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EvtBtoXsllUtil.cpp
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EvtBtoXsllUtil.cpp
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/***********************************************************************
* Copyright 1998-2020 CERN for the benefit of the EvtGen authors *
* *
* This file is part of EvtGen. *
* *
* EvtGen is free software: you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
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* EvtGen is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
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* You should have received a copy of the GNU General Public License *
* along with EvtGen. If not, see <https://www.gnu.org/licenses/>. *
***********************************************************************/
#include "EvtGenModels/EvtBtoXsllUtil.hh"
#include "EvtGenBase/EvtComplex.hh"
#include "EvtGenBase/EvtConst.hh"
#include "EvtGenBase/EvtDiLog.hh"
#include "EvtGenBase/EvtGenKine.hh"
#include "EvtGenBase/EvtPDL.hh"
#include "EvtGenBase/EvtParticle.hh"
#include "EvtGenBase/EvtPatches.hh"
#include "EvtGenBase/EvtRandom.hh"
#include "EvtGenBase/EvtReport.hh"
#include <stdlib.h>
EvtComplex EvtBtoXsllUtil::GetC7Eff0( double sh, bool nnlo )
{
// This function returns the zeroth-order alpha_s part of C7
if ( !nnlo )
return -0.313;
double A7;
// use energy scale of 2.5 GeV as a computational trick (G.Hiller)
// at least for shat > 0.25
A7 = -0.353 + 0.023;
EvtComplex c7eff;
if ( sh > 0.25 ) {
c7eff = A7;
return c7eff;
}
// change energy scale to 5.0 for full NNLO calculation below shat = 0.25
A7 = -0.312 + 0.008;
c7eff = A7;
return c7eff;
}
EvtComplex EvtBtoXsllUtil::GetC7Eff1( double sh, double mbeff, bool nnlo )
{
// This function returns the first-order alpha_s part of C7
if ( !nnlo )
return 0.0;
double logsh;
logsh = log( sh );
EvtComplex uniti( 0.0, 1.0 );
EvtComplex c7eff = 0.0;
if ( sh > 0.25 ) {
return c7eff;
}
// change energy scale to 5.0 for full NNLO calculation below shat = 0.25
double muscale = 5.0;
double alphas = 0.215;
//double A7 = -0.312 + 0.008;
double A8 = -0.148;
//double A9 = 4.174 + (-0.035);
//double A10 = -4.592 + 0.379;
double C1 = -0.487;
double C2 = 1.024;
//double T9 = 0.374 + 0.252;
//double U9 = 0.033 + 0.015;
//double W9 = 0.032 + 0.012;
double Lmu = log( muscale / mbeff );
