EvtD0TopipiEta.cc

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//--------------------------------------------------------------------------
//
// Environment:
//      This software is part of the EvtGen package developed jointly
//      for the BaBar and CLEO collaborations.  If you use all or part
//      of it, please give an appropriate acknowledgement.
//
// Copyright Information: See EvtGen/COPYRIGHT
//      Copyright (C) 1998      Caltech, UCSB
//
// Module: EvtD0TopipiEta.cc
//
// Description: Routine to handle three-body decays of D (BAM-608)
//
// Modification history:
//
//    Liaoyuan Dong    Aug 11 2022    Module created
//
//------------------------------------------------------------------------
#include "EvtD0TopipiEta.hh"
#include "../EvtGenBase/EvtComplex.hh"
#include "../EvtGenBase/EvtDecayTable.hh"
#include "../EvtGenBase/EvtGenKine.hh"
#include "../EvtGenBase/EvtPDL.hh"
#include "../EvtGenBase/EvtParticle.hh"
#include "../EvtGenBase/EvtPatches.hh"
#include "../EvtGenBase/EvtReport.hh"
#include "../EvtGenBase/EvtVector4R.hh"
#include <stdlib.h>
using namespace std;
 
EvtD0TopipiEta::~EvtD0TopipiEta() {}
 
void EvtD0TopipiEta::getName( std::string& model_name ) { model_name = "D0TopipiEta"; }
 
EvtDecayBase* EvtD0TopipiEta::clone() { return new EvtD0TopipiEta; }
 
void EvtD0TopipiEta::init() {
  // check that there are 0 arguments
  checkNArg( 0 );
  checkNDaug( 3 );
  checkSpinParent( EvtSpinType::SCALAR );
  checkSpinDaughter( 0, EvtSpinType::SCALAR );
  checkSpinDaughter( 1, EvtSpinType::SCALAR );
  checkSpinDaughter( 2, EvtSpinType::SCALAR );
 
  phi[0] = 0;
  rho[0] = 1; // rho eta
  phi[1] = -0.98109;
  rho[1] = -0.02447; // omega eta (rho-omega mixing)
  phi[2] = 0.71358;
  rho[2] = 1.0848; // a0- pi+
  phi[3] = -0.83115;
  rho[3] = 2.6444; // a0+ pi-
  phi[4] = -0.058521;
  rho[4] = 7.0274; //(pi+ eta)_{2+} pi-
 
  // cout << "Initializing D0TopipiEta" << endl;
  // for (int i=0; i<5; i++) {
  //    cout << i << " rho= " << rho[i] << " phi= " << phi[i] << endl;
  // }
  mrho = 0.77511;
  ma0  = 0.99;
  Grho = 0.1491;
  Ga0  = 0.0756;
 
  const double mk0       = 0.497614;
  const double mass_Kaon = 0.49368;
  const double mass_Pion = 0.13957;
  const double mass_Pi0  = 0.1349766;
  const double meta      = 0.547862;
  mpi                    = 0.13957;
  mD                     = 1.86483;
  sD                     = mD * mD;
  spi                    = mpi * mpi;
  snk                    = mk0 * mk0;
  sck                    = mass_Kaon * mass_Kaon;
  scpi                   = mass_Pion * mass_Pion;
  snpi                   = mass_Pi0 * mass_Pi0;
  seta                   = meta * meta;
 
  pi = 3.1415926;
 
  ci  = EvtComplex( 0.0, 1.0 );
  one = EvtComplex( 1.0, 0.0 );
 
  int GG[4][4] = { { 1, 0, 0, 0 }, { 0, -1, 0, 0 }, { 0, 0, -1, 0 }, { 0, 0, 0, -1 } };
  for ( int i = 0; i < 4; i++ )
  {
    for ( int j = 0; j < 4; j++ ) { G[i][j] = GG[i][j]; }
  }
}
 
void EvtD0TopipiEta::initProbMax() { setProbMax( 476.5 ); }
 
void EvtD0TopipiEta::decay( EvtParticle* p ) {
  /*
     // This piece of code could in principle be used to calculate maximum
     // probablity on fly. But as it uses high number of points and model
     // deals with single final state, we keep hardcoded number for now rather
     // than adapting code to work here.
 
