
503 double C10;
504 double x;
505 double sin2W = 0.224; /* the square of the Winberg angle */
506
507 x = pow( mt / Mw, 2.0 );
508
509 C10 = -Y( x ) / sin2W;
510
511 return C10;
512}
513
514/* The real part of the q\bar q loop contribution *
515 * Re(h(z,\hat s)) *
516 * A.J.Buras and M.Munz, Phys.Rev. D52, 186; *
517 * the equation (2.29). *
518 * *
519 * mu - the scale parameter (GeV); *
520 * mQ - the mass of the u- or c-quark (GeV); *
521 * q2 - the square of transition 4-momentum (GeV^2). */
522double EvtbTosllWilsCoeffNLO::Reh( double mu, double mQ, double q2 )
523{
524 double reh, swh;
525 double x; /* Buras variable "x" from (2.29) */
526
527 x = 4.0 * pow( mQ, 2.0 ) / q2;
528
529 reh = 8.0 / 27.0 - 8.0 * log( mQ / mu ) / 9.0 + 4.0 * x / 9.0;
530
531 swh = 2.0 * ( 2.0 + x ) * sqrt( fabs( 1.0 - x ) ) / 9.0;
532
533 if ( x <= 1.0 ) {
534 swh = swh * log( fabs( ( sqrt( 1.0 - x ) + 1.0 ) /
535 ( sqrt( 1.0 - x ) - 1.0 ) ) );
536 } else {
537 swh = swh * 2.0 * atan( 1.0 / sqrt( x - 1.0 ) );
538 };
539
540 reh = reh - swh;
541
542 return reh;
543}
544
545/* Im(h(z,\hat s)) by Buras */
546double EvtbTosllWilsCoeffNLO::Imh( double mQ, double q2 )
547{
548 double x; /* Buras variable "x" from (2.29) */
549 double imh;
550
551 x = 4.0 * pow( mQ, 2.0 ) / q2;
552
553 if ( x <= 1.0 ) {
554 imh = 2.0 * EvtConst::pi * ( 2.0 + x ) * sqrt( fabs( 1.0 - x ) ) / 9.0;
555 } else {
556 imh = 0.0;
557 };
558 return imh;
559}
560
561/* The real part of the one resonant contribution *
562 * q2 - the square of transition 4-momentum (GeV^2); *
563 * GV - the decay width of the resonance (GeV); *
564 * GllV - the decay width of the resonance into l^+ l^- - pair (GeV); *
565 * MV - the mass of the resonance. */
566double EvtbTosllWilsCoeffNLO::ReResonant( double q2, double GV, double GllV,
567 double MV )
568{
569 double reresonant;
570 double resa, resb;
571
572 resa = q2 * ( MV * MV - q2 ) * GllV;
573 resb = MV * ( ( MV * MV - q2 ) * ( MV * MV - q2 ) + MV * MV * GV * GV );
574 reresonant = resa / resb;
575
576 return reresonant;
577}
578
579/* The imaginary part of the one resonant contribution *
580 * q2 - the square of transition 4-momentum (GeV^2); *
581 * GV - the decay width of the resonance (GeV); *
582 * GllV - the decay width of the resonance into l^+ l^- - pair (GeV); *
583 * MV - the mass of the resonance. */
584double EvtbTosllWilsCoeffNLO::ImResonant( double q2, double GV, double GllV,
585 double MV )
586{
587 double imresonant;
588 double resa, resb;
589
590 resa = q2 * GV * GllV;
591 resb = ( MV * MV - q2 ) * ( MV * MV - q2 ) + MV * MV * GV * GV;
592 imresonant = resa / resb;
593
594 return imresonant;
595}
596
597/* The real part of the total q\barq-contribution *
598 * *
599 * qflavour = 0 corresponding the u-quark contribution *
600 * = 1 corresponding the c-quark contribution; *
601 * *
602 * res_swch = 0 the resonant contribution switch OFF *
603 * = 1 the resonant contribution switch ON; *
604 * *
605 * ias -- switching parameter for Lms[] in the As(..) function. *
606 * *
607 * Nf - number of "effective" flavours (for b-quark Nf=5); *
608 * mu - the scale parameter (GeV); *
609 * mQ - the mass of the u- or c-quark (GeV); *
610 * q2 - the square of transition 4-momentum (GeV^2); *
611 * ml - the mass of the final leptons (GeV); *
612 * Mw - the mass of the W--meson (GeV). *
613 * */
614double EvtbTosllWilsCoeffNLO::ReHtot( int qflavour, int res_swch, int ias,