EvtComplex F71;
EvtComplex f71;
EvtComplex k7100( -0.68192, -0.074998 );
EvtComplex k7101( 0.0, 0.0 );
EvtComplex k7110( -0.23935, -0.12289 );
EvtComplex k7111( 0.0027424, 0.019676 );
EvtComplex k7120( -0.0018555, -0.175 );
EvtComplex k7121( 0.022864, 0.011456 );
EvtComplex k7130( 0.28248, -0.12783 );
EvtComplex k7131( 0.029027, -0.0082265 );
f71 = k7100 + k7101 * logsh + sh * ( k7110 + k7111 * logsh ) +
sh * sh * ( k7120 + k7121 * logsh ) +
sh * sh * sh * ( k7130 + k7131 * logsh );
F71 = ( -208.0 / 243.0 ) * Lmu + f71;
EvtComplex F72;
EvtComplex f72;
EvtComplex k7200( 4.0915, 0.44999 );
EvtComplex k7201( 0.0, 0.0 );
EvtComplex k7210( 1.4361, 0.73732 );
EvtComplex k7211( -0.016454, -0.11806 );
EvtComplex k7220( 0.011133, 1.05 );
EvtComplex k7221( -0.13718, -0.068733 );
EvtComplex k7230( -1.6949, 0.76698 );
EvtComplex k7231( -0.17416, 0.049359 );
f72 = k7200 + k7201 * logsh + sh * ( k7210 + k7211 * logsh ) +
sh * sh * ( k7220 + k7221 * logsh ) +
sh * sh * sh * ( k7230 + k7231 * logsh );
F72 = ( 416.0 / 81.0 ) * Lmu + f72;
EvtComplex F78;
F78 = ( -32.0 / 9.0 ) * Lmu + 8.0 * EvtConst::pi * EvtConst::pi / 27.0 +
( -44.0 / 9.0 ) + ( -8.0 * EvtConst::pi / 9.0 ) * uniti +
( 4.0 / 3.0 * EvtConst::pi * EvtConst::pi - 40.0 / 3.0 ) * sh +
( 32.0 * EvtConst::pi * EvtConst::pi / 9.0 - 316.0 / 9.0 ) * sh * sh +
( 200.0 * EvtConst::pi * EvtConst::pi / 27.0 - 658.0 / 9.0 ) * sh *
sh * sh +
( -8.0 * logsh / 9.0 ) * ( sh + sh * sh + sh * sh * sh );
c7eff = -alphas / ( 4.0 * EvtConst::pi ) * ( C1 * F71 + C2 * F72 + A8 * F78 );
return c7eff;
}
EvtComplex EvtBtoXsllUtil::GetC9Eff0( double sh, double /* mbeff */, bool nnlo,
bool btod )
{
// This function returns the zeroth-order alpha_s part of C9
if ( !nnlo )
return 4.344;
double mch = 0.29;
double A9;
A9 = 4.287 + ( -0.218 );
double C1;
C1 = -0.697;
double C2;
C2 = 1.046;
double T9;
T9 = 0.114 + 0.280;
double U9;
U9 = 0.045 + 0.023;
double W9;
W9 = 0.044 + 0.016;
EvtComplex uniti( 0.0, 1.0 );
EvtComplex hc;
double xarg;
xarg = 4.0 * mch / sh;
hc = -4.0 / 9.0 * log( mch * mch ) + 8.0 / 27.0 + 4.0 * xarg / 9.0;
if ( xarg < 1.0 ) {
hc = hc - 2.0 / 9.0 * ( 2.0 + xarg ) * sqrt( fabs( 1.0 - xarg ) ) *
( log( ( sqrt( 1.0 - xarg ) + 1.0 ) /
( sqrt( 1.0 - xarg ) - 1.0 ) ) -
uniti * EvtConst::pi );
} else {
hc = hc - 2.0 / 9.0 * ( 2.0 + xarg ) * sqrt( fabs( 1.0 - xarg ) ) *
2.0 * atan( 1.0 / sqrt( xarg - 1.0 ) );
}
