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EvtGen  2.0.0
Monte Carlo generator of particle decays, in particular the weak decays of heavy flavour particles such as B mesons.
EvtbTosllWilsCoeffNLO.cpp
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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 // **************************************************************
44 double 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 // ************************************************************
91 double 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. */
108 double 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. */
136 double 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. */
164 double 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. */
193 double 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. */
222 double 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. */
250 double 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. */
277 double 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. */
290 double 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. */
301 double 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. */
313 double 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. */
327 double 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. */
340 double 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. */
352 double 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. */
362 double 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. */
373 double 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). */
417 double 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). */
441 double 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, -0.2011, 0.1328, -0.0292, -0.1858};
452  double s[] = {0.0, 0.0, -0.2009, -0.3579, 0.0490, -0.3616, -0.3554, 0.0072};
453 
454  sum = 0.0;
455  i = 0;
456  while ( i < 8 ) {
457  sum = sum + p[i] * pow( eta, ( a[i] + 1.0 ) );
458  i++;
459  };
460  P00ndr = EvtConst::pi * ( -0.1875 + sum ) / asW;
461  P00ndr = P00ndr + 1.2468;
462  sum = 0.0;
463  i = 0;
464  while ( i < 8 ) {
465  sum = sum + ( r[i] + s[i] * eta ) * pow( eta, a[i] );
466  i++;
467  };
468  P00ndr = P00ndr + sum;
469 
470  return P00ndr;
471 }
472 
473 /* Coefficient C_{9V} (in the NDR schime) *
474  * by A.J.Buras and M.Munz, Phys.Rev. D52, 186 *
475  * accordint to the equation (2.10). */
476 double EvtbTosllWilsCoeffNLO::C9v( double mu, double Mw, double mt, int Nf,
477  int ias )
478 {
479  double C9;
480  double x, eta;
481  double asW, asmu;
482  double sin2W = 0.224; /* the square of the weak angle */
483 
484  x = pow( mt / Mw, 2.0 );
485  asW = As( Mw, Nf, ias );
486  asmu = As( mu, Nf, ias );
487  eta = asW / asmu;
488 
489  /* C9 */
490  C9 = P0ndr( asW, eta ) + ( Y( x ) / sin2W ) - 4.0 * Z( x ) +
491  Pe( eta ) * E( x );
492 
493  return C9;
494 }
495 
496 /* Coefficient C_{10A} *
497  * by A.J.Buras and M.Munz, Phys.Rev. D52, 186; *
498  * see formula (2.8). */
499 double EvtbTosllWilsCoeffNLO::C10a( double mt, double Mw )
500 {
501  double C10;
502  double x;
503  double sin2W = 0.224; /* the square of the Winberg angle */
504 
505  x = pow( mt / Mw, 2.0 );
506 
507  C10 = -Y( x ) / sin2W;
508 
509  return C10;
510 }
511 
512 /* The real part of the q\bar q loop contribution *
513  * Re(h(z,\hat s)) *
514  * A.J.Buras and M.Munz, Phys.Rev. D52, 186; *
515  * the equation (2.29). *
516  * *
517  * mu - the scale parameter (GeV); *
518  * mQ - the mass of the u- or c-quark (GeV); *
519  * q2 - the square of transition 4-momentum (GeV^2). */
520 double EvtbTosllWilsCoeffNLO::Reh( double mu, double mQ, double q2 )
521 {
522  double reh, swh;
523  double x; /* Buras variable "x" from (2.29) */
524 
525  x = 4.0 * pow( mQ, 2.0 ) / q2;
526 
527  reh = 8.0 / 27.0 - 8.0 * log( mQ / mu ) / 9.0 + 4.0 * x / 9.0;
528 
529  swh = 2.0 * ( 2.0 + x ) * sqrt( fabs( 1.0 - x ) ) / 9.0;
530 
531  if ( x <= 1.0 ) {
532  swh = swh * log( fabs( ( sqrt( 1.0 - x ) + 1.0 ) /
533  ( sqrt( 1.0 - x ) - 1.0 ) ) );
534  } else {
535  swh = swh * 2.0 * atan( 1.0 / sqrt( x - 1.0 ) );
536  };
537 
