EvtBtoXsllUtil.cpp

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#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 * 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;
}