615 int Nf, double mu, double mQ, double q2,
616 double ml, double Mw )
617{
618 double rehtot;
619 double rehres, c1, c2;
620 int i;
621
622 /* Total decay widths of the resonances (GeV) */
623 double Gamma[6];
624 /* The decay width of the resonances into l^+ l^- - pair (GeV) */
625 double Gamma_ll[6];
626 /* The mass of the resonances */
627 double M[6];
628
629 double alpha_qed = 1.0 / 137.0;
630
631 switch ( qflavour ) {
632 /* u-quark contribution */
633 case 0:
634 switch ( res_swch ) {
635 /* The resonant contribution switch OFF */
636 case 0:
637 rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
638 rehres = 0.0;
639 break;
640 /* the resonant contribution switch ON */
641 case 1:
642 rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
643
644 /* \pho */
645 M[0] = 0.7755; /* GeV */
646 Gamma[0] = 0.1494; /* GeV */
647 /* \omega' */
648 M[1] = 0.7827; /* GeV */
649 Gamma[1] = 0.0085; /* GeV */
650
651 if ( ml < 1.0 ) {
652 /* in e^+e^- or mu^+mu^- */
653 Gamma_ll[0] = 0.000007; /* \rho */
654 Gamma_ll[1] = 0.0000006; /* \omega */
655 } else {
656 /* in \tau^+\tau^- */
657 Gamma_ll[0] = 0.0; /* \rho */
658 Gamma_ll[1] = 0.0; /* \omega */
659 };
660
661 c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
662 c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
663
664 i = 0;
665 rehres = 0.0;
666 while ( i < 2 ) {
667 rehres = rehres +
668 3.0 * EvtConst::pi *
669 EvtbTosllWilsCoeffNLO::ReResonant(
670 q2, Gamma[i], Gamma_ll[i], M[i] ) /
671 ( sqrt( 2.0 ) * ( 3.0 * c1 + c2 ) *
672 alpha_qed * alpha_qed );
673 i++;
674 };
675
676 /* The sign plus are corresponded to the relation:
677 \kappa*(3C_1+C_2)=1
678 with sign of Wilson coefficien C_2(M_W)=+1 as at work
679 A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
680 rehtot = rehtot + rehres;
681 break;
682 default:
683 rehtot = 0.0;
684 rehres = 0.0;
685 };
686 break;
687 /* c-quark contribution */
688 case 1:
689 switch ( res_swch ) {
690 /* The resonant contribution switch OFF */
691 case 0:
692 rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
693 rehres = 0.0;
694 break;
695 /* the resonant contribution switch ON */
696 case 1:
697 rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
698
699 /* J/psi */
700 M[0] = 3.096916; /* GeV */
701 Gamma[0] = 0.000093; /* GeV */
702 /* psi' */
703 M[1] = 3.68609; /* GeV */
704 Gamma[1] = 0.000317; /* GeV */
705 /* psi(3770) */
706 M[2] = 3.77292; /* GeV */
707 Gamma[2] = 0.0273; /* GeV */
708 /* psi(4040) */
709 M[3] = 4.039; /* GeV */
710 Gamma[3] = 0.08; /* GeV */
711 /* psi(4160) */
712 M[4] = 4.153; /* GeV */
713 Gamma[4] = 0.103; /* GeV */
714 /* psi(4415) */
715 M[5] = 4.421; /* GeV */
716 Gamma[5] = 0.062; /* GeV */
717
718 if ( ml < 1.0 ) {
719 /* in e^+e^- or mu^+mu^- */
720 Gamma_ll[0] = Gamma[0] * 0.059; /* J/psi */
721 Gamma_ll[1] = Gamma[1] * 0.0075; /* psi' */
722 Gamma_ll[2] = Gamma[2] * 0.0000097; /* psi(3770) */
723 Gamma_ll[3] = Gamma[3] * 0.00001; /* psi(4040) */
724 Gamma_ll[4] = Gamma[4] * 0.0000081; /* psi(4160) */
725 Gamma_ll[5] = Gamma[5] * 0.0000094; /* psi(4415) */
726 } else {
727 /* in \tau^+\tau^- */
728 Gamma_ll[0] = 0.0; /* J/psi */
729 Gamma_ll[1] = Gamma[1] * 0.003; /* psi' */
730 Gamma_ll[2] = Gamma[2] * 0.0; /* psi(3770) */
731 Gamma_ll[3] = Gamma[3] * 0.0; /* psi(4040) */
732 Gamma_ll[4] = Gamma[4] * 0.0; /* psi(4160) */
733 Gamma_ll[5] = Gamma[5] * 0.0; /* psi(4415) */
734 };
735