538  reh = reh - swh;
539 
540  return reh;
541 }
542 
543 /* Im(h(z,\hat s)) by Buras */
544 double EvtbTosllWilsCoeffNLO::Imh( double mQ, double q2 )
545 {
546  double x; /* Buras variable "x" from (2.29) */
547  double imh;
548 
549  x = 4.0 * pow( mQ, 2.0 ) / q2;
550 
551  if ( x <= 1.0 ) {
552  imh = 2.0 * EvtConst::pi * ( 2.0 + x ) * sqrt( fabs( 1.0 - x ) ) / 9.0;
553  } else {
554  imh = 0.0;
555  };
556  return imh;
557 }
558 
559 /* The real part of the one resonant contribution *
560  * q2 - the square of transition 4-momentum (GeV^2); *
561  * GV - the decay width of the resonance (GeV); *
562  * GllV - the decay width of the resonance into l^+ l^- - pair (GeV); *
563  * MV - the mass of the resonance. */
564 double EvtbTosllWilsCoeffNLO::ReResonant( double q2, double GV, double GllV,
565  double MV )
566 {
567  double reresonant;
568  double resa, resb;
569 
570  resa = q2 * ( MV * MV - q2 ) * GllV;
571  resb = MV * ( ( MV * MV - q2 ) * ( MV * MV - q2 ) + MV * MV * GV * GV );
572  reresonant = resa / resb;
573 
574  return reresonant;
575 }
576 
577 /* The imaginary part of the one resonant contribution *
578  * q2 - the square of transition 4-momentum (GeV^2); *
579  * GV - the decay width of the resonance (GeV); *
580  * GllV - the decay width of the resonance into l^+ l^- - pair (GeV); *
581  * MV - the mass of the resonance. */
582 double EvtbTosllWilsCoeffNLO::ImResonant( double q2, double GV, double GllV,
583  double MV )
584 {
585  double imresonant;
586  double resa, resb;
587 
588  resa = q2 * GV * GllV;
589  resb = ( MV * MV - q2 ) * ( MV * MV - q2 ) + MV * MV * GV * GV;
590  imresonant = resa / resb;
591 
592  return imresonant;
593 }
594 
595 /* The real part of the total q\barq-contribution *
596  * *
597  * qflavour = 0 corresponding the u-quark contribution *
598  * = 1 corresponding the c-quark contribution; *
599  * *
600  * res_swch = 0 the resonant contribution switch OFF *
601  * = 1 the resonant contribution switch ON; *
602  * *
603  * ias -- switching parameter for Lms[] in the As(..) function. *
604  * *
605  * Nf - number of "effective" flavours (for b-quark Nf=5); *
606  * mu - the scale parameter (GeV); *
607  * mQ - the mass of the u- or c-quark (GeV); *
608  * q2 - the square of transition 4-momentum (GeV^2); *
609  * ml - the mass of the final leptons (GeV); *
610  * Mw - the mass of the W--meson (GeV). *
611  * */
612 double EvtbTosllWilsCoeffNLO::ReHtot( int qflavour, int res_swch, int ias,
613  int Nf, double mu, double mQ, double q2,
614  double ml, double Mw )
615 {
616  double rehtot;
617  double rehres, c1, c2;
618  int i;
619 
620  /* Total decay widths of the resonances (GeV) */
621  double Gamma[6];
622  /* The decay width of the resonances into l^+ l^- - pair (GeV) */
623  double Gamma_ll[6];
624  /* The mass of the resonances */
625  double M[6];
626 
627  double alpha_qed = 1.0 / 137.0;
628 
629  switch ( qflavour ) {
630  /* u-quark contribution */
631  case 0:
632  switch ( res_swch ) {
633  /* The resonant contribution switch OFF */
634  case 0:
635  rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
636  rehres = 0.0;
637  break;
638  /* the resonant contribution switch ON */
639  case 1:
640  rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
641 
642  /* \pho */
643  M[0] = 0.7755; /* GeV */
644  Gamma[0] = 0.1494; /* GeV */
645  /* \omega' */
646  M[1] = 0.7827; /* GeV */
647  Gamma[1] = 0.0085; /* GeV */
648 
649  if ( ml < 1.0 ) {
650  /* in e^+e^- or mu^+mu^- */
651  Gamma_ll[0] = 0.000007; /* \rho */
652  Gamma_ll[1] = 0.0000006; /* \omega */
653  } else {
654  /* in \tau^+\tau^- */
655  Gamma_ll[0] = 0.0; /* \rho */
656  Gamma_ll[1] = 0.0; /* \omega */
657  };
658 
659  c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
660  c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
661 
662  i = 0;
663  rehres = 0.0;
664  while ( i < 2 ) {
665  rehres = rehres +
666  3.0 * EvtConst::pi *
667  EvtbTosllWilsCoeffNLO::ReResonant(
668  q2, Gamma[i], Gamma_ll[i], M[i] ) /
669  ( sqrt( 2.0 ) * ( 3.0 * c1 + c2 ) *
670  alpha_qed * alpha_qed );
671  i++;
672  };
673 
674  /* The sign plus are corresponded to the relation:
