EvtVub.cpp

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#include "EvtGenModels/EvtVub.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 "EvtGenBase/EvtVector4R.hh"

#include "EvtGenModels/EvtPFermi.hh"

#include <stdlib.h>
#include <string>
using std::endl;

std::string EvtVub::getName()
{
    return "VUB";
}

EvtDecayBase* EvtVub::clone()
{
    return new EvtVub;
}

void EvtVub::init()
{
    // check that there are at least 6 arguments

    if ( getNArg() < 6 ) {
        EvtGenReport( EVTGEN_ERROR, "EvtGen" )
            << "EvtVub generator expected "
            << " at least 6 arguments (mb,a,alpha_s,Nbins,m1,w1,...) but found: "
            << getNArg() << endl;
        EvtGenReport( EVTGEN_ERROR, "EvtGen" )
            << "Will terminate execution!" << endl;
        ::abort();
    }

    _mb = getArg( 0 );
    _a = getArg( 1 );
    _alphas = getArg( 2 );
    _nbins = abs( (int)getArg( 3 ) );
    _storeQplus = ( getArg( 3 ) < 0 ? 1 : 0 );
    _masses = std::vector<double>( _nbins );
    _weights = std::vector<double>( _nbins );

    if ( getNArg() - 4 != 2 * _nbins ) {
        EvtGenReport( EVTGEN_ERROR, "EvtGen" )
            << "EvtVub generator expected " << _nbins
            << " masses and weights but found: " << ( getNArg() - 4 ) / 2
            << endl;
        EvtGenReport( EVTGEN_ERROR, "EvtGen" )
            << "Will terminate execution!" << endl;
        ::abort();
    }
    int i, j = 4;
    double maxw = 0.;
    for ( i = 0; i < _nbins; i++ ) {
        _masses[i] = getArg( j++ );
        if ( i > 0 && _masses[i] <= _masses[i - 1] ) {
            EvtGenReport( EVTGEN_ERROR, "EvtGen" )
                << "EvtVub generator expected "
                << " mass bins in ascending order!"
                << "Will terminate execution!" << endl;
            ::abort();
        }
        _weights[i] = getArg( j++ );
        if ( _weights[i] < 0 ) {
            EvtGenReport( EVTGEN_ERROR, "EvtGen" )
                << "EvtVub generator expected "
                << " weights >= 0, but found: " << _weights[i] << endl;
            EvtGenReport( EVTGEN_ERROR, "EvtGen" )
                << "Will terminate execution!" << endl;
            ::abort();
        }
        if ( _weights[i] > maxw )
            maxw = _weights[i];
    }
    if ( maxw == 0 ) {
        EvtGenReport( EVTGEN_ERROR, "EvtGen" )
            << "EvtVub generator expected at least one "
            << " weight > 0, but found none! "
            << "Will terminate execution!" << endl;
        ::abort();
    }
    for ( i = 0; i < _nbins; i++ )
        _weights[i] /= maxw;

    // the maximum dGamma*p2 value depends on alpha_s only:

    const double dGMax0 = 3.;
    _dGMax = 0.21344 + 8.905 * _alphas;
    if ( _dGMax < dGMax0 )
        _dGMax = dGMax0;

    // for the Fermi Motion we need a B-Meson mass - but it's not critical
    // to get an exact value; in order to stay in the phase space for
    // B+- and B0 use the smaller mass

    EvtId BP = EvtPDL::getId( "B+" );
    EvtId B0 = EvtPDL::getId( "B0" );

    double mB0 = EvtPDL::getMaxMass( B0 );
    double mBP = EvtPDL::getMaxMass( BP );

    double mB = ( mB0 < mBP ? mB0 : mBP );

    const double xlow = -_mb;
    const double xhigh = mB - _mb;
    const int aSize = 10000;

    EvtPFermi pFermi( _a, mB, _mb );
    // pf is the cumulative distribution
    // normalized to 1.
    _pf.resize( aSize );
    for ( i = 0; i < aSize; i++ ) {
        double kplus = xlow + (double)( i + 0.5 ) / ( (double)aSize ) *
                                  ( xhigh - xlow );
        if ( i == 0 )
            _pf[i] = pFermi.getFPFermi( kplus );
        else
            _pf[i] = _pf[i - 1] + pFermi.getFPFermi( kplus );
    }
    for ( size_t index = 0; index < _pf.size(); index++ ) {
        _pf[index] /= _pf[_pf.size() - 1];
    }

    //  static EvtHepRandomEngine myEngine;

    //  _pFermi = new RandGeneral(myEngine,pf,aSize,0);
    _dGamma = std::make_unique<EvtVubdGamma>( _alphas );

    // check that there are 3 daughters
    checkNDaug( 3 );
}

void EvtVub::initProbMax()
{
    noProbMax();
}

void EvtVub::decay( EvtParticle* p )
{
    int j;
    // B+ -> u-bar specflav l+ nu