EvtComplex h1;
xarg = 4.0 / sh;
h1 = 8.0 / 27.0 + 4.0 * xarg / 9.0;
if ( xarg < 1.0 ) {
h1 = h1 - 2.0 / 9.0 * ( 2.0 + xarg ) * sqrt( fabs( 1.0 - xarg ) ) *
( log( ( sqrt( 1.0 - xarg ) + 1.0 ) /
( sqrt( 1.0 - xarg ) - 1.0 ) ) -
uniti * EvtConst::pi );
} else {
h1 = h1 - 2.0 / 9.0 * ( 2.0 + xarg ) * sqrt( fabs( 1.0 - xarg ) ) *
2.0 * atan( 1.0 / sqrt( xarg - 1.0 ) );
}
EvtComplex h0;
h0 = 8.0 / 27.0 - 4.0 * log( 2.0 ) / 9.0 + 4.0 * uniti * EvtConst::pi / 9.0;
// X=V_{ud}^* V_ub / V_{td}^* V_tb * (4/3 C_1 +C_2) * (h(\hat m_c^2, hat s)-
// h(\hat m_u^2, hat s))
EvtComplex Vudstar( 1.0 - 0.2279 * 0.2279 / 2.0, 0.0 );
EvtComplex Vub( ( 0.118 + 0.273 ) / 2.0, -1.0 * ( 0.305 + 0.393 ) / 2.0 );
EvtComplex Vtdstar( 1.0 - ( 0.118 + 0.273 ) / 2.0, ( 0.305 + 0.393 ) / 2.0 );
EvtComplex Vtb( 1.0, 0.0 );
EvtComplex Xd;
Xd = ( Vudstar * Vub / Vtdstar * Vtb ) * ( 4.0 / 3.0 * C1 + C2 ) *
( hc - h0 );
EvtComplex c9eff = 4.344;
if ( sh > 0.25 ) {
c9eff = A9 + T9 * hc + U9 * h1 + W9 * h0;
if ( btod ) {
c9eff += Xd;
}
return c9eff;
}
// change energy scale to 5.0 for full NNLO calculation below shat = 0.25
A9 = 4.174 + ( -0.035 );
C1 = -0.487;
C2 = 1.024;
T9 = 0.374 + 0.252;
U9 = 0.033 + 0.015;
W9 = 0.032 + 0.012;
Xd = ( Vudstar * Vub / Vtdstar * Vtb ) * ( 4.0 / 3.0 * C1 + C2 ) *
( hc - h0 );
c9eff = A9 + T9 * hc + U9 * h1 + W9 * h0;
if ( btod ) {
c9eff += Xd;
}
return c9eff;
}
EvtComplex EvtBtoXsllUtil::GetC9Eff1( double sh, double mbeff, bool nnlo,
bool /*btod*/ )
{
// This function returns the first-order alpha_s part of C9
if ( !nnlo )
return 0.0;
double logsh;
logsh = log( sh );
double mch = 0.29;
EvtComplex uniti( 0.0, 1.0 );
EvtComplex c9eff = 0.0;
if ( sh > 0.25 ) {
return c9eff;
}
// change energy scale to 5.0 for full NNLO calculation below shat = 0.25
double muscale = 5.0;
double alphas = 0.215;
double C1 = -0.487;
double C2 = 1.024;
double A8 = -0.148;
double Lmu = log( muscale / mbeff );
EvtComplex F91;
EvtComplex f91;
EvtComplex k9100( -11.973, 0.16371 );
EvtComplex k9101( -0.081271, -0.059691 );
EvtComplex k9110( -28.432, -0.25044 );
EvtComplex k9111( -0.040243, 0.016442 );
EvtComplex k9120( -57.114, -0.86486 );
EvtComplex k9121( -0.035191, 0.027909 );
EvtComplex k9130( -128.8, -2.5243 );
EvtComplex k9131( -0.017587, 0.050639 );
f91 = k9100 + k9101 * logsh + sh * ( k9110 + k9111 * logsh ) +
sh * sh * ( k9120 + k9121 * logsh ) +