675  \kappa*(3C_1+C_2)=1
676  with sign of Wilson coefficien C_2(M_W)=+1 as at work
677  A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
678  rehtot = rehtot + rehres;
679  break;
680  default:
681  rehtot = 0.0;
682  rehres = 0.0;
683  };
684  break;
685  /* c-quark contribution */
686  case 1:
687  switch ( res_swch ) {
688  /* The resonant contribution switch OFF */
689  case 0:
690  rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
691  rehres = 0.0;
692  break;
693  /* the resonant contribution switch ON */
694  case 1:
695  rehtot = EvtbTosllWilsCoeffNLO::Reh( mu, mQ, q2 );
696 
697  /* J/psi */
698  M[0] = 3.096916; /* GeV */
699  Gamma[0] = 0.000093; /* GeV */
700  /* psi' */
701  M[1] = 3.68609; /* GeV */
702  Gamma[1] = 0.000317; /* GeV */
703  /* psi(3770) */
704  M[2] = 3.77292; /* GeV */
705  Gamma[2] = 0.0273; /* GeV */
706  /* psi(4040) */
707  M[3] = 4.039; /* GeV */
708  Gamma[3] = 0.08; /* GeV */
709  /* psi(4160) */
710  M[4] = 4.153; /* GeV */
711  Gamma[4] = 0.103; /* GeV */
712  /* psi(4415) */
713  M[5] = 4.421; /* GeV */
714  Gamma[5] = 0.062; /* GeV */
715 
716  if ( ml < 1.0 ) {
717  /* in e^+e^- or mu^+mu^- */
718  Gamma_ll[0] = Gamma[0] * 0.059; /* J/psi */
719  Gamma_ll[1] = Gamma[1] * 0.0075; /* psi' */
720  Gamma_ll[2] = Gamma[2] * 0.0000097; /* psi(3770) */
721  Gamma_ll[3] = Gamma[3] * 0.00001; /* psi(4040) */
722  Gamma_ll[4] = Gamma[4] * 0.0000081; /* psi(4160) */
723  Gamma_ll[5] = Gamma[5] * 0.0000094; /* psi(4415) */
724  } else {
725  /* in \tau^+\tau^- */
726  Gamma_ll[0] = 0.0; /* J/psi */
727  Gamma_ll[1] = Gamma[1] * 0.003; /* psi' */
728  Gamma_ll[2] = Gamma[2] * 0.0; /* psi(3770) */
729  Gamma_ll[3] = Gamma[3] * 0.0; /* psi(4040) */
730  Gamma_ll[4] = Gamma[4] * 0.0; /* psi(4160) */
731  Gamma_ll[5] = Gamma[5] * 0.0; /* psi(4415) */
732  };
733 
734  c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
735  c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
736 
737  i = 0;
738  rehres = 0.0;
739  while ( i < 6 ) {
740  rehres = rehres +
741  3.0 * EvtConst::pi *
742  EvtbTosllWilsCoeffNLO::ReResonant(
743  q2, Gamma[i], Gamma_ll[i], M[i] ) /
744  ( ( 3.0 * c1 + c2 ) * alpha_qed * alpha_qed );
745  i++;
746  };
747 
748  /* The sign plus are corresponded to the relation:
749  \kappa*(3C_1+C_2)=1
750  with sign of Wilson coefficien C_2(M_W)=+1 as at work
751  A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
752  rehtot = rehtot + rehres;
753  break;
754  default:
755  rehtot = 0.0;
756  rehres = 0.0;
757  };
758  break;
759  default:
760  rehtot = 0.0;
761  rehres = 0.0;
762  };
763 
764  return rehtot;
765 }
766 
767 /* The imaginary of the total q\barq-contribution *
768  * *
769  * qflavour = 0 corresponding the u-quark contribution *
770  * = 1 corresponding the c-quark contribution; *
771  * *
772  * res_swch = 0 the resonant contribution switch OFF *
773  * = 1 the resonant contribution switch ON; *
774  * *
775  * ias -- switching parameter for Lms[] in the As(..) function. *
776  * *
777  * Nf - number of "effective" flavours (for b-quark Nf=5); *
778  * mu - the scale parameter (GeV); *
779  * mQ - the mass of the u- or c-quark (GeV); *
780  * q2 - the square of transition 4-momentum (GeV^2); *
781  * ml - the mass of the final leptons (GeV); *
782  * Mw - the mass of the W--meson (GeV). *
783  * */
784 double EvtbTosllWilsCoeffNLO::ImHtot( int qflavour, int res_swch, int ias,
785  int Nf, double mu, double mQ, double q2,
786  double ml, double Mw )
787 {
788  double imhtot;
789  double imhres, c1, c2;
790  int i;
791 
792  /* Total decay widths of the resonances (GeV) */
793  double Gamma[6];
794  /* The decay width of the resonances into l^+ l^- - pair (GeV) */
795  double Gamma_ll[6];
796  /* The mass of the resonances */
797  double M[6];
798 
799  double alpha_qed = 1.0 / 137.0;
800 
801  switch ( qflavour ) {
802  /* u-quark contribution */
803  case 0:
804  switch ( res_swch ) {
805  /* The resonant contribution switch OFF */
806  case 0:
807  imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
808  imhres = 0.0;
809  break;
810  /* the resonant contribution switch ON */