    EvtParticle *xuhad( 0 ), *lepton( 0 ), *neutrino( 0 );
    EvtVector4R p4;
    // R. Faccini 21/02/03
    // move the reweighting up , before also shooting the fermi distribution
    double x, z, p2;
    double sh = 0.0;
    double mB, ml, xlow, xhigh, qplus;
    double El = 0.0;
    double Eh = 0.0;
    double kplus;
    const double lp2epsilon = -10;
    bool rew( true );
    while ( rew ) {
        p->initializePhaseSpace( getNDaug(), getDaugs() );

        xuhad = p->getDaug( 0 );
        lepton = p->getDaug( 1 );
        neutrino = p->getDaug( 2 );

        mB = p->mass();
        ml = lepton->mass();

        xlow = -_mb;
        xhigh = mB - _mb;

        // Fermi motion does not need to be computed inside the
        // tryit loop as m_b in Gamma0 does not need to be replaced by (m_b+kplus).
        // The difference however should be of the Order (lambda/m_b)^2 which is
        // beyond the considered orders in the paper anyway ...

        // for alpha_S = 0 and a mass cut on X_u not all values of kplus are
        // possible. The maximum value is mB/2-_mb + sqrt(mB^2/4-_masses[0]^2)
        kplus = 2 * xhigh;

        while ( kplus >= xhigh || kplus <= xlow ||
                ( _alphas == 0 &&
                  kplus >= mB / 2 - _mb +
                               sqrt( mB * mB / 4 - _masses[0] * _masses[0] ) ) ) {
            kplus = findPFermi();    //_pFermi->shoot();
            kplus = xlow + kplus * ( xhigh - xlow );
        }
        qplus = mB - _mb - kplus;
        if ( ( mB - qplus ) / 2. <= ml )
            continue;

        int tryit = 1;
        while ( tryit ) {
            x = EvtRandom::Flat();
            z = EvtRandom::Flat( 0, 2 );
            p2 = EvtRandom::Flat();
            p2 = pow( 10.0, lp2epsilon * p2 );

            El = x * ( mB - qplus ) / 2;
            if ( El > ml && El < mB / 2 ) {
                Eh = z * ( mB - qplus ) / 2 + qplus;
                if ( Eh > 0 && Eh < mB ) {
                    sh = p2 * pow( mB - qplus, 2 ) +
                         2 * qplus * ( Eh - qplus ) + qplus * qplus;
                    if ( sh > _masses[0] * _masses[0] &&
                         mB * mB + sh - 2 * mB * Eh > ml * ml ) {
                        double xran = EvtRandom::Flat();

                        double y = _dGamma->getdGdxdzdp( x, z, p2 ) / _dGMax * p2;

                        if ( y > 1 )
                            EvtGenReport( EVTGEN_WARNING, "EvtGen" )
                                << "EvtVub decay probability > 1 found: " << y
                                << endl;
                        if ( y >= xran )
                            tryit = 0;
                    }
                }
            }
        }
        // reweight the Mx distribution
        if ( _nbins > 0 ) {
            double xran1 = EvtRandom::Flat();
            double m = sqrt( sh );
            j = 0;
            while ( j < _nbins && m > _masses[j] )
                j++;
            double w = _weights[j - 1];
            if ( w >= xran1 )
                rew = false;
        } else {
            rew = false;
        }
    }

    // o.k. we have the three kineamtic variables
    // now calculate a flat cos Theta_H [-1,1] distribution of the
    // hadron flight direction w.r.t the B flight direction
    // because the B is a scalar and should decay isotropic.
    // Then chose a flat Phi_H [0,2Pi] w.r.t the B flight direction
    // and and a flat Phi_L [0,2Pi] in the W restframe w.r.t the
    // W flight direction.

    double ctH = EvtRandom::Flat( -1, 1 );
    double phH = EvtRandom::Flat( 0, 2 * EvtConst::pi );
    double phL = EvtRandom::Flat( 0, 2 * EvtConst::pi );

    // now compute the four vectors in the B Meson restframe

    double ptmp, sttmp;
    // calculate the hadron 4 vector in the B Meson restframe

    sttmp = sqrt( 1 - ctH * ctH );
    ptmp = sqrt( Eh * Eh - sh );
    double pHB[4] = {Eh, ptmp * sttmp * cos( phH ), ptmp * sttmp * sin( phH ),
                     ptmp * ctH};
    p4.set( pHB[0], pHB[1], pHB[2], pHB[3] );
    xuhad->init( getDaug( 0 ), p4 );

    if ( _storeQplus ) {
        // cludge to store the hidden parameter q+ with the decay;
        // the lifetime of the Xu is abused for this purpose.
        // tau = 1 ps corresponds to ctau = 0.3 mm -> in order to
        // stay well below BaBars sensitivity we take q+/(10000 GeV) which
        // goes up to 0.0005 in the most extreme cases as ctau in mm.
        // To extract q+ back from the StdHepTrk its necessary to get
        // delta_ctau = Xu->anyDaughter->getVertexTime()-Xu->getVertexTime()
        // where these pseudo calls refere to the StdHep time stored at
        // the production vertex in the lab for each particle. The boost
        // has to be reversed and the result is:
        //
        // q+ = delta_ctau * 10000 GeV/mm * Mass_Xu/Energy_Xu
        //
        xuhad->setLifetime( qplus / 10000. );
    }