sh * sh * sh * ( k9130 + k9131 * logsh );
F91 = ( -1424.0 / 729.0 + 16.0 * uniti * EvtConst::pi / 243.0 +
64.0 / 27.0 * log( mch ) ) *
Lmu -
16.0 * Lmu * logsh / 243.0 +
( 16.0 / 1215.0 - 32.0 / 135.0 / mch / mch ) * Lmu * sh +
( 4.0 / 2835.0 - 8.0 / 315.0 / mch / mch / mch / mch ) * Lmu * sh * sh +
( 16.0 / 76545.0 - 32.0 / 8505.0 / mch / mch / mch / mch / mch / mch ) *
Lmu * sh * sh * sh -
256.0 * Lmu * Lmu / 243.0 + f91;
EvtComplex F92;
EvtComplex f92;
EvtComplex k9200( 6.6338, -0.98225 );
EvtComplex k9201( 0.48763, 0.35815 );
EvtComplex k9210( 3.3585, 1.5026 );
EvtComplex k9211( 0.24146, -0.098649 );
EvtComplex k9220( -1.1906, 5.1892 );
EvtComplex k9221( 0.21115, -0.16745 );
EvtComplex k9230( -17.12, 15.146 );
EvtComplex k9231( 0.10552, -0.30383 );
f92 = k9200 + k9201 * logsh + sh * ( k9210 + k9211 * logsh ) +
sh * sh * ( k9220 + k9221 * logsh ) +
sh * sh * sh * ( k9230 + k9231 * logsh );
F92 = ( 256.0 / 243.0 - 32.0 * uniti * EvtConst::pi / 81.0 -
128.0 / 9.0 * log( mch ) ) *
Lmu +
32.0 * Lmu * logsh / 81.0 +
( -32.0 / 405.0 + 64.0 / 45.0 / mch / mch ) * Lmu * sh +
( -8.0 / 945.0 + 16.0 / 105.0 / mch / mch / mch / mch ) * Lmu * sh * sh +
( -32.0 / 25515.0 + 64.0 / 2835.0 / mch / mch / mch / mch / mch / mch ) *
Lmu * sh * sh * sh +
512.0 * Lmu * Lmu / 81.0 + f92;
EvtComplex F98;
F98 = 104.0 / 9.0 - 32.0 * EvtConst::pi * EvtConst::pi / 27.0 +
( 1184.0 / 27.0 - 40.0 * EvtConst::pi * EvtConst::pi / 9.0 ) * sh +
( 14212.0 / 135.0 - 32.0 * EvtConst::pi * EvtConst::pi / 3.0 ) * sh *
sh +
( 193444.0 / 945.0 - 560.0 * EvtConst::pi * EvtConst::pi / 27.0 ) *
sh * sh * sh +
16.0 * logsh / 9.0 * ( 1.0 + sh + sh * sh + sh * sh * sh );
c9eff = -alphas / ( 4.0 * EvtConst::pi ) * ( C1 * F91 + C2 * F92 + A8 * F98 );
return c9eff;
}
EvtComplex EvtBtoXsllUtil::GetC10Eff( double /*sh*/, bool nnlo )
{
if ( !nnlo )
return -4.669;
double A10;
A10 = -4.592 + 0.379;
EvtComplex c10eff;
c10eff = A10;
return c10eff;
}
double EvtBtoXsllUtil::dGdsProb( double mb, double ms, double ml, double s )
{
// Compute the decay probability density function given a value of s
// according to Ali-Lunghi-Greub-Hiller's 2002 paper
// Note that the form given below is taken from
// F.Kruger and L.M.Sehgal, Phys. Lett. B380, 199 (1996)
// but the differential rate as a function of dilepton mass
// in this latter paper reduces to Eq.(12) in ALGH's 2002 paper
// for ml = 0 and ms = 0.