811  case 1:
812  imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
813 
814  /* \pho */
815  M[0] = 0.7755; /* GeV */
816  Gamma[0] = 0.1494; /* GeV */
817  /* \omega' */
818  M[1] = 0.7827; /* GeV */
819  Gamma[1] = 0.0085; /* GeV */
820 
821  if ( ml < 1.0 ) {
822  /* in e^+e^- or mu^+mu^- */
823  Gamma_ll[0] = 0.000007; /* \rho */
824  Gamma_ll[1] = 0.0000006; /* \omega */
825  } else {
826  /* in \tau^+\tau^- */
827  Gamma_ll[0] = 0.0; /* \rho */
828  Gamma_ll[1] = 0.0; /* \omega */
829  };
830 
831  c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
832  c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
833 
834  i = 0;
835  imhres = 0.0;
836  while ( i < 2 ) {
837  imhres = imhres +
838  3.0 * EvtConst::pi *
839  EvtbTosllWilsCoeffNLO::ImResonant(
840  q2, Gamma[i], Gamma_ll[i], M[i] ) /
841  ( sqrt( 2.0 ) * ( 3.0 * c1 + c2 ) *
842  alpha_qed * alpha_qed );
843  i++;
844  };
845 
846  /* The sign plus are corresponded to the relation:
847  \kappa*(3C_1+C_2)=1
848  with sign of Wilson coefficien C_2(M_W)=+1 as at work
849  A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
850  imhtot = imhtot + imhres;
851  break;
852  default:
853  imhtot = 0.0;
854  imhres = 0.0;
855  };
856  break;
857  /* c-quark contribution */
858  case 1:
859  switch ( res_swch ) {
860  /* The resonant contribution switch OFF */
861  case 0:
862  imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
863  imhres = 0.0;
864  break;
865  /* the resonant contribution switch ON */
866  case 1:
867  imhtot = EvtbTosllWilsCoeffNLO::Imh( mQ, q2 );
868 
869  /* J/psi */
870  M[0] = 3.096916; /* GeV */
871  Gamma[0] = 0.000093; /* GeV */
872  /* psi' */
873  M[1] = 3.68609; /* GeV */
874  Gamma[1] = 0.000317; /* GeV */
875  /* psi(3770) */
876  M[2] = 3.77292; /* GeV */
877  Gamma[2] = 0.0273; /* GeV */
878  /* psi(4040) */
879  M[3] = 4.039; /* GeV */
880  Gamma[3] = 0.08; /* GeV */
881  /* psi(4160) */
882  M[4] = 4.153; /* GeV */
883  Gamma[4] = 0.103; /* GeV */
884  /* psi(4415) */
885  M[5] = 4.421; /* GeV */
886  Gamma[5] = 0.062; /* GeV */
887 
888  if ( ml < 1.0 ) {
889  /* in e^+e^- or mu^+mu^- */
890  Gamma_ll[0] = Gamma[0] * 0.059; /* J/psi */
891  Gamma_ll[1] = Gamma[1] * 0.0075; /* psi' */
892  Gamma_ll[2] = Gamma[2] * 0.0000097; /* psi(3770) */
893  Gamma_ll[3] = Gamma[3] * 0.00001; /* psi(4040) */
894  Gamma_ll[4] = Gamma[4] * 0.0000081; /* psi(4160) */
895  Gamma_ll[5] = Gamma[5] * 0.0000094; /* psi(4415) */
896  } else {
897  /* in \tau^+\tau^- */
898  Gamma_ll[0] = 0.0; /* J/psi */
899  Gamma_ll[1] = Gamma[1] * 0.003; /* psi' */
900  Gamma_ll[2] = Gamma[2] * 0.0; /* psi(3770) */
901  Gamma_ll[3] = Gamma[3] * 0.0; /* psi(4040) */
902  Gamma_ll[4] = Gamma[4] * 0.0; /* psi(4160) */
903  Gamma_ll[5] = Gamma[5] * 0.0; /* psi(4415) */
904  };
905 
906  c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
907  c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
908 
909  i = 0;
910  imhres = 0.0;
911  while ( i < 6 ) {
912  imhres = imhres +
913  3.0 * EvtConst::pi *
914  EvtbTosllWilsCoeffNLO::ImResonant(
915  q2, Gamma[i], Gamma_ll[i], M[i] ) /
916  ( ( 3.0 * c1 + c2 ) * alpha_qed * alpha_qed );
917  i++;
918  };
919 
920  /* The sign plus are corresponded to the relation:
921  \kappa*(3C_1+C_2)=1
922  with sign of Wilson coefficien C_2(M_W)=+1 as at work
923  A.J.Buras and M.Munz, Phys.Rev. D52, 186. */
924  imhtot = imhtot + imhres;
925  break;
926  default:
927  imhtot = 0.0;
928  imhres = 0.0;
929  };
930  break;
931  default:
932  imhtot = 0.0;
933  imhres = 0.0;
934  };
935 
936  return imhtot;
937 }
938 
939 /* Function \omega(\hat s) *
940  * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189. *
941  * *
942  * q2 - the square of transition 4-momentum (GeV^2); *
943  * m2 - the mass of the b-quark (GeV). */
944 double EvtbTosllWilsCoeffNLO::omega( double q2, double m2 )
945 {
946  double oomega;
947  double s;
948 
949  s = q2 / ( m2 * m2 ); /* see definition in the equation (2.26) */
950 
951  if ( s > 1.0 ) {
952  s = 0.999999;
953  }
954  oomega = -2.0 * pow( EvtConst::pi, 2.0 ) / 9.0 - 4.0 * Li2( s ) / 3.0;
955  oomega = oomega - 2.0 * log( s ) * log( 1.0 - s ) / 3.0;
