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EvtDalitzReso.cpp
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EvtDalitzReso.cpp
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/***********************************************************************
* Copyright 1998-2020 CERN for the benefit of the EvtGen authors *
* *
* This file is part of EvtGen. *
* *
* EvtGen is free software: you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation, either version 3 of the License, or *
* (at your option) any later version. *
* *
* EvtGen is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with EvtGen. If not, see <https://www.gnu.org/licenses/>. *
***********************************************************************/
#include "EvtGenBase/EvtDalitzReso.hh"
#include "EvtGenBase/EvtCyclic3.hh"
#include "EvtGenBase/EvtGenKine.hh"
#include "EvtGenBase/EvtMatrix.hh"
#include "EvtGenBase/EvtPDL.hh"
#include "EvtGenBase/EvtParticle.hh"
#include "EvtGenBase/EvtPatches.hh"
#include "EvtGenBase/EvtReport.hh"
#include "EvtGenBase/EvtdFunction.hh"
#include <assert.h>
#include <cmath>
#include <iostream>
#include <stdlib.h>
#define PRECISION ( 1.e-3 )
using EvtCyclic3::Index;
using EvtCyclic3::Pair;
// single Breit-Wigner
EvtDalitzReso::EvtDalitzReso( const EvtDalitzPlot& dp, Pair pairAng, Pair pairRes,
EvtSpinType::spintype spin, double m0, double g0,
NumType typeN, double f_b, double f_d ) :
_dp( dp ),
_pairAng( pairAng ),
_pairRes( pairRes ),
_spin( spin ),
_typeN( typeN ),
_m0( m0 ),
_g0( g0 ),
_massFirst( dp.m( first( pairRes ) ) ),
_massSecond( dp.m( second( pairRes ) ) ),
_m0_mix( -1. ),
_g0_mix( 0. ),
_delta_mix( 0. ),
_amp_mix( 0., 0. ),
_g1( -1. ),
_g2( -1. ),
_coupling2( Undefined ),
_f_b( f_b ),
_f_d( f_d ),
_kmatrix_index( -1 ),
_fr12prod( 0., 0. ),
_fr13prod( 0., 0. ),
_fr14prod( 0., 0. ),
_fr15prod( 0., 0. ),
_s0prod( 0. ),
_a( 0. ),
_r( 0. ),
_Blass( 0. ),
_phiB( 0. ),
_R( 0. ),
_phiR( 0. ),
_cutoff( -1. ),
_scaleByMOverQ( false ),
_alpha( 0. )
{
_vb = EvtTwoBodyVertex( _m0, _dp.m( EvtCyclic3::other( _pairRes ) ),
_dp.bigM(), _spin );
_vd = EvtTwoBodyVertex( _massFirst, _massSecond, _m0, _spin );
_vb.set_f( _f_b ); // Default values for Blatt-Weisskopf factors are 0.0 and 1.5.
_vd.set_f( _f_d );
assert( _typeN != K_MATRIX && _typeN != K_MATRIX_I &&
_typeN != K_MATRIX_II ); // single BW cannot be K-matrix
}
// Breit-Wigner with electromagnetic mass mixing
EvtDalitzReso::EvtDalitzReso( const EvtDalitzPlot& dp, Pair pairAng, Pair pairRes,
EvtSpinType::spintype spin, double m0, double g0,
NumType typeN, double m0_mix, double g0_mix,
double delta_mix, EvtComplex amp_mix ) :
_dp( dp ),
_pairAng( pairAng ),
_pairRes( pairRes ),
_spin( spin ),
_typeN( typeN ),
_m0( m0 ),
_g0( g0 ),
_massFirst( dp.m( first( pairRes ) ) ),
_massSecond( dp.m( second( pairRes ) ) ),
_m0_mix( m0_mix ),
_g0_mix( g0_mix ),
_delta_mix( delta_mix ),
_amp_mix( amp_mix ),
_g1( -1. ),
_g2( -1. ),
_coupling2( Undefined ),
_f_b( 0.0 ),
_f_d( 1.5 ),
_kmatrix_index( -1 ),
_fr12prod( 0., 0. ),
_fr13prod( 0., 0. ),
_fr14prod( 0., 0. ),
_fr15prod( 0., 0. ),
_s0prod( 0. ),
_a( 0. ),
_r( 0. ),
_Blass( 0. ),
_phiB( 0. ),
_R( 0. ),
_phiR( 0. ),
_cutoff( -1. ),
_scaleByMOverQ( false ),
_alpha( 0. )
{
_vb = EvtTwoBodyVertex( _m0, _dp.m( EvtCyclic3::other( _pairRes ) ),
_dp.bigM(), _spin );
_vd = EvtTwoBodyVertex( _massFirst, _massSecond, _m0, _spin );
_vb.set_f( 0.0 ); // Default values for Blatt-Weisskopf factors.