bool btod = false;
bool nnlo = true;
double delta, lambda, prob;
double f1, f2, f3, f4;
double msh, mlh, sh;
double mbeff = 4.8;
mlh = ml / mb;
msh = ms / mb;
// set lepton and strange-quark masses to 0 if need to
// be in strict agreement with ALGH 2002 paper
// mlh = 0.0; msh = 0.0;
// sh = s / (mb*mb);
sh = s / ( mbeff * mbeff );
// if sh >1.0 code will return a nan. so just skip it
if ( sh > 1.0 )
return 0.0;
EvtComplex c7eff0 = EvtBtoXsllUtil::GetC7Eff0( sh, nnlo );
EvtComplex c7eff1 = EvtBtoXsllUtil::GetC7Eff1( sh, mbeff, nnlo );
EvtComplex c9eff0 = EvtBtoXsllUtil::GetC9Eff0( sh, mbeff, nnlo, btod );
EvtComplex c9eff1 = EvtBtoXsllUtil::GetC9Eff1( sh, mbeff, nnlo, btod );
EvtComplex c10eff = EvtBtoXsllUtil::GetC10Eff( sh, nnlo );
double alphas = 0.119 /
( 1 + 0.119 * log( pow( 4.8, 2 ) / pow( 91.1867, 2 ) ) *
23.0 / 12.0 / EvtConst::pi );
double omega7 = -8.0 / 3.0 * log( 4.8 / mb ) -
4.0 / 3.0 * EvtDiLog::DiLog( sh ) -
2.0 / 9.0 * EvtConst::pi * EvtConst::pi -
2.0 / 3.0 * log( sh ) * log( 1.0 - sh ) -
log( 1 - sh ) * ( 8.0 + sh ) / ( 2.0 + sh ) / 3.0 -
2.0 / 3.0 * sh * ( 2.0 - 2.0 * sh - sh * sh ) * log( sh ) /
pow( ( 1.0 - sh ), 2 ) / ( 2.0 + sh ) -
( 16.0 - 11.0 * sh - 17.0 * sh * sh ) / 18.0 /
( 2.0 + sh ) / ( 1.0 - sh );
double eta7 = 1.0 + alphas * omega7 / EvtConst::pi;
double omega79 = -4.0 / 3.0 * log( 4.8 / mb ) -
4.0 / 3.0 * EvtDiLog::DiLog( sh ) -
2.0 / 9.0 * EvtConst::pi * EvtConst::pi -
2.0 / 3.0 * log( sh ) * log( 1.0 - sh ) -
1.0 / 9.0 * ( 2.0 + 7.0 * sh ) * log( 1.0 - sh ) / sh -
2.0 / 9.0 * sh * ( 3.0 - 2.0 * sh ) * log( sh ) /
pow( ( 1.0 - sh ), 2 ) +
1.0 / 18.0 * ( 5.0 - 9.0 * sh ) / ( 1.0 - sh );
double eta79 = 1.0 + alphas * omega79 / EvtConst::pi;
double omega9 = -2.0 / 9.0 * EvtConst::pi * EvtConst::pi -
4.0 / 3.0 * EvtDiLog::DiLog( sh ) -
2.0 / 3.0 * log( sh ) * log( 1.0 - sh ) -
( 5.0 + 4.0 * sh ) / ( 3.0 * ( 1.0 + 2.0 * sh ) ) *
log( 1.0 - sh ) -
2.0 * sh * ( 1.0 + sh ) * ( 1.0 - 2.0 * sh ) /
( 3.0 * pow( 1.0 - sh, 2 ) * ( 1.0 + 2.0 * sh ) ) *
log( sh ) +
( 5.0 + 9.0 * sh - 6.0 * sh * sh ) /
( 6.0 * ( 1.0 - sh ) * ( 1.0 + 2.0 * sh ) );
double eta9 = 1.0 + alphas * omega9 / EvtConst::pi;
EvtComplex c7eff = eta7 * c7eff0 + c7eff1;
EvtComplex c9eff = eta9 * c9eff0 + c9eff1;
c10eff *= eta9;
double c7c7 = abs2( c7eff );
double c7c9 = real( ( eta79 * c7eff0 + c7eff1 ) *
conj( eta79 * c9eff0 + c9eff1 ) );