736 c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
737 c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
738
739 i = 0;
740 rehres = 0.0;
741 while ( i < 6 ) {
742 rehres = rehres +
743 3.0 * EvtConst::pi *
744 EvtbTosllWilsCoeffNLO::ReResonant(
745 q2, Gamma[i], Gamma_ll[i], M[i] ) /
746 ( ( 3.0 * c1 + c2 ) * alpha_qed * alpha_qed );
747 i++;
748 };
749
750 /* The sign plus are corresponded to the relation:
751 \kappa*(3C_1+C_2)=1
752 with sign of Wilson coefficien C_2(M_W)=+1 as at work
753 A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
754 rehtot = rehtot + rehres;
755 break;
756 default:
757 rehtot = 0.0;
758 rehres = 0.0;
759 };
760 break;
761 default:
762 rehtot = 0.0;
763 rehres = 0.0;
764 };
765
766 return rehtot;
767}
768
769/* The imaginary of the total q\barq-contribution *
770 * *
771 * qflavour = 0 corresponding the u-quark contribution *
772 * = 1 corresponding the c-quark contribution; *
773 * *
774 * res_swch = 0 the resonant contribution switch OFF *
775 * = 1 the resonant contribution switch ON; *
776 * *
777 * ias -- switching parameter for Lms[] in the As(..) function. *
778 * *
779 * Nf - number of "effective" flavours (for b-quark Nf=5); *
780 * mu - the scale parameter (GeV); *
781 * mQ - the mass of the u- or c-quark (GeV); *
782 * q2 - the square of transition 4-momentum (GeV^2); *
783 * ml - the mass of the final leptons (GeV); *
784 * Mw - the mass of the W--meson (GeV). *
785 * */
786double EvtbTosllWilsCoeffNLO::ImHtot( int qflavour, int res_swch, int ias,
787 int Nf, double mu, double mQ, double q2,
788 double ml, double Mw )
789{
790 double imhtot;
791 double imhres, c1, c2;
792 int i;
793
794 /* Total decay widths of the resonances (GeV) */
795 double Gamma[6];
796 /* The decay width of the resonances into l^+ l^- - pair (GeV) */
797 double Gamma_ll[6];
798 /* The mass of the resonances */
799 double M[6];
800
801 double alpha_qed = 1.0 / 137.0;
802
803 switch ( qflavour ) {
804 /* u-quark contribution */
805 case 0:
806 switch ( res_swch ) {
807 /* The resonant contribution switch OFF */
808 case 0:
809 imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
810 imhres = 0.0;
811 break;
812 /* the resonant contribution switch ON */
813 case 1:
814 imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
815
816 /* \pho */
817 M[0] = 0.7755; /* GeV */
818 Gamma[0] = 0.1494; /* GeV */
819 /* \omega' */
820 M[1] = 0.7827; /* GeV */
821 Gamma[1] = 0.0085; /* GeV */
822
823 if ( ml < 1.0 ) {
824 /* in e^+e^- or mu^+mu^- */
825 Gamma_ll[0] = 0.000007; /* \rho */
826 Gamma_ll[1] = 0.0000006; /* \omega */
827 } else {
828 /* in \tau^+\tau^- */
829 Gamma_ll[0] = 0.0; /* \rho */
830 Gamma_ll[1] = 0.0; /* \omega */
831 };
832
833 c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
834 c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
835
836 i = 0;
837 imhres = 0.0;
838 while ( i < 2 ) {
839 imhres = imhres +
840 3.0 * EvtConst::pi *
841 EvtbTosllWilsCoeffNLO::ImResonant(
842 q2, Gamma[i], Gamma_ll[i], M[i] ) /
843 ( sqrt( 2.0 ) * ( 3.0 * c1 + c2 ) *
844 alpha_qed * alpha_qed );
845 i++;
846 };
847
848 /* The sign plus are corresponded to the relation:
849 \kappa*(3C_1+C_2)=1
850 with sign of Wilson coefficien C_2(M_W)=+1 as at work
851 A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
852 imhtot = imhtot + imhres;
853 break;
854 default:
855 imhtot = 0.0;
856 imhres = 0.0;
857 };
858 break;
859 /* c-quark contribution */
