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 "EvtGenBase/EvtPatches.hh"
#include "EvtGenBase/EvtParticle.hh"
#include "EvtGenBase/EvtGenKine.hh"
#include "EvtGenBase/EvtPDL.hh"
#include "EvtGenBase/EvtReport.hh"
#include "EvtGenBase/EvtVector4R.hh"
#include "EvtGenBase/EvtComplex.hh"
#include "EvtGenModels/EvtD0TopipiEta.hh"
#include "EvtGenBase/EvtDecayTable.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;
}