     double maxprob = 0.0;
     for(int ir=0;ir<=60000000;ir++){
        p->initializePhaseSpace(getNDaug(),getDaugs());
        EvtVector4R D1 = p->getDaug(0)->getP4();
        EvtVector4R D2 = p->getDaug(1)->getP4();
        EvtVector4R D3 = p->getDaug(2)->getP4();
 
        double P1[4], P2[4], P3[4];
        P1[0] = D1.get(0); P1[1] = D1.get(1); P1[2] = D1.get(2); P1[3] = D1.get(3);
        P2[0] = D2.get(0); P2[1] = D2.get(1); P2[2] = D2.get(2); P2[3] = D2.get(3);
        P3[0] = D3.get(0); P3[1] = D3.get(1); P3[2] = D3.get(2); P3[3] = D3.get(3);
 
        double value;
        value = calDalEva(P1, P2, P3);
        if(value>maxprob) {
           maxprob=value;
           cout << "ir = " << ir << " maxProb= " << value << endl;
        }
     }
     cout << "maxProb = " << maxprob << endl;
  */
  p->initializePhaseSpace( getNDaug(), getDaugs() );
  EvtVector4R D1 = p->getDaug( 0 )->getP4();
  EvtVector4R D2 = p->getDaug( 1 )->getP4();
  EvtVector4R D3 = p->getDaug( 2 )->getP4();
 
  double P1[4], P2[4], P3[4];
  P1[0] = D1.get( 0 );
  P1[1] = D1.get( 1 );
  P1[2] = D1.get( 2 );
  P1[3] = D1.get( 3 );
  P2[0] = D2.get( 0 );
  P2[1] = D2.get( 1 );
  P2[2] = D2.get( 2 );
  P2[3] = D2.get( 3 );
  P3[0] = D3.get( 0 );
  P3[1] = D3.get( 1 );
  P3[2] = D3.get( 2 );
  P3[3] = D3.get( 3 );
 
  double value;
  value = calDalEva( P1, P2, P3 );
  setProb( value );
 
  return;
}
 
double EvtD0TopipiEta::calDalEva( double P1[], double P2[], double P3[] ) {
  // pi- pi+ eta
  // 0: non-resonance
  // 1: resonance, RBW
  // 2: resonance, GS
  // 3: resonance, Flatte
  // 4: rho-omega mxing for omega
  EvtComplex PDF[6];
  EvtComplex cof, pdf, module;
  double     value;
  PDF[0] = Spin_factor( P1, P2, P3, 1, 2, mrho, Grho );   // rho eta
  PDF[1] = Spin_factor( P1, P2, P3, 1, 4, mrho, Grho );   // rho-omega mixing
  PDF[2] = Spin_factor( P1, P3, P2, 0, 3, ma0, Ga0 );     // a0- pi+
  PDF[3] = Spin_factor( P2, P3, P1, 0, 3, ma0, Ga0 );     // a0+ pi-
  PDF[4] = Spin_factor( P2, P3, P1, 2, 0, 1.698, 0.265 ); // pi+ eta 2+ non-res
 
  pdf = EvtComplex( 0.0, 0.0 );
  for ( int i = 0; i < 5; i++ )
  {
    cof = EvtComplex( rho[i] * cos( phi[i] ), rho[i] * sin( phi[i] ) );
    pdf = pdf + cof * PDF[i];
  }
  module = conj( pdf ) * pdf;
  value  = real( module );
  return ( value <= 0 ) ? 1e-20 : value;
}
 
EvtComplex EvtD0TopipiEta::Spin_factor( double P1[], double P2[], double P3[], int spin,
                                        int flag, double mass_R, double width_R ) {
  // D-> R P3, R->P1 P2, 0: non-resonance 1: resonance, RBW 2: resonance, GS 3: resonance,
  // Flatte 4: rho-omega mxing for omega
  double R[4], s[3], sp2, B[2];
  double tmp;
  for ( int i = 0; i < 4; i++ ) { R[i] = P1[i] + P2[i]; }
  s[0] = dot( R, R );
  s[1] = dot( P1, P1 );
  s[2] = dot( P2, P2 );
  sp2  = dot( P3, P3 );
 
  EvtComplex amp, prop, prop1, prop2;
 