956  oomega = oomega -
957  ( 5.0 + 4.0 * s ) * log( 1.0 - s ) / ( 3.0 * ( 1.0 + 2.0 * s ) );
958  oomega = oomega - 2.0 * s * ( 1.0 + s ) * ( 1.0 - 2.0 * s ) * log( s ) /
959  ( 3.0 * pow( ( 1.0 - s ), 2.0 ) * ( 1.0 + 2.0 * s ) );
960  oomega = oomega + ( 5.0 + 9.0 * s - 6.0 * s * s ) /
961  ( 6.0 * ( 1.0 - s ) * ( 1.0 + 2.0 * s ) );
962 
963  return oomega;
964 }
965 
966 /* REAL PART of the effective coefficient C_9V^{eff}: *
967  * *
968  * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189; *
969  * F.Kruger, L.M.Sehgal, Phys.Rev.D55 (1997), p.2799. *
970  * *
971  * decay_id = 0 for b -> q l^+ i^- transitions *
972  * 1 for \bar b -> \bar q l^+ l^- transitions; *
973  * *
974  * res_swch = 0 the resonant contribution switch OFF *
975  * = 1 the resonant contribution switch ON; *
976  * *
977  * ias -- switching parameter for Lms[] in the As(..) function. *
978  * *
979  * Nf -- number of "effective" flavors (for b-quark Nf=5); *
980  * *
981  * q2 -- the square of transition 4-momentum; *
982  * m2 -- b-quark mass (in the heavy meson M1), GeV; *
983  * md -- mass of the u- and d-quarks, GeV; *
984  * mc -- c-quark mass, GeV; *
985  * mu -- scale parameter, GeV; *
986  * mt -- t-quark mass, GeV; *
987  * Mw -- mass of the W, GeV; *
988  * ml -- leptonic mass, GeV; *
989  * *
990  * Relambda_qu -- Re(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
991  * Imlambda_qu -- Im(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
992  * */
993 double EvtbTosllWilsCoeffNLO::ReC9eff( int decay_id, int res_swch, int ias,
994  int Nf, double q2, double m2, double md,
995  double mc, double mu, double mt,
996  double Mw, double ml, double Relambda_qu,
997  double Imlambda_qu )
998 {
999  double RReC9eff;
1000  double tilde_eta; /* Buras variable " \tilde\eta" in (2.33) */
1001  double c1, c2, c3, c4, c5, c6, c9;
1002  double RReh_d, RReh_b, RReHtot_u, IImHtot_u, RReHtot_c, IImHtot_c;
1003 
1004  tilde_eta = 1.0 + EvtbTosllWilsCoeffNLO::As( mu, Nf, ias ) *
1005  EvtbTosllWilsCoeffNLO::omega( q2, m2 ) / EvtConst::pi;
1006 
1007  c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
1008  c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
1009  c3 = EvtbTosllWilsCoeffNLO::C3( mu, Mw, Nf, ias );
1010  c4 = EvtbTosllWilsCoeffNLO::C4( mu, Mw, Nf, ias );
1011  c5 = EvtbTosllWilsCoeffNLO::C5( mu, Mw, Nf, ias );
1012  c6 = EvtbTosllWilsCoeffNLO::C6( mu, Mw, Nf, ias );
1013  c9 = EvtbTosllWilsCoeffNLO::C9v( mu, Mw, mt, Nf, ias );
1014 
1015  RReh_d = EvtbTosllWilsCoeffNLO::Reh( mu, md, q2 );
1016  RReh_b = EvtbTosllWilsCoeffNLO::Reh( mu, m2, q2 );
1017  RReHtot_u = EvtbTosllWilsCoeffNLO::ReHtot( 0, res_swch, ias, Nf, mu, md, q2,
1018  ml, Mw );
1019  IImHtot_u = EvtbTosllWilsCoeffNLO::ImHtot( 0, res_swch, ias, Nf, mu, md, q2,
1020  ml, Mw );
1021  RReHtot_c = EvtbTosllWilsCoeffNLO::ReHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1022  ml, Mw );
1023  IImHtot_c = EvtbTosllWilsCoeffNLO::ImHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1024  ml, Mw );
1025 
1026  RReC9eff = c9 * tilde_eta + 2.0 * ( 3.0 * c3 + c4 + 3.0 * c5 + c6 ) / 9.0;
1027  RReC9eff = RReC9eff +
1028  ( 3.0 * c1 + c2 + 3.0 * c3 + c4 + 3.0 * c5 + c6 ) * RReHtot_c;
1029  RReC9eff = RReC9eff - 0.5 * ( 4.0 * c3 + 4.0 * c4 + 3.0 * c5 + c6 ) * RReh_b;
1030  RReC9eff = RReC9eff - 0.5 * ( c3 + 3.0 * c4 ) * RReh_d;
1031 
1032  switch ( decay_id ) {
1033  /* b -> q l^+ i^- transitions */
1034  case 0:
1035  RReC9eff = RReC9eff + ( 3.0 * c1 + c2 ) *
1036  ( Relambda_qu * ( RReHtot_c - RReHtot_u ) -
1037  Imlambda_qu * ( IImHtot_c - IImHtot_u ) );
1038  break;
1039  /* \bar b -> \bar q l^+ i^- transitions */
1040  case 1:
1041  RReC9eff = RReC9eff + ( 3.0 * c1 + c2 ) *
1042  ( Relambda_qu * ( RReHtot_c - RReHtot_u ) +
1043  Imlambda_qu * ( IImHtot_c - IImHtot_u ) );
1044  break;
1045  };
1046 
1047  // EvtGenReport(EVTGEN_NOTICE,"EvtGen")
1048  // << "\n =============================================================="
1049  // << "\n =============================================================="
1050  // << "\n\n The function EvtbTosllWilsCoeffNLO::ReC9eff(...) passed."