double c9c9plusc10c10 = abs2( c9eff ) + abs2( c10eff );
double c9c9minusc10c10 = abs2( c9eff ) - abs2( c10eff );
// Power corrections according to ALGH 2002
double lambda_1 = -0.2;
double lambda_2 = 0.12;
double C1 = -0.487;
double C2 = 1.024;
double mc = 0.29 * mb;
EvtComplex F;
double r = s / ( 4.0 * mc * mc );
EvtComplex uniti( 0.0, 1.0 );
F = 3.0 / ( 2.0 * r );
if ( r < 1 ) {
F *= 1.0 / sqrt( r * ( 1.0 - r ) ) * atan( sqrt( r / ( 1.0 - r ) ) ) -
1.0;
} else {
F *= 0.5 / sqrt( r * ( r - 1.0 ) ) *
( log( ( 1.0 - sqrt( 1.0 - 1.0 / r ) ) /
( 1.0 + sqrt( 1.0 - 1.0 / r ) ) ) +
uniti * EvtConst::pi ) -
1.0;
}
double G1 = 1.0 + lambda_1 / ( 2.0 * mb * mb ) +
3.0 * ( 1.0 - 15.0 * sh * sh + 10.0 * sh * sh * sh ) /
( ( 1.0 - sh ) * ( 1.0 - sh ) * ( 1.0 + 2.0 * sh ) ) *
lambda_2 / ( 2.0 * mb * mb );
double G2 = 1.0 + lambda_1 / ( 2.0 * mb * mb ) -
3.0 * ( 6.0 + 3.0 * sh - 5.0 * sh * sh * sh ) /
( ( 1.0 - sh ) * ( 1.0 - sh ) * ( 2.0 + sh ) ) * lambda_2 /
( 2.0 * mb * mb );
double G3 = 1.0 + lambda_1 / ( 2.0 * mb * mb ) -
( 5.0 + 6.0 * sh - 7.0 * sh * sh ) /
( ( 1.0 - sh ) * ( 1.0 - sh ) ) * lambda_2 /
( 2.0 * mb * mb );
double Gc = -8.0 / 9.0 * ( C2 - C1 / 6.0 ) * lambda_2 / ( mc * mc ) *
real( F * ( conj( c9eff ) * ( 2.0 + sh ) +
conj( c7eff ) * ( 1.0 + 6.0 * sh - sh * sh ) / sh ) );
// end of power corrections section
// now back to Kruger & Sehgal expressions
double msh2 = msh * msh;
lambda = 1.0 + sh * sh + msh2 * msh2 - 2.0 * ( sh + sh * msh2 + msh2 );
// negative lambda screw up sqrt below!
if ( lambda < 0.0 )
return 0.0;
f1 = pow( 1.0 - msh2, 2 ) - sh * ( 1.0 + msh2 );
f2 = 2.0 * ( 1.0 + msh2 ) * pow( 1.0 - msh2, 2 ) -
sh * ( 1.0 + 14.0 * msh2 + pow( msh, 4 ) ) - sh * sh * ( 1.0 + msh2 );
f3 = pow( 1.0 - msh2, 2 ) + sh * ( 1.0 + msh2 ) - 2.0 * sh * sh +
lambda * 2.0 * mlh * mlh / sh;
f4 = 1.0 - sh + msh2;
delta = ( 12.0 * c7c9 * f1 * G3 + 4.0 * c7c7 * f2 * G2 / sh ) *
( 1.0 + 2.0 * mlh * mlh / sh ) +
c9c9plusc10c10 * f3 * G1 + 6.0 * mlh * mlh * c9c9minusc10c10 * f4 +
Gc;
// avoid negative probs
if ( delta < 0.0 )
delta = 0.;
// negative when sh < 4*mlh*mlh
// s < 4*ml*ml
/// prob = sqrt(lambda*(1.0 - 4.0*mlh*mlh/sh)) * delta;
prob = sqrt( lambda * ( 1.0 - 4.0 * ml * ml / s ) ) * delta;
// if ( !(prob>=0.0) && !(prob<=0.0) ) {
//nan
// std::cout << lambda << " " << mlh << " " << sh << " " << delta << " " << mb << " " << mbeff << std::endl;