860 case 1:
861 switch ( res_swch ) {
862 /* The resonant contribution switch OFF */
863 case 0:
864 imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
865 imhres = 0.0;
866 break;
867 /* the resonant contribution switch ON */
868 case 1:
869 imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
870
871 /* J/psi */
872 M[0] = 3.096916; /* GeV */
873 Gamma[0] = 0.000093; /* GeV */
874 /* psi' */
875 M[1] = 3.68609; /* GeV */
876 Gamma[1] = 0.000317; /* GeV */
877 /* psi(3770) */
878 M[2] = 3.77292; /* GeV */
879 Gamma[2] = 0.0273; /* GeV */
880 /* psi(4040) */
881 M[3] = 4.039; /* GeV */
882 Gamma[3] = 0.08; /* GeV */
883 /* psi(4160) */
884 M[4] = 4.153; /* GeV */
885 Gamma[4] = 0.103; /* GeV */
886 /* psi(4415) */
887 M[5] = 4.421; /* GeV */
888 Gamma[5] = 0.062; /* GeV */
889
890 if ( ml < 1.0 ) {
891 /* in e^+e^- or mu^+mu^- */
892 Gamma_ll[0] = Gamma[0] * 0.059; /* J/psi */
893 Gamma_ll[1] = Gamma[1] * 0.0075; /* psi' */
894 Gamma_ll[2] = Gamma[2] * 0.0000097; /* psi(3770) */
895 Gamma_ll[3] = Gamma[3] * 0.00001; /* psi(4040) */
896 Gamma_ll[4] = Gamma[4] * 0.0000081; /* psi(4160) */
897 Gamma_ll[5] = Gamma[5] * 0.0000094; /* psi(4415) */
898 } else {
899 /* in \tau^+\tau^- */
900 Gamma_ll[0] = 0.0; /* J/psi */
901 Gamma_ll[1] = Gamma[1] * 0.003; /* psi' */
902 Gamma_ll[2] = Gamma[2] * 0.0; /* psi(3770) */
903 Gamma_ll[3] = Gamma[3] * 0.0; /* psi(4040) */
904 Gamma_ll[4] = Gamma[4] * 0.0; /* psi(4160) */
905 Gamma_ll[5] = Gamma[5] * 0.0; /* psi(4415) */
906 };
907
908 c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
909 c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
910
911 i = 0;
912 imhres = 0.0;
913 while ( i < 6 ) {
914 imhres = imhres +
915 3.0 * EvtConst::pi *
916 EvtbTosllWilsCoeffNLO::ImResonant(
917 q2, Gamma[i], Gamma_ll[i], M[i] ) /
918 ( ( 3.0 * c1 + c2 ) * alpha_qed * alpha_qed );
919 i++;
920 };
921
922 /* The sign plus are corresponded to the relation:
923 \kappa*(3C_1+C_2)=1
924 with sign of Wilson coefficien C_2(M_W)=+1 as at work
925 A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
926 imhtot = imhtot + imhres;
927 break;
928 default:
929 imhtot = 0.0;
930 imhres = 0.0;
931 };
932 break;
933 default:
934 imhtot = 0.0;
935 imhres = 0.0;
936 };
937
938 return imhtot;
939}
940
941/* Function \omega(\hat s) *
942 * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189. *
943 * *
944 * q2 - the square of transition 4-momentum (GeV^2); *
945 * m2 - the mass of the b-quark (GeV). */
946double EvtbTosllWilsCoeffNLO::omega( double q2, double m2 )
947{
948 double oomega;
949 double s;
950
951 s = q2 / ( m2 * m2 ); /* see definition in the equation (2.26) */
952
953 if ( s > 1.0 ) {
954 s = 0.999999;
955 }
956 oomega = -2.0 * pow( EvtConst::pi, 2.0 ) / 9.0 - 4.0 * Li2( s ) / 3.0;
957 oomega = oomega - 2.0 * log( s ) * log( 1.0 - s ) / 3.0;
958 oomega = oomega -
959 ( 5.0 + 4.0 * s ) * log( 1.0 - s ) / ( 3.0 * ( 1.0 + 2.0 * s ) );
960 oomega = oomega - 2.0 * s * ( 1.0 + s ) * ( 1.0 - 2.0 * s ) * log( s ) /
961 ( 3.0 * pow( ( 1.0 - s ), 2.0 ) * ( 1.0 + 2.0 * s ) );
962 oomega = oomega + ( 5.0 + 9.0 * s - 6.0 * s * s ) /
963 ( 6.0 * ( 1.0 - s ) * ( 1.0 + 2.0 * s ) );
964
965 return oomega;
966}
967
968/* REAL PART of the effective coefficient C_9V^{eff}: *
969 * *
970 * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189; *
971 * F.Kruger, L.M.Sehgal, Phys.Rev.D55 (1997), p.2799. *
972 * *
973 * decay_id = 0 for b -> q l^+ i^- transitions *