1051  // << "\n Particle masses:"
1052  // << "\n q2 = " << q2
1053  // << "\n s = " << q2/(m2*m2)
1054  // << "\n leptonic mass ml = " << ml
1055  // << "\n u or d - quarks mass md = " << md
1056  // << "\n c - quark mass mc = " << mc
1057  // << "\n b - quark mass mb = " << m2
1058  // << "\n t - quark mass mt = " << mt
1059  // << "\n W - boson mass Mw = " << Mw
1060  // << "\n ==============================================================="
1061  // << "\n Input parameters:"
1062  // << "\n scale parameter mu = " << mu
1063  // << "\n number of flavors Nf = " << Nf
1064  // << "\n resonant switching = " << res_swch
1065  // << "\n decay id = " << decay_id
1066  // << "\n parameter for alpha_s(M_Z) = " << ias
1067  // << "\n Relambda_qu = " << Relambda_qu
1068  // << "\n Imlambda_qu = " << Imlambda_qu
1069  // << "\n ================================================================"
1070  // << "\n Wilson Coefficients:"
1071  // << "\n c1 = " << c1
1072  // << "\n c2 = " << c2
1073  // << "\n c3 = " << c3
1074  // << "\n c4 = " << c4
1075  // << "\n c5 = " << c5
1076  // << "\n c6 = " << c6
1077  // << "\n c9 = " << c9
1078  // << "\n Reh_d = " << RReh_d
1079  // << "\n Reh_b = " << RReh_b
1080  // << "\n ReHtot_u = " << RReHtot_u
1081  // << "\n ReHtot_c = " << RReHtot_c
1082  // << "\n ImHtot_u = " << IImHtot_u
1083  // << "\n ImHtot_c = " << IImHtot_c
1084  // << "\n RReC9eff = " << RReC9eff
1085  // << "\n tilde_eta = " << tilde_eta
1086  // << "\n ================================================================="
1087  // << "\n ================================================================="
1088  // << std::endl;
1089 
1090  return RReC9eff;
1091 }
1092 
1093 /* IMAGINARY PART of the effective coefficient C_9V^{eff}: *
1094  * *
1095  * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189; *
1096  * F.Kruger, L.M.Sehgal, Phys.Rev.D55 (1997), p.2799. *
1097  * *
1098  * decay_id = 0 for b -> q l^+ i^- transitions *
1099  * 1 for \bar b -> \bar q l^+ l^- transitions; *
1100  * *
1101  * res_swch = 0 the resonant contribution switch OFF *
1102  * = 1 the resonant contribution switch ON; *
1103  * *
1104  * ias -- switching parameter for Lms[] in the As(..) function. *
1105  * *
1106  * Nf -- number of "effective" flavors (for b-quark Nf=5); *
1107  * *
1108  * q2 -- the square of transition 4-momentum; *
1109  * m2 -- b-quark mass (in the heavy meson M1), GeV; *
1110  * md -- mass of the u- and d-quarks, GeV; *
1111  * mc -- c-quark mass, GeV; *
1112  * mu -- scale parameter, GeV; *
1113  * Mw -- mass of the W, GeV; *
1114  * ml -- leptonic mass, GeV; *
1115  * *
1116  * Relambda_qu -- Re(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1117  * Imlambda_qu -- Im(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1118  * */
1119 double EvtbTosllWilsCoeffNLO::ImC9eff( int decay_id, int res_swch, int ias,
1120  int Nf, double q2, double m2, double md,
1121  double mc, double mu, double Mw, double ml,
1122  double Relambda_qu, double Imlambda_qu )
1123 {
1124  double IImC9eff;
1125  double c1, c2, c3, c4, c5, c6;
1126  double IImh_d, IImh_b, RReHtot_u, IImHtot_u, RReHtot_c, IImHtot_c;
1127 
1128  c1 = EvtbTosllWilsCoeffNLO::C1( mu, Mw, Nf, ias );
1129  c2 = EvtbTosllWilsCoeffNLO::C2( mu, Mw, Nf, ias );
1130  c3 = EvtbTosllWilsCoeffNLO::C3( mu, Mw, Nf, ias );
1131  c4 = EvtbTosllWilsCoeffNLO::C4( mu, Mw, Nf, ias );
1132  c5 = EvtbTosllWilsCoeffNLO::C5( mu, Mw, Nf, ias );
1133  c6 = EvtbTosllWilsCoeffNLO::C6( mu, Mw, Nf, ias );
1134 
1135  IImh_d = EvtbTosllWilsCoeffNLO::Imh( md, q2 );