// std::cout << 4.0*mlh*mlh/sh << " " << 4.0*ml*ml/s << " " << s-4.0*ml*ml << " " << ml << std::endl;
// std::cout << sh << " " << sh*sh << " " << msh2*msh2 << " " << msh << std::endl;
//std::cout << ( 12.0*c7c9*f1*G3 + 4.0*c7c7*f2*G2/sh ) * (1.0 + 2.0*mlh*mlh/sh)
// <<" " << c9c9plusc10c10*f3*G1
// << " "<< 6.0*mlh*mlh*c9c9minusc10c10*f4
// << " "<< Gc << std::endl;
//std::cout << C2 << " " << C1 << " "<< lambda_2 << " " << mc << " " << real(F*(conj(c9eff)*(2.0+sh)+conj(c7eff)*(1.0 + 6.0*sh - sh*sh)/sh)) << " " << sh << " " << r << std::endl;
//std::cout << c9eff << " " << eta9 << " " <<c9eff0 << " " << c9eff1 << " " << alphas << " " << omega9 << " " << sh << std::endl;
//}
// else{
// if ( sh > 1.0) std::cout << "not a nan \n";
// }
return prob;
}
double EvtBtoXsllUtil::dGdsdupProb( double mb, double ms, double ml, double s,
double u )
{
// Compute the decay probability density function given a value of s and u
// according to Ali-Hiller-Handoko-Morozumi's 1997 paper
// see Appendix E
bool btod = false;
bool nnlo = true;
double prob;
double f1sp, f2sp, f3sp;
double mbeff = 4.8;
// double sh = s / (mb*mb);
double sh = s / ( mbeff * mbeff );
// if sh >1.0 code will return a nan. so just skip it
if ( sh > 1.0 )
return 0.0;
EvtComplex c7eff0 = EvtBtoXsllUtil::GetC7Eff0( sh, nnlo );
EvtComplex c7eff1 = EvtBtoXsllUtil::GetC7Eff1( sh, mbeff, nnlo );
EvtComplex c9eff0 = EvtBtoXsllUtil::GetC9Eff0( sh, mbeff, nnlo, btod );
EvtComplex c9eff1 = EvtBtoXsllUtil::GetC9Eff1( sh, mbeff, nnlo, btod );
EvtComplex c10eff = EvtBtoXsllUtil::GetC10Eff( sh, nnlo );
double alphas = 0.119 /
( 1 + 0.119 * log( pow( 4.8, 2 ) / pow( 91.1867, 2 ) ) *
23.0 / 12.0 / EvtConst::pi );
double omega7 = -8.0 / 3.0 * log( 4.8 / mb ) -
4.0 / 3.0 * EvtDiLog::DiLog( sh ) -
2.0 / 9.0 * EvtConst::pi * EvtConst::pi -
2.0 / 3.0 * log( sh ) * log( 1.0 - sh ) -
log( 1 - sh ) * ( 8.0 + sh ) / ( 2.0 + sh ) / 3.0 -
2.0 / 3.0 * sh * ( 2.0 - 2.0 * sh - sh * sh ) * log( sh ) /
pow( ( 1.0 - sh ), 2 ) / ( 2.0 + sh ) -
( 16.0 - 11.0 * sh - 17.0 * sh * sh ) / 18.0 /
( 2.0 + sh ) / ( 1.0 - sh );
double eta7 = 1.0 + alphas * omega7 / EvtConst::pi;
double omega79 = -4.0 / 3.0 * log( 4.8 / mb ) -
4.0 / 3.0 * EvtDiLog::DiLog( sh ) -
2.0 / 9.0 * EvtConst::pi * EvtConst::pi -
2.0 / 3.0 * log( sh ) * log( 1.0 - sh ) -
1.0 / 9.0 * ( 2.0 + 7.0 * sh ) * log( 1.0 - sh ) / sh -
2.0 / 9.0 * sh * ( 3.0 - 2.0 * sh ) * log( sh ) /
pow( ( 1.0 - sh ), 2 ) +