  //-----------for prop-------------------------
  EvtComplex rhokk, rhopieta;
  if ( spin == 0 )
  {
    if ( flag == 0 ) prop = one;
    if ( flag == 1 ) prop = propagatorRBW( mass_R, width_R, s[0], s[1], s[2], 3.0, 0 );
    if ( flag == 3 )
    {
      rhokk    = Flatte_rhoab( s[0], snk, sck );
      rhopieta = Flatte_rhoab( s[0], scpi, seta );
      prop =
          1.0 / ( mass_R * mass_R - s[0] - ci * ( 0.341 * rhopieta + 0.341 * 0.892 * rhokk ) );
    }
    amp = prop;
  }
  else if ( spin == 1 )
  {
    if ( flag == 0 ) { prop = EvtComplex( 1.0, 0.0 ); }
    if ( flag == 1 ) { prop = propagatorRBW( mass_R, width_R, s[0], s[1], s[2], 3.0, 1 ); }
    if ( flag == 2 ) { prop = propagatorGS( mass_R, width_R, s[0], s[1], s[2], 3.0, 1 ); }
    if ( flag == 4 )
    {
      prop1 = propagatorGS( mass_R, width_R, s[0], s[1], s[2], 3.0, 1 );
      prop2 = propagatorRBW( 0.78266, 0.01358, s[0], s[1], s[2], 3.0, 1 );
      prop  = prop1 * prop2;
    }
    double T1[4], t1[4];
    calt1( R, P3, T1 );
    calt1( P1, P2, t1 );
    B[0] = barrier( 1, s[0], s[1], s[2], 3.0, mass_R );
    B[1] = barrier( 1, sD, s[0], sp2, 5.0, mD );
    tmp  = 0.0;
    for ( int i = 0; i < 4; i++ ) { tmp += T1[i] * t1[i] * G[i][i]; }
    amp = tmp * prop * B[0] * B[1];
  }
  else if ( spin == 2 )
  {
    double T2[4][4], t2[4][4];
    calt2( R, P3, T2 );
    calt2( P1, P2, t2 );
    B[0] = barrier( 2, s[0], s[1], s[2], 3.0, mass_R );
    B[1] = barrier( 2, sD, s[0], sp2, 5.0, mD );
    tmp  = 0.0;
    for ( int i = 0; i < 4; i++ )
    {
      for ( int j = 0; j < 4; j++ ) { tmp += T2[i][j] * t2[j][i] * G[j][j] * G[i][i]; }
    }
    if ( flag == 0 ) prop = one;
    if ( flag == 1 ) prop = propagatorRBW( mass_R, width_R, s[0], s[1], s[2], 3.0, 2 );
    amp = tmp * prop * B[0] * B[1];
  }
  else { cout << "Only S, P, D wave allowed" << endl; }
  return amp;
}
 
double EvtD0TopipiEta::dot( double* a1, double* a2 ) {
  double Dot = 0;
  for ( int i = 0; i != 4; i++ ) { Dot += a1[i] * a2[i] * G[i][i]; }
  return Dot;
}
 
double EvtD0TopipiEta::Qabcs( double sa, double sb, double sc ) {
  double Qabcs = ( sa + sb - sc ) * ( sa + sb - sc ) / ( 4 * sa ) - sb;
  if ( Qabcs < 0 ) Qabcs = 1e-16;
  return Qabcs;
}
 
double EvtD0TopipiEta::barrier( double l, double sa, double sb, double sc, double r,
                                double mass ) {
  double sa0 = mass * mass;
  double q0  = Qabcs( sa0, sb, sc );
  double z0  = q0 * r * r;
  double q   = Qabcs( sa, sb, sc );
  q          = sqrt( q );
  double z   = q * r;
  z          = z * z;
  double F   = 1;
  if ( l > 2 ) F = 0;
  if ( l == 0 ) F = 1;
  if ( l == 1 ) F = sqrt( ( 1 + z0 ) / ( 1 + z ) );
  if ( l == 2 ) F = sqrt( ( 9 + 3 * z0 + z0 * z0 ) / ( 9 + 3 * z + z * z ) );
  return F;
}
 
void EvtD0TopipiEta::calt1( double daug1[], double daug2[], double t1[] ) {
  double p, pq;
  double pa[4], qa[4];
  for ( int i = 0; i != 4; i++ )
  {
    pa[i] = daug1[i] + daug2[i];
    qa[i] = daug1[i] - daug2[i];
  }
  p  = dot( pa, pa );
  pq = dot( pa, qa );
  for ( int i = 0; i != 4; i++ ) { t1[i] = qa[i] - pq / p * pa[i]; }
}
 