1136  IImh_b = EvtbTosllWilsCoeffNLO::Imh( m2, q2 );
1137  RReHtot_u = EvtbTosllWilsCoeffNLO::ReHtot( 0, res_swch, ias, Nf, mu, md, q2,
1138  ml, Mw );
1139  IImHtot_u = EvtbTosllWilsCoeffNLO::ImHtot( 0, res_swch, ias, Nf, mu, md, q2,
1140  ml, Mw );
1141  RReHtot_c = EvtbTosllWilsCoeffNLO::ReHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1142  ml, Mw );
1143  IImHtot_c = EvtbTosllWilsCoeffNLO::ImHtot( 1, res_swch, ias, Nf, mu, mc, q2,
1144  ml, Mw );
1145 
1146  IImC9eff = ( 3.0 * c1 + c2 + 3.0 * c3 + c4 + 3.0 * c5 + c6 ) * IImHtot_c;
1147  IImC9eff = IImC9eff - 0.5 * ( 4.0 * c3 + 4.0 * c4 + 3.0 * c5 + c6 ) * IImh_b;
1148  IImC9eff = IImC9eff - 0.5 * ( c3 + 3.0 * c4 ) * IImh_d;
1149 
1150  switch ( decay_id ) {
1151  /* b -> q l^+ i^- transitions */
1152  case 0:
1153  IImC9eff = IImC9eff + ( 3.0 * c1 + c2 ) *
1154  ( Relambda_qu * ( IImHtot_c - IImHtot_u ) +
1155  Imlambda_qu * ( RReHtot_c - RReHtot_u ) );
1156  break;
1157  /* \bar b -> \bar q l^+ i^- transitions */
1158  case 1:
1159  IImC9eff = IImC9eff + ( 3.0 * c1 + c2 ) *
1160  ( Relambda_qu * ( IImHtot_c - IImHtot_u ) -
1161  Imlambda_qu * ( RReHtot_c - RReHtot_u ) );
1162  break;
1163  };
1164 
1165  return IImC9eff;
1166 }
1167 
1168 /* Complex representation for the coefficient C_9V: *
1169  * *
1170  * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189; *
1171  * F.Kruger, L.M.Sehgal, Phys.Rev.D55 (1997), p.2799. *
1172  * *
1173  * decay_id = 0 for b -> q l^+ i^- transitions *
1174  * 1 for \bar b -> \bar q l^+ l^- transitions; *
1175  * *
1176  * res_swch = 0 the resonant contribution switch OFF *
1177  * = 1 the resonant contribution switch ON; *
1178  * *
1179  * ias -- switching parameter for Lms[] in the As(..) function. *
1180  * *
1181  * Nf -- number of "effective" flavors (for b-quark Nf=5); *
1182  * *
1183  * q2 -- the square of transition 4-momentum; *
1184  * m2 -- b-quark mass (in the heavy meson M1), GeV; *
1185  * md -- mass of the u- and d-quarks, GeV; *
1186  * mc -- c-quark mass, GeV; *
1187  * mu -- scale parameter, GeV; *
1188  * mt -- t-quark mass, GeV; *
1189  * Mw -- mass of the W, GeV; *
1190  * ml -- leptonic mass, GeV; *
1191  * *
1192  * Relambda_qu -- Re(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1193  * Imlambda_qu -- Im(V^*_{uq}*V_{ub}/V^*_{tq}*V_{tb}), q={d,s}; *
1194  * */
1195 EvtComplex EvtbTosllWilsCoeffNLO::GetC9Eff( int decay_id, int res_swch, int ias,
1196  int Nf, double q2, double m2,
1197  double md, double mc, double mu,
1198  double mt, double Mw, double ml,
1199  double Relambda_qu,
1200  double Imlambda_qu )
1201 {
1202  double RReC9eff, IImC9eff;
1203  EvtComplex unit1( 1.0, 0.0 );
1204  EvtComplex uniti( 0.0, 1.0 );
1205  EvtComplex c9eff;
1206 
1207  RReC9eff = EvtbTosllWilsCoeffNLO::ReC9eff( decay_id, res_swch, ias, Nf, q2,
1208  m2, md, mc, mu, mt, Mw, ml,
1209  Relambda_qu, Imlambda_qu );
1210  IImC9eff = EvtbTosllWilsCoeffNLO::ImC9eff( decay_id, res_swch, ias, Nf, q2,
1211  m2, md, mc, mu, Mw, ml,
1212  Relambda_qu, Imlambda_qu );
1213 
1214  c9eff = RReC9eff * unit1 + IImC9eff * uniti;
1215  return c9eff;
1216 }
1217 
1218 /* Complex representation for the coefficient C7gamma: *
1219  * C7gamma=ReC7gamma *
1220  * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189 *
1221  * *
1222  * mu -- scale parameter, GeV; *
1223  * mt -- t-quark mass, GeV; *
1224  * Mw -- mass of the W--meson, GeV; *
1225  * Nf -- number of "effective" flavors *
1226  * (for b-quark Nf=5); *
1227  * ias -- switching parameter for Lms[] *
1228  * in the As(..) function. *
1229  * */