1.0 / 18.0 * ( 5.0 - 9.0 * sh ) / ( 1.0 - sh );
double eta79 = 1.0 + alphas * omega79 / EvtConst::pi;
double omega9 = -2.0 / 9.0 * EvtConst::pi * EvtConst::pi -
4.0 / 3.0 * EvtDiLog::DiLog( sh ) -
2.0 / 3.0 * log( sh ) * log( 1.0 - sh ) -
( 5.0 + 4.0 * sh ) / ( 3.0 * ( 1.0 + 2.0 * sh ) ) *
log( 1.0 - sh ) -
2.0 * sh * ( 1.0 + sh ) * ( 1.0 - 2.0 * sh ) /
( 3.0 * pow( 1.0 - sh, 2 ) * ( 1.0 + 2.0 * sh ) ) *
log( sh ) +
( 5.0 + 9.0 * sh - 6.0 * sh * sh ) /
( 6.0 * ( 1.0 - sh ) * ( 1.0 + 2.0 * sh ) );
double eta9 = 1.0 + alphas * omega9 / EvtConst::pi;
EvtComplex c7eff = eta7 * c7eff0 + c7eff1;
EvtComplex c9eff = eta9 * c9eff0 + c9eff1;
c10eff *= eta9;
double c7c7 = abs2( c7eff );
double c7c9 = real( ( eta79 * c7eff0 + c7eff1 ) *
conj( eta79 * c9eff0 + c9eff1 ) );
double c7c10 = real( ( eta79 * c7eff0 + c7eff1 ) * conj( eta9 * c10eff ) );
double c9c10 = real( ( eta9 * c9eff0 + c9eff1 ) * conj( eta9 * c10eff ) );
double c9c9plusc10c10 = abs2( c9eff ) + abs2( c10eff );
f1sp = ( pow( mb * mb - ms * ms, 2 ) - s * s ) * c9c9plusc10c10 +
4.0 *
( pow( mb, 4 ) - ms * ms * mb * mb -
pow( ms, 4 ) * ( 1.0 - ms * ms / ( mb * mb ) ) -
8.0 * s * ms * ms - s * s * ( 1.0 + ms * ms / ( mb * mb ) ) ) *
mb * mb * c7c7 /
s
// kludged mass term
* ( 1.0 + 2.0 * ml * ml / s ) -
8.0 * ( s * ( mb * mb + ms * ms ) - pow( mb * mb - ms * ms, 2 ) ) *
c7c9
// kludged mass term
* ( 1.0 + 2.0 * ml * ml / s );
f2sp = 4.0 * s * c9c10 + 8.0 * ( mb * mb + ms * ms ) * c7c10;
f3sp = -( c9c9plusc10c10 ) + 4.0 * ( 1.0 + pow( ms / mb, 4 ) ) * mb * mb *
c7c7 /
s
// kludged mass term
* ( 1.0 + 2.0 * ml * ml / s );
prob = ( f1sp + f2sp * u + f3sp * u * u ) / pow( mb, 3 );
if ( prob < 0.0 )
prob = 0.;
return prob;
}
double EvtBtoXsllUtil::FermiMomentum( double pf )
{
// Pick a value for the b-quark Fermi motion momentum
// according to Ali's Gaussian model
double pb, pbmax, xbox, ybox;
pb = 0.0;
pbmax = 5.0 * pf;
while ( pb == 0.0 ) {
xbox = EvtRandom::Flat( pbmax );
ybox = EvtRandom::Flat();
if ( ybox < FermiMomentumProb( xbox, pf ) ) {
pb = xbox;
}
}
return pb;
}
double EvtBtoXsllUtil::FermiMomentumProb( double pb, double pf )
{
// Compute probability according to Ali's Gaussian model
// the function chosen has a convenient maximum value of 1 for pb = pf
double prsq = ( pb * pb ) / ( pf * pf );
double prob = prsq * exp( 1.0 - prsq );
return prob;
}

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