974 * 1 for \bar b -> \bar q l^+ l^- transitions; *
975 * *
976 * res_swch = 0 the resonant contribution switch OFF *
977 * = 1 the resonant contribution switch ON; *
978 * *
979 * ias -- switching parameter for Lms[] in the As(..) function. *
980 * *
981 * Nf -- number of "effective" flavors (for b-quark Nf=5); *
982 * *
983 * q2 -- the square of transition 4-momentum; *
984 * m2 -- b-quark mass (in the heavy meson M1), GeV; *
985 * md -- mass of the u- and d-quarks, GeV; *
986 * mc -- c-quark mass, GeV; *
987 * mu -- scale parameter, GeV; *
988 * mt -- t-quark mass, GeV; *
989 * Mw -- mass of the W, GeV; *
990 * ml -- leptonic mass, GeV; *
991 * *
992 * Relambda_qu -- Re(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
993 * Imlambda_qu -- Im(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
994 * */
995double EvtbTosllWilsCoeffNLO::ReC9eff( int decay_id, int res_swch, int ias,
996 int Nf, double q2, double m2, double md,
997 double mc, double mu, double mt,
998 double Mw, double ml, double Relambda_qu,
999 double Imlambda_qu )
1000{
1001 double RReC9eff;
1002 double tilde_eta; /* Buras variable " \tilde\eta" in (2.33) */
1003 double c1, c2, c3, c4, c5, c6, c9;
1004 double RReh_d, RReh_b, RReHtot_u, IImHtot_u, RReHtot_c, IImHtot_c;
1005
1006 tilde_eta = 1.0 + EvtbTosllWilsCoeffNLO::As( mu, Nf, ias ) *
1007 EvtbTosllWilsCoeffNLO::omega( q2, m2 ) / EvtConst::pi;
1008
1009 c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
1010 c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
1011 c3 = EvtbTosllWilsCoeffNLO::C3( mu, Mw, Nf, ias );
1012 c4 = EvtbTosllWilsCoeffNLO::C4( mu, Mw, Nf, ias );
1013 c5 = EvtbTosllWilsCoeffNLO::C5( mu, Mw, Nf, ias );
1014 c6 = EvtbTosllWilsCoeffNLO::C6( mu, Mw, Nf, ias );
1015 c9 = EvtbTosllWilsCoeffNLO::C9v( mu, Mw, mt, Nf, ias );
1016
1017 RReh_d = EvtbTosllWilsCoeffNLO::Reh( mu, md, q2 );
1018 RReh_b = EvtbTosllWilsCoeffNLO::Reh( mu, m2, q2 );
1019 RReHtot_u = EvtbTosllWilsCoeffNLO::ReHtot( 0, res_swch, ias, Nf, mu, md, q2,
1020 ml, Mw );
1021 IImHtot_u = EvtbTosllWilsCoeffNLO::ImHtot( 0, res_swch, ias, Nf, mu, md, q2,
1022 ml, Mw );
1023 RReHtot_c = EvtbTosllWilsCoeffNLO::ReHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1024 ml, Mw );
1025 IImHtot_c = EvtbTosllWilsCoeffNLO::ImHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1026 ml, Mw );
1027
1028 RReC9eff = c9 * tilde_eta + 2.0 * ( 3.0 * c3 + c4 + 3.0 * c5 + c6 ) / 9.0;
1029 RReC9eff = RReC9eff +
1030 ( 3.0 * c1 + c2 + 3.0 * c3 + c4 + 3.0 * c5 + c6 ) * RReHtot_c;
1031 RReC9eff = RReC9eff - 0.5 * ( 4.0 * c3 + 4.0 * c4 + 3.0 * c5 + c6 ) * RReh_b;
1032 RReC9eff = RReC9eff - 0.5 * ( c3 + 3.0 * c4 ) * RReh_d;
1033
1034 switch ( decay_id ) {
1035 /* b -> q l^+ i^- transitions */
1036 case 0:
1037 RReC9eff = RReC9eff + ( 3.0 * c1 + c2 ) *
1038 ( Relambda_qu * ( RReHtot_c - RReHtot_u ) -
1039 Imlambda_qu * ( IImHtot_c - IImHtot_u ) );
1040 break;
1041 /* \bar b -> \bar q l^+ i^- transitions */
1042 case 1:
1043 RReC9eff = RReC9eff + ( 3.0 * c1 + c2 ) *
1044 ( Relambda_qu * ( RReHtot_c - RReHtot_u ) +
1045 Imlambda_qu * ( IImHtot_c - IImHtot_u ) );
1046 break;
1047 };
1048
1049 // EvtGenReport(EVTGEN_NOTICE,"EvtGen")
1050 // << "\n =============================================================="
1051 // << "\n =============================================================="
1052 // << "\n\n The function EvtbTosllWilsCoeffNLO::ReC9eff(...) passed."
