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EvtRareLbToLllWC.cpp
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EvtRareLbToLllWC.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 *
* the Free Software Foundation, either version 3 of the License, or *
* (at your option) any later version. *
* *
* 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. *
* *
* 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/EvtRareLbToLllWC.hh"
//-----------------------------------------------------------------------------
// Implementation file for class : EvtRareLbToLllWC
//
// 2013-11-27 : Thomas Blake
//-----------------------------------------------------------------------------
EvtComplex EvtRareLbToLllWC::GetC7Eff( const double q2 ) const
{
static double mbeff = 4.8;
double shat = q2 / mbeff / mbeff;
double logshat;
logshat = log( shat );
double muscale;
muscale = 2.5;
double alphas;
alphas = 0.267;
double A7;
A7 = -0.353 + 0.023;
double A8;
A8 = -0.164;
double C1;
C1 = -0.697;
double C2;
C2 = 1.046;
double Lmu;
Lmu = log( muscale / mbeff );
EvtComplex uniti( 0.0, 1.0 );
EvtComplex c7eff;
if ( shat > 0.25 ) {
c7eff = A7;
return c7eff;
}
// change energy scale to 5.0 for full NNLO calculation below shat = 0.25
muscale = 5.0;
alphas = 0.215;
A7 = -0.312 + 0.008;
A8 = -0.148;
C1 = -0.487;
C2 = 1.024;
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 * logshat + shat * ( k7110 + k7111 * logshat ) +
shat * shat * ( k7120 + k7121 * logshat ) +
shat * shat * shat * ( k7130 + k7131 * logshat );
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 * logshat + shat * ( k7210 + k7211 * logshat ) +
shat * shat * ( k7220 + k7221 * logshat ) +
shat * shat * shat * ( k7230 + k7231 * logshat );
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 ) * shat +
( 32.0 * EvtConst::pi * EvtConst::pi / 9.0 - 316.0 / 9.0 ) * shat *
shat +
( 200.0 * EvtConst::pi * EvtConst::pi / 27.0 - 658.0 / 9.0 ) * shat *
shat * shat +
( -8.0 * logshat / 9.0 ) * ( shat + shat * shat + shat * shat * shat );
c7eff = A7 - alphas / ( 4.0 * EvtConst::pi ) *
( C1 * F71 + C2 * F72 + A8 * F78 );
return c7eff;
}
EvtComplex EvtRareLbToLllWC::GetC9Eff( const double q2, const bool btod ) const
{
static double mbeff = 4.8;
double shat = q2 / mbeff / mbeff;
double logshat;
logshat = log( shat );
double mchat = 0.29;
double muscale;
muscale = 2.5;
double alphas;
alphas = 0.267;
double A8;
A8 = -0.164;
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;
double Lmu;
Lmu = log( muscale / mbeff );
EvtComplex uniti( 0.0, 1.0 );
EvtComplex hc;
double xarg;
xarg = 4.0 * mchat / shat;
hc = -4.0 / 9.0 * log( mchat * mchat ) + 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( fabs( ( 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 / shat;
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( fabs( ( 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 ( shat > 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
muscale = 5.0;
alphas = 0.215;
A9 = 4.174 + ( -0.035 );
C1 = -0.487;
C2 = 1.024;
A8 = -0.148;
T9 = 0.374 + 0.252;
U9 = 0.033 + 0.015;
W9 = 0.032 + 0.012;
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 * logshat + shat * ( k9110 + k9111 * logshat ) +
shat * shat * ( k9120 + k9121 * logshat ) +
shat * shat * shat * ( k9130 + k9131 * logshat );
F91 = ( -1424.0 / 729.0 + 16.0 * uniti * EvtConst::pi / 243.0 +
64.0 / 27.0 * log( mchat ) ) *
Lmu -
16.0 * Lmu * logshat / 243.0 +
( 16.0 / 1215.0 - 32.0 / 135.0 / mchat / mchat ) * Lmu * shat +
( 4.0 / 2835.0 - 8.0 / 315.0 / mchat / mchat / mchat / mchat ) * Lmu *
shat * shat +
( 16.0 / 76545.0 -
32.0 / 8505.0 / mchat / mchat / mchat / mchat / mchat / mchat ) *
Lmu * shat * shat * shat -
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 * logshat + shat * ( k9210 + k9211 * logshat ) +
shat * shat * ( k9220 + k9221 * logshat ) +
shat * shat * shat * ( k9230 + k9231 * logshat );
F92 = ( 256.0 / 243.0 - 32.0 * uniti * EvtConst::pi / 81.0 -
128.0 / 9.0 * log( mchat ) ) *
Lmu +
32.0 * Lmu * logshat / 81.0 +
( -32.0 / 405.0 + 64.0 / 45.0 / mchat / mchat ) * Lmu * shat +
( -8.0 / 945.0 + 16.0 / 105.0 / mchat / mchat / mchat / mchat ) *
Lmu * shat * shat +
( -32.0 / 25515.0 +
64.0 / 2835.0 / mchat / mchat / mchat / mchat / mchat / mchat ) *
Lmu * shat * shat * shat +
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 ) * shat +
( 14212.0 / 135.0 - 32.0 * EvtConst::pi * EvtConst::pi / 3.0 ) *
shat * shat +
( 193444.0 / 945.0 - 560.0 * EvtConst::pi * EvtConst::pi / 27.0 ) *
shat * shat * shat +
16.0 * logshat / 9.0 *
( 1.0 + shat + shat * shat + shat * shat * shat );
Xd = ( Vudstar * Vub / Vtdstar * Vtb ) * ( 4.0 / 3.0 * C1 + C2 ) *
( hc - h0 );
c9eff = A9 + T9 * hc + U9 * h1 + W9 * h0 -
alphas / ( 4.0 * EvtConst::pi ) * ( C1 * F91 + C2 * F92 + A8 * F98 );
if ( btod ) {
c9eff += Xd;
}
return c9eff;
}
/*
Calculate C10 coefficient
C10 is scale (and q^2) independent
*/
EvtComplex EvtRareLbToLllWC::GetC10Eff( double /*q2*/ ) const
{
double A10;
A10 = -4.592 + 0.379;
EvtComplex c10eff;
c10eff = A10;
return c10eff;
}
//=============================================================================

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