EvtPto3PAmp.cc

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#include "EvtGenBase/EvtPatches.hh"
/*******************************************************************************
 * Project: BaBar detector at the SLAC PEP-II B-factory
 * Package: EvtGenBase
 *    File: $Id: EvtPto3PAmp.cc,v 1.1.1.2 2007/10/26 05:03:14 pingrg Exp $
 *  Author: Alexei Dvoretskii, [email protected], 2001-2002
 *
 * Copyright (C) 2002 Caltech
 *******************************************************************************/
 
#include <assert.h>
#include <math.h>
#include <iostream>
#include "EvtGenBase/EvtComplex.hh"
#include "EvtGenBase/EvtPto3PAmp.hh"
#include "EvtGenBase/EvtDalitzCoord.hh"
#include "EvtGenBase/EvtdFunction.hh"
#include "EvtGenBase/EvtCyclic3.hh"
using std::endl;
using EvtCyclic3::Index;
using EvtCyclic3::Pair;
 
 
EvtPto3PAmp::EvtPto3PAmp(EvtDalitzPlot dp, Pair pairAng, Pair pairRes, 
             EvtSpinType::spintype spin, 
             const EvtPropagator& prop, NumType typeN) 
  : EvtAmplitude<EvtDalitzPoint>(),
  _pairAng(pairAng), _pairRes(pairRes),
  _spin(spin),
  _typeN(typeN),
  _prop((EvtPropagator*) prop.clone()), 
  _g0(prop.g0()),
  _vb(prop.m0(),dp.m(EvtCyclic3::other(pairRes)),dp.bigM(),spin), 
  _vd(dp.m(EvtCyclic3::first(pairRes)),dp.m(EvtCyclic3::second(pairRes)),prop.m0(),spin)
{}
 
 
 
EvtPto3PAmp::EvtPto3PAmp(const EvtPto3PAmp& other) 
  : EvtAmplitude<EvtDalitzPoint>(other),
  _pairAng(other._pairAng),
  _pairRes(other._pairRes),
  _spin(other._spin),
  _typeN(other._typeN),
  _prop( (other._prop) ? (EvtPropagator*) other._prop->clone() : 0),
  _g0(other._g0),
  _vb(other._vb), _vd(other._vd)
{}
 
 
EvtPto3PAmp::~EvtPto3PAmp()
{
  if(_prop) delete _prop;
}
 
 
void EvtPto3PAmp::set_fd(double R)
{
  _vd.set_f(R);
}
 
void EvtPto3PAmp::set_fb(double R)
{
  _vb.set_f(R);
}
 
 
EvtComplex EvtPto3PAmp::amplitude(const EvtDalitzPoint& x) const
{
  EvtComplex amp(1.0,0.0);
 
  double m = sqrt(x.q(_pairRes));
  EvtTwoBodyKine vd(x.m(EvtCyclic3::first(_pairRes)),
            x.m(EvtCyclic3::second(_pairRes)),m);
  EvtTwoBodyKine vb(m,x.m(EvtCyclic3::other(_pairRes)),x.bigM());
 
 
  // Compute mass-dependent width for relativistic propagators
 
  if(_typeN != NBW) {
    
    _prop->set_g0(_g0*_vd.widthFactor(vd));
  }
  
  // Compute propagator
 
  amp *= _prop->evaluate(m);
 
  // Compute form-factors
 
  amp *= _vd.formFactor(vd);
  amp *= _vb.formFactor(vb);
 
  amp *= numerator(x);
  
  return amp;
}
 
 
EvtComplex EvtPto3PAmp::numerator(const EvtDalitzPoint& x) const
{
  EvtComplex ret(0.,0.);
  double m = sqrt(x.q(_pairRes)); 
  EvtTwoBodyKine vd(x.m(EvtCyclic3::first(_pairRes)),
            x.m(EvtCyclic3::second(_pairRes)),m);
  EvtTwoBodyKine vb(m,x.m(EvtCyclic3::other(_pairRes)),x.bigM());
 
  // Non-relativistic Breit-Wigner
 
  if(NBW == _typeN) {
 
    ret = angDep(x);
  }
 
  // Standard relativistic Zemach propagator
 
  else if(RBW_ZEMACH == _typeN) {
 
    ret = _vd.phaseSpaceFactor(vd,EvtTwoBodyKine::AB)*angDep(x);
  }
    
  // Kuehn-Santamaria normalization:
  
  else if(RBW_KUEHN == _typeN) {
 
    ret = _prop->m0()*_prop->m0() * angDep(x);
  }
 
 
  // CLEO amplitude is not factorizable
  //
  // The CLEO amplitude numerator is proportional to:
  //
  // m2_AC - m2_BC + (m2_D - m2_C)(m2_B - m2_A)/m2_0
  //
  // m2_AC = (eA + eC)^2 + (P - P_C cosTh(BC))^2
  // m2_BC = (eB + eC)^2 + (P + P_C cosTh(BC))^2
  //
  // The first term m2_AB-m2_BC is therefore a p-wave term
  // - 4PP_C cosTh(BC) 
  // The second term is an s-wave, the amplitude
  // does not factorize!
  //
  // The first term is just Zemach. However, the sign is flipped! 
  // Let's consistently use the convention in which the amplitude
  // is proportional to +cosTh(BC). In the CLEO expressions, I will
  // therefore exchange AB to get rid of the sign flip.
  
 
  if(RBW_CLEO == _typeN) {
 
    Index iA = other(_pairAng);           // A = other(BC)
    Index iB = common(_pairRes,_pairAng); // B = common(AB,BC)
    Index iC = other(_pairRes);           // C = other(AB)
    
    double M = x.bigM();
    double mA = x.m(iA);
    double mB = x.m(iB);
    double mC = x.m(iC);
    double qAB = x.q(combine(iA,iB));
    double qBC = x.q(combine(iB,iC));
    double qCA = x.q(combine(iC,iA));
    
    double m0 = _prop->m0();
 
    if(_spin == EvtSpinType::SCALAR) ret = EvtComplex(1.,0.);
    else
      if(_spin == EvtSpinType::VECTOR) {
    
    ret = qBC - qCA + (M*M - mC*mC)*(mA*mA - mB*mB)/m0/m0;;
      }
      else
    if(_spin == EvtSpinType::TENSOR) {
      
      double x1 = qBC - qCA + (M*M - mC*mC)*(mA*mA - mB*mB)/m0/m0;       
      double x2 = M*M - mC*mC;      
      double x3 = qAB - 2*M*M - 2*mC*mC + x2*x2/m0/m0;      
      double x4 = mB*mB - mA*mA;
      double x5 = qAB - 2*mB*mB - 2*mA*mA + x4*x4/m0/m0;
      ret = (x1*x1 - 1./3.*x3*x5);
    }
    else assert(0);
  }
 
  return ret;
}
 
 
double EvtPto3PAmp::angDep(const EvtDalitzPoint& x) const 
{ 
  // Angular dependece for factorizable amplitudes  
  // unphysical cosines indicate we are in big trouble
 
  double cosTh = x.cosTh(_pairAng,_pairRes);  
  if(fabs(cosTh) > 1.) {
    
    report(INFO,"EvtGen") << "cosTh " << cosTh << endl; 
    assert(0);
  }
  
  // in units of half-spin
  
  return EvtdFunction::d(EvtSpinType::getSpin2(_spin),2*0,2*0,acos(cosTh));
}