1053 // << "\n Particle masses:"
1054 // << "\n q2 = " << q2
1055 // << "\n s = " << q2/(m2*m2)
1056 // << "\n leptonic mass ml = " << ml
1057 // << "\n u or d - quarks mass md = " << md
1058 // << "\n c - quark mass mc = " << mc
1059 // << "\n b - quark mass mb = " << m2
1060 // << "\n t - quark mass mt = " << mt
1061 // << "\n W - boson mass Mw = " << Mw
1062 // << "\n ==============================================================="
1063 // << "\n Input parameters:"
1064 // << "\n scale parameter mu = " << mu
1065 // << "\n number of flavors Nf = " << Nf
1066 // << "\n resonant switching = " << res_swch
1067 // << "\n decay id = " << decay_id
1068 // << "\n parameter for alpha_s(M_Z) = " << ias
1069 // << "\n Relambda_qu = " << Relambda_qu
1070 // << "\n Imlambda_qu = " << Imlambda_qu
1071 // << "\n ================================================================"
1072 // << "\n Wilson Coefficients:"
1073 // << "\n c1 = " << c1
1074 // << "\n c2 = " << c2
1075 // << "\n c3 = " << c3
1076 // << "\n c4 = " << c4
1077 // << "\n c5 = " << c5
1078 // << "\n c6 = " << c6
1079 // << "\n c9 = " << c9
1080 // << "\n Reh_d = " << RReh_d
1081 // << "\n Reh_b = " << RReh_b
1082 // << "\n ReHtot_u = " << RReHtot_u
1083 // << "\n ReHtot_c = " << RReHtot_c
1084 // << "\n ImHtot_u = " << IImHtot_u
1085 // << "\n ImHtot_c = " << IImHtot_c
1086 // << "\n RReC9eff = " << RReC9eff
1087 // << "\n tilde_eta = " << tilde_eta
1088 // << "\n ================================================================="
1089 // << "\n ================================================================="
1090 // << std::endl;
1091
1092 return RReC9eff;
1093}
1094
1095/* IMAGINARY PART of the effective coefficient C_9V^{eff}: *
1096 * *
1097 * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189; *
1098 * F.Kruger, L.M.Sehgal, Phys.Rev.D55 (1997), p.2799. *
1099 * *
1100 * decay_id = 0 for b -> q l^+ i^- transitions *
1101 * 1 for \bar b -> \bar q l^+ l^- transitions; *
1102 * *
1103 * res_swch = 0 the resonant contribution switch OFF *
1104 * = 1 the resonant contribution switch ON; *
1105 * *
1106 * ias -- switching parameter for Lms[] in the As(..) function. *
1107 * *
1108 * Nf -- number of "effective" flavors (for b-quark Nf=5); *
1109 * *
1110 * q2 -- the square of transition 4-momentum; *
1111 * m2 -- b-quark mass (in the heavy meson M1), GeV; *
1112 * md -- mass of the u- and d-quarks, GeV; *
1113 * mc -- c-quark mass, GeV; *
1114 * mu -- scale parameter, GeV; *
1115 * Mw -- mass of the W, GeV; *
1116 * ml -- leptonic mass, GeV; *
1117 * *
1118 * Relambda_qu -- Re(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1119 * Imlambda_qu -- Im(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1120 * */
1121double EvtbTosllWilsCoeffNLO::ImC9eff( int decay_id, int res_swch, int ias,
1122 int Nf, double q2, double m2, double md,
1123 double mc, double mu, double Mw, double ml,
1124 double Relambda_qu, double Imlambda_qu )
1125{
1126 double IImC9eff;
1127 double c1, c2, c3, c4, c5, c6;
1128 double IImh_d, IImh_b, RReHtot_u, IImHtot_u, RReHtot_c, IImHtot_c;
1129
1130 c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
1131 c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
1132 c3 = EvtbTosllWilsCoeffNLO::C3( mu, Mw, Nf, ias );
1133 c4 = EvtbTosllWilsCoeffNLO::C4( mu, Mw, Nf, ias );
1134 c5 = EvtbTosllWilsCoeffNLO::C5( mu, Mw, Nf, ias );
1135 c6 = EvtbTosllWilsCoeffNLO::C6( mu, Mw, Nf, ias );
1136
1137 IImh_d = EvtbTosllWilsCoeffNLO::Imh( md, q2 );
1138 IImh_b = EvtbTosllWilsCoeffNLO::Imh( m2, q2 );
1139 RReHtot_u = EvtbTosllWilsCoeffNLO::ReHtot( 0, res_swch, ias, Nf, mu, md, q2,
1140 ml, Mw );
1141 IImHtot_u = EvtbTosllWilsCoeffNLO::ImHtot( 0, res_swch, ias, Nf, mu, md, q2,
1142 ml, Mw );
1143 RReHtot_c = EvtbTosllWilsCoeffNLO::ReHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1144 ml, Mw );