void EvtD0TopipiEta::calt2( double daug1[], double daug2[], double t2[][4] ) {
  double p, r;
  double pa[4], t1[4];
  calt1( daug1, daug2, t1 );
  r = dot( t1, t1 );
  for ( int i = 0; i != 4; i++ ) { pa[i] = daug1[i] + daug2[i]; }
  p = dot( pa, pa );
  for ( int i = 0; i != 4; i++ )
  {
    for ( int j = 0; j != 4; j++ )
    { t2[i][j] = t1[i] * t1[j] - 1.0 / 3 * r * ( G[i][j] - pa[i] * pa[j] / p ); }
  }
}
 
double EvtD0TopipiEta::wid( double mass, double sa, double sb, double sc, double r, int l ) {
  double widm( 0. ), q( 0. ), q0( 0. );
  double sa0 = mass * mass;
  double m   = sqrt( sa );
  q          = Qabcs( sa, sb, sc );
  q0         = Qabcs( sa0, sb, sc );
  double z, z0;
  z        = q * r * r;
  z0       = q0 * r * r;
  double t = q / q0;
  double F( 0. );
  if ( l == 0 ) F = 1;
  if ( l == 1 ) F = sqrt( ( 1 + z0 ) / ( 1 + z ) );
  if ( l == 2 ) F = sqrt( ( 9 + 3 * z0 + z0 * z0 ) / ( 9 + 3 * z + z * z ) );
  widm = pow( t, l + 0.5 ) * mass / m * F * F;
  return widm;
}
 
EvtComplex EvtD0TopipiEta::propagatorRBW( double mass, double width, double sa, double sb,
                                          double sc, double r, int l ) {
  EvtComplex prop =
      1.0 / ( mass * mass - sa - ci * mass * width * wid( mass, sa, sb, sc, r, l ) );
  return prop;
}
 
double EvtD0TopipiEta::h( double m, double q ) {
  double h( 0. );
  h = 2 / pi * q / m * log( ( m + 2 * q ) / ( 2 * mpi ) );
  return h;
}
 
double EvtD0TopipiEta::dh( double mass, double q0 ) {
  double dh = h( mass, q0 ) * ( 1.0 / ( 8 * q0 * q0 ) - 1.0 / ( 2 * mass * mass ) ) +
              1.0 / ( 2 * pi * mass * mass );
  return dh;
}
 
double EvtD0TopipiEta::f( double mass, double sx, double q0, double q ) {
  double m = sqrt( sx );
  double f = mass * mass / ( pow( q0, 3 ) ) *
             ( q * q * ( h( m, q ) - h( mass, q0 ) ) +
               ( mass * mass - sx ) * q0 * q0 * dh( mass, q0 ) );
  return f;
}
 
double EvtD0TopipiEta::d( double mass, double q0 ) {
  double d = 3.0 / pi * spi / ( q0 * q0 ) * log( ( mass + 2 * q0 ) / ( 2 * mpi ) ) +
             mass / ( 2 * pi * q0 ) - ( spi * mass ) / ( pi * pow( q0, 3 ) );
  return d;
}
 
EvtComplex EvtD0TopipiEta::propagatorGS( double mass, double width, double sa, double sb,
                                         double sc, double r, int l ) {
  double q        = Qabcs( sa, sb, sc );
  double sa0      = mass * mass;
  double q0       = Qabcs( sa0, sb, sc );
  q               = sqrt( q );
  q0              = sqrt( q0 );
  EvtComplex prop = ( 1 + d( mass, q0 ) * width / mass ) /
                    ( mass * mass - sa + width * f( mass, sa, q0, q ) -
                      ci * mass * width * wid( mass, sa, sb, sc, r, l ) );
  return prop;
}
 
EvtComplex EvtD0TopipiEta::Flatte_rhoab( double sa, double sb, double sc ) {
  double     q = ( sa + sb - sc ) * ( sa + sb - sc ) / ( 4 * sa ) - sb;
  EvtComplex rho;
  if ( q > 0 ) { rho = 2.0 * sqrt( q / sa ) * one; }
  if ( q < 0 ) { rho = 2.0 * sqrt( -q / sa ) * ci; }
  return rho;
}
 
EvtComplex EvtD0TopipiEta::propagatorFlatte( double mass, double width, double sx, double* sb,
                                             double* sc ) {
  const double g1sq = 0.5468 * 0.5468;
  const double g2sq = 0.23 * 0.23;
  EvtComplex   rho1 = Flatte_rhoab( sx, sb[0], sc[0] );
  EvtComplex   rho2 = Flatte_rhoab( sx, sb[1], sc[1] );
  EvtComplex   prop = 1.0 / ( mass * mass - sx - ci * ( g1sq * rho1 + g2sq * rho2 ) );
  return prop;
}