1230 EvtComplex EvtbTosllWilsCoeffNLO::GetC7Eff( double mu, double Mw, double mt,
1231  int Nf, int ias )
1232 {
1233  double CC7gamma;
1234  EvtComplex c7eff;
1235  EvtComplex unit1( 1.0, 0.0 );
1236 
1237  CC7gamma = EvtbTosllWilsCoeffNLO::C7gamma( mu, Mw, mt, Nf, ias );
1238  c7eff = unit1 * CC7gamma;
1239 
1240  return c7eff;
1241 }
1242 
1243 /* Complex representation for the coefficient C_10A: *
1244  * C_10A=ReC_10 *
1245  * by A.J.Buras, M.Munz, Phys.Rev.D52 (1995), p189 *
1246  * *
1247  * mt -- t-quark mass, GeV; *
1248  * Mw -- mass of the W--meson, GeV; *
1249  * */
1250 EvtComplex EvtbTosllWilsCoeffNLO::GetC10Eff( double mt, double Mw )
1251 {
1252  double ReC10;
1253  EvtComplex c10eff;
1254  EvtComplex unit1( 1.0, 0.0 );
1255 
1256  ReC10 = EvtbTosllWilsCoeffNLO::C10a( mt, Mw );
1257 
1258  c10eff = unit1 * ReC10;
1259 
1260  return c10eff;
1261 }
EvtbTosllWilsCoeffNLO::omega
double omega(double q2, double m2)
Definition: EvtbTosllWilsCoeffNLO.cpp:944
EvtbTosllWilsCoeffNLO::P0ndr
double P0ndr(double asW, double eta)
Definition: EvtbTosllWilsCoeffNLO.cpp:441
EvtbTosllWilsCoeffNLO::GetC7Eff
EvtComplex GetC7Eff(double mu, double Mw, double mt, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:1230
EvtbTosllWilsCoeffNLO::Reh
double Reh(double mu, double mQ, double q2)
Definition: EvtbTosllWilsCoeffNLO.cpp:520
EvtbTosllWilsCoeffNLO::C6
double C6(double mu, double Mw, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:250
EvtGenReport
std::ostream & EvtGenReport(EvtGenSeverity severity, const char *facility=0)
Definition: EvtReport.cpp:33
EvtbTosllWilsCoeffNLO::C5
double C5(double mu, double Mw, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:222
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:784
EvtbTosllWilsCoeffNLO::As
double As(double mu, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:44
EvtbTosllWilsCoeffNLO::Imh
double Imh(double mQ, double q2)
Definition: EvtbTosllWilsCoeffNLO.cpp:544
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:612
EvtConst::pi
static const double pi
Definition: EvtConst.hh:26
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:993
EvtbTosllWilsCoeffNLO::ImResonant
double ImResonant(double q2, double GV, double GllV, double MV)
Definition: EvtbTosllWilsCoeffNLO.cpp:582
EvtbTosllWilsCoeffNLO::C2
double C2(double mu, double Mw, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:136
EvtbTosllWilsCoeffNLO::C3
double C3(double mu, double Mw, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:164
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:1195
EvtbTosllWilsCoeffNLO::ReResonant
double ReResonant(double q2, double GV, double GllV, double MV)
Definition: EvtbTosllWilsCoeffNLO.cpp:564
EvtbTosllWilsCoeffNLO::C10a
double C10a(double mt, double Mw)
Definition: EvtbTosllWilsCoeffNLO.cpp:499
EvtbTosllWilsCoeffNLO::C9v
double C9v(double mu, double Mw, double mt, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:476
EvtbTosllWilsCoeffNLO::GetC10Eff
EvtComplex GetC10Eff(double mt, double Mw)
Definition: EvtbTosllWilsCoeffNLO.cpp:1250
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:1119
EvtbTosllWilsCoeffNLO::C4
double C4(double mu, double Mw, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:193
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double C1(double mu, double Mw, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:108
EvtbTosllWilsCoeffNLO::C7gamma
double C7gamma(double mu, double Mw, double mt, int Nf, int ias)
Definition: EvtbTosllWilsCoeffNLO.cpp:373
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