1145 IImHtot_c = EvtbTosllWilsCoeffNLO::ImHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1146 ml, Mw );
1147
1148 IImC9eff = ( 3.0 * c1 + c2 + 3.0 * c3 + c4 + 3.0 * c5 + c6 ) * IImHtot_c;
1149 IImC9eff = IImC9eff - 0.5 * ( 4.0 * c3 + 4.0 * c4 + 3.0 * c5 + c6 ) * IImh_b;
1150 IImC9eff = IImC9eff - 0.5 * ( c3 + 3.0 * c4 ) * IImh_d;
1151
1152 switch ( decay_id ) {
1153 /* b -> q l^+ i^- transitions */
1154 case 0:
1155 IImC9eff = IImC9eff + ( 3.0 * c1 + c2 ) *
1156 ( Relambda_qu * ( IImHtot_c - IImHtot_u ) +
1157 Imlambda_qu * ( RReHtot_c - RReHtot_u ) );
1158 break;
1159 /* \bar b -> \bar q l^+ i^- transitions */
1160 case 1:
1161 IImC9eff = IImC9eff + ( 3.0 * c1 + c2 ) *
1162 ( Relambda_qu * ( IImHtot_c - IImHtot_u ) -
1163 Imlambda_qu * ( RReHtot_c - RReHtot_u ) );
1164 break;
1165 };
1166
1167 return IImC9eff;
1168}
1169
1170/* Complex representation for the coefficient C_9V: *
1171 * *
1172 * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189; *
1173 * F.Kruger, L.M.Sehgal, Phys.Rev.D55 (1997), p.2799. *
1174 * *
1175 * decay_id = 0 for b -> q l^+ i^- transitions *
1176 * 1 for \bar b -> \bar q l^+ l^- transitions; *
1177 * *
1178 * res_swch = 0 the resonant contribution switch OFF *
1179 * = 1 the resonant contribution switch ON; *
1180 * *
1181 * ias -- switching parameter for Lms[] in the As(..) function. *
1182 * *
1183 * Nf -- number of "effective" flavors (for b-quark Nf=5); *
1184 * *
1185 * q2 -- the square of transition 4-momentum; *
1186 * m2 -- b-quark mass (in the heavy meson M1), GeV; *
1187 * md -- mass of the u- and d-quarks, GeV; *
1188 * mc -- c-quark mass, GeV; *
1189 * mu -- scale parameter, GeV; *
1190 * mt -- t-quark mass, GeV; *
1191 * Mw -- mass of the W, GeV; *
1192 * ml -- leptonic mass, GeV; *
1193 * *
1194 * Relambda_qu -- Re(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1195 * Imlambda_qu -- Im(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1196 * */
1197EvtComplex EvtbTosllWilsCoeffNLO::GetC9Eff( int decay_id, int res_swch, int ias,
1198 int Nf, double q2, double m2,
1199 double md, double mc, double mu,
1200 double mt, double Mw, double ml,
1201 double Relambda_qu,
1202 double Imlambda_qu )
1203{
1204 double RReC9eff, IImC9eff;
1205 EvtComplex unit1( 1.0, 0.0 );
1206 EvtComplex uniti( 0.0, 1.0 );
1207 EvtComplex c9eff;
1208
1209 RReC9eff = EvtbTosllWilsCoeffNLO::ReC9eff( decay_id, res_swch, ias, Nf, q2,
1210 m2, md, mc, mu, mt, Mw, ml,
1211 Relambda_qu, Imlambda_qu );
1212 IImC9eff = EvtbTosllWilsCoeffNLO::ImC9eff( decay_id, res_swch, ias, Nf, q2,
1213 m2, md, mc, mu, Mw, ml,
1214 Relambda_qu, Imlambda_qu );
1215
1216 c9eff = RReC9eff * unit1 + IImC9eff * uniti;
1217 return c9eff;
1218}
1219
1220/* Complex representation for the coefficient C7gamma: *
1221 * C7gamma=ReC7gamma *
1222 * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189 *
1223 * *
1224 * mu -- scale parameter, GeV; *
1225 * mt -- t-quark mass, GeV; *
1226 * Mw -- mass of the W--meson, GeV; *
1227 * Nf -- number of "effective" flavors *
1228 * (for b-quark Nf=5); *
1229 * ias -- switching parameter for Lms[] *
1230 * in the As(..) function. *
1231 * */
1232EvtComplex EvtbTosllWilsCoeffNLO::GetC7Eff( double mu, double Mw, double mt,
1233 int Nf, int ias )
1234{
1235 double CC7gamma;
1236 EvtComplex c7eff;
1237 EvtComplex unit1( 1.0, 0.0 );
1238
1239 CC7gamma = EvtbTosllWilsCoeffNLO::C7gamma( mu, Mw, mt, Nf, ias );
1240 c7eff = unit1 * CC7gamma;
1241
1242 return c7eff;
1243}
1244
1245/* Complex representation for the coefficient C_10A: *
1246 * C_10A=ReC_10 *
1247 * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189 *
1248 * *
1249 * mt -- t-quark mass, GeV; *
1250 * Mw -- mass of the W--meson, GeV; *
1251 * */
1252EvtComplex EvtbTosllWilsCoeffNLO::GetC10Eff( double mt, double Mw )