    // calculate the W 4 vector in the B Meson restrframe

    double apWB = ptmp;
    double pWB[4] = {mB - Eh, -pHB[1], -pHB[2], -pHB[3]};

    // first go in the W restframe and calculate the lepton and
    // the neutrino in the W frame

    double mW2 = mB * mB + sh - 2 * mB * Eh;
    double beta = ptmp / pWB[0];
    double gamma = pWB[0] / sqrt( mW2 );

    double pLW[4];

    ptmp = ( mW2 - ml * ml ) / 2 / sqrt( mW2 );
    pLW[0] = sqrt( ml * ml + ptmp * ptmp );

    double ctL = ( El - gamma * pLW[0] ) / beta / gamma / ptmp;
    if ( ctL < -1 )
        ctL = -1;
    if ( ctL > 1 )
        ctL = 1;
    sttmp = sqrt( 1 - ctL * ctL );

    // eX' = eZ x eW
    double xW[3] = {-pWB[2], pWB[1], 0};
    // eZ' = eW
    double zW[3] = {pWB[1] / apWB, pWB[2] / apWB, pWB[3] / apWB};

    double lx = sqrt( xW[0] * xW[0] + xW[1] * xW[1] );
    for ( j = 0; j < 2; j++ )
        xW[j] /= lx;

    // eY' = eZ' x eX'
    double yW[3] = {-pWB[1] * pWB[3], -pWB[2] * pWB[3],
                    pWB[1] * pWB[1] + pWB[2] * pWB[2]};
    double ly = sqrt( yW[0] * yW[0] + yW[1] * yW[1] + yW[2] * yW[2] );
    for ( j = 0; j < 3; j++ )
        yW[j] /= ly;

    // p_lep = |p_lep| * (  sin(Theta) * cos(Phi) * eX'
    //                    + sin(Theta) * sin(Phi) * eY'
    //                    + cos(Theta) *            eZ')
    for ( j = 0; j < 3; j++ )
        pLW[j + 1] = sttmp * cos( phL ) * ptmp * xW[j] +
                     sttmp * sin( phL ) * ptmp * yW[j] + ctL * ptmp * zW[j];

    double apLW = ptmp;

    // boost them back in the B Meson restframe
    double appLB = beta * gamma * pLW[0] + gamma * ctL * apLW;

    ptmp = sqrt( El * El - ml * ml );
    double ctLL = appLB / ptmp;

    if ( ctLL > 1 )
        ctLL = 1;
    if ( ctLL < -1 )
        ctLL = -1;

    double pLB[4] = {El, 0, 0, 0};
    double pNB[4] = {pWB[0] - El, 0, 0, 0};

    for ( j = 1; j < 4; j++ ) {
        pLB[j] = pLW[j] + ( ctLL * ptmp - ctL * apLW ) / apWB * pWB[j];
        pNB[j] = pWB[j] - pLB[j];
    }

    p4.set( pLB[0], pLB[1], pLB[2], pLB[3] );
    lepton->init( getDaug( 1 ), p4 );

    p4.set( pNB[0], pNB[1], pNB[2], pNB[3] );
    neutrino->init( getDaug( 2 ), p4 );

    return;
}

double EvtVub::findPFermi()
{
    double ranNum = EvtRandom::Flat();
    double oOverBins = 1.0 / ( float( _pf.size() ) );
    int nBinsBelow = 0;    // largest k such that I[k] is known to be <= rand
    int nBinsAbove = _pf.size();    // largest k such that I[k] is known to be >  rand
    int middle;

    while ( nBinsAbove > nBinsBelow + 1 ) {
        middle = ( nBinsAbove + nBinsBelow + 1 ) >> 1;
        if ( ranNum >= _pf[middle] ) {
            nBinsBelow = middle;
        } else {
            nBinsAbove = middle;
        }
    }

    double bSize = _pf[nBinsAbove] - _pf[nBinsBelow];
    // binMeasure is always aProbFunc[nBinsBelow],

    if ( bSize == 0 ) {
        // rand lies right in a bin of measure 0.  Simply return the center
        // of the range of that bin.  (Any value between k/N and (k+1)/N is
        // equally good, in this rare case.)
        return ( nBinsBelow + .5 ) * oOverBins;
    }

    double bFract = ( ranNum - _pf[nBinsBelow] ) / bSize;

    return ( nBinsBelow + bFract ) * oOverBins;
}