1253{
1254 double ReC10;
1255 EvtComplex c10eff;
1256 EvtComplex unit1( 1.0, 0.0 );
1257
1258 ReC10 = EvtbTosllWilsCoeffNLO::C10a( mt, Mw );
1259
1260 c10eff = unit1 * ReC10;
1261
1262 return c10eff;
1263}
EvtGenReport
std::ostream & EvtGenReport(EvtGenSeverity severity, const char *facility=nullptr)
Definition EvtReport.cpp:32
EVTGEN_ERROR
@ EVTGEN_ERROR
Definition EvtReport.hh:49
EvtConst::pi
static const double pi
Definition EvtConst.hh:26
EvtbTosllWilsCoeffNLO::ImC9eff
double ImC9eff(int decay_id, int res_swch, int ias, int Nf, double q2, double m2, double md, double mc, double mu, double Mw, double ml, double Relambda_qu, double Imlambda_qu)
Definition EvtbTosllWilsCoeffNLO.cpp:1121
EvtbTosllWilsCoeffNLO::C6
double C6(double mu, double Mw, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:250
EvtbTosllWilsCoeffNLO::P0ndr
double P0ndr(double asW, double eta)
Definition EvtbTosllWilsCoeffNLO.cpp:441
EvtbTosllWilsCoeffNLO::GetC10Eff
EvtComplex GetC10Eff(double mt, double Mw)
Definition EvtbTosllWilsCoeffNLO.cpp:1252
EvtbTosllWilsCoeffNLO::C7gamma
double C7gamma(double mu, double Mw, double mt, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:373
EvtbTosllWilsCoeffNLO::C5
double C5(double mu, double Mw, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:222
EvtbTosllWilsCoeffNLO::C10a
double C10a(double mt, double Mw)
Definition EvtbTosllWilsCoeffNLO.cpp:501
EvtbTosllWilsCoeffNLO::omega
double omega(double q2, double m2)
Definition EvtbTosllWilsCoeffNLO.cpp:946
EvtbTosllWilsCoeffNLO::C9v
double C9v(double mu, double Mw, double mt, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:478
EvtbTosllWilsCoeffNLO::C4
double C4(double mu, double Mw, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:193
EvtbTosllWilsCoeffNLO::As
double As(double mu, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:44
EvtbTosllWilsCoeffNLO::Reh
double Reh(double mu, double mQ, double q2)
Definition EvtbTosllWilsCoeffNLO.cpp:522
EvtbTosllWilsCoeffNLO::GetC7Eff
EvtComplex GetC7Eff(double mu, double Mw, double mt, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:1232
EvtbTosllWilsCoeffNLO::C2
double C2(double mu, double Mw, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:136
EvtbTosllWilsCoeffNLO::ReHtot
double ReHtot(int qflavour, int res_swch, int ias, int Nf, double mu, double mQ, double q2, double ml, double Mw)
Definition EvtbTosllWilsCoeffNLO.cpp:614
EvtbTosllWilsCoeffNLO::GetC9Eff
EvtComplex GetC9Eff(int decay_id, int res_swch, int ias, int Nf, double q2, double m2, double md, double mc, double mu, double mt, double Mw, double ml, double Relambda_qu, double Imlambda_qu)
Definition EvtbTosllWilsCoeffNLO.cpp:1197
EvtbTosllWilsCoeffNLO::C1
double C1(double mu, double Mw, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:108
EvtbTosllWilsCoeffNLO::ReC9eff
double ReC9eff(int decay_id, int res_swch, int ias, int Nf, double q2, double m2, double md, double mc, double mu, double mt, double Mw, double ml, double Relambda_qu, double Imlambda_qu)
Definition EvtbTosllWilsCoeffNLO.cpp:995
EvtbTosllWilsCoeffNLO::ReResonant
double ReResonant(double q2, double GV, double GllV, double MV)
Definition EvtbTosllWilsCoeffNLO.cpp:566
EvtbTosllWilsCoeffNLO::ImHtot
double ImHtot(int qflavour, int res_swch, int ias, int Nf, double mu, double mQ, double q2, double ml, double Mw)
Definition EvtbTosllWilsCoeffNLO.cpp:786
EvtbTosllWilsCoeffNLO::ImResonant
double ImResonant(double q2, double GV, double GllV, double MV)
Definition EvtbTosllWilsCoeffNLO.cpp:584
EvtbTosllWilsCoeffNLO::Imh
double Imh(double mQ, double q2)
Definition EvtbTosllWilsCoeffNLO.cpp:546
EvtbTosllWilsCoeffNLO::C3
double C3(double mu, double Mw, int Nf, int ias)
Definition EvtbTosllWilsCoeffNLO.cpp:164
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