_vd.set_f( 1.5 );
// single BW (with electromagnetic mixing) cannot be K-matrix
assert( _typeN != K_MATRIX && _typeN != K_MATRIX_I && _typeN != K_MATRIX_II );
}
// coupled Breit-Wigner
EvtDalitzReso::EvtDalitzReso( const EvtDalitzPlot& dp, Pair pairAng,
Pair pairRes, EvtSpinType::spintype spin,
double m0, NumType typeN, double g1, double g2,
CouplingType coupling2 ) :
_dp( dp ),
_pairAng( pairAng ),
_pairRes( pairRes ),
_spin( spin ),
_typeN( typeN ),
_m0( m0 ),
_g0( -1. ),
_massFirst( dp.m( first( pairRes ) ) ),
_massSecond( dp.m( second( pairRes ) ) ),
_m0_mix( -1. ),
_g0_mix( 0. ),
_delta_mix( 0. ),
_amp_mix( 0., 0. ),
_g1( g1 ),
_g2( g2 ),
_coupling2( coupling2 ),
_f_b( 0.0 ),
_f_d( 1.5 ),
_kmatrix_index( -1 ),
_fr12prod( 0., 0. ),
_fr13prod( 0., 0. ),
_fr14prod( 0., 0. ),
_fr15prod( 0., 0. ),
_s0prod( 0. ),
_a( 0. ),
_r( 0. ),
_Blass( 0. ),
_phiB( 0. ),
_R( 0. ),
_phiR( 0. ),
_cutoff( -1. ),
_scaleByMOverQ( false ),
_alpha( 0. )
{
_vb = EvtTwoBodyVertex( _m0, _dp.m( EvtCyclic3::other( _pairRes ) ),
_dp.bigM(), _spin );
_vd = EvtTwoBodyVertex( _massFirst, _massSecond, _m0, _spin );
_vb.set_f( 0.0 ); // Default values for Blatt-Weisskopf factors.
_vd.set_f( 1.5 );
assert( _coupling2 != Undefined );
assert( _typeN != K_MATRIX && _typeN != K_MATRIX_I &&
_typeN != K_MATRIX_II ); // coupled BW cannot be K-matrix
assert( _typeN != LASS ); // coupled BW cannot be LASS
assert( _typeN != NBW ); // for coupled BW, only relativistic BW
}
// K-Matrix (A&S)
EvtDalitzReso::EvtDalitzReso( const EvtDalitzPlot& dp, Pair pairRes,
std::string nameIndex, NumType typeN,
EvtComplex fr12prod, EvtComplex fr13prod,
EvtComplex fr14prod, EvtComplex fr15prod,
double s0prod ) :
_dp( dp ),
_pairRes( pairRes ),
_typeN( typeN ),
_m0( 0. ),
_g0( 0. ),
_massFirst( dp.m( first( pairRes ) ) ),
_massSecond( dp.m( second( pairRes ) ) ),
_m0_mix( -1. ),
_g0_mix( 0. ),
_delta_mix( 0. ),
_amp_mix( 0., 0. ),
_g1( -1. ),
_g2( -1. ),
_coupling2( Undefined ),
_f_b( 0. ),
_f_d( 0. ),
_kmatrix_index( -1 ),
_fr12prod( fr12prod ),
_fr13prod( fr13prod ),
_fr14prod( fr14prod ),
_fr15prod( fr15prod ),
_s0prod( s0prod ),
_a( 0. ),
_r( 0. ),
_Blass( 0. ),
_phiB( 0. ),
_R( 0. ),
_phiR( 0. ),
_cutoff( -1. ),
_scaleByMOverQ( false ),
_alpha( 0. )
{
assert( _typeN == K_MATRIX || _typeN == K_MATRIX_I || _typeN == K_MATRIX_II );
_spin = EvtSpinType::SCALAR;
if ( nameIndex == "Pole1" )
_kmatrix_index = 1;
else if ( nameIndex == "Pole2" )
_kmatrix_index = 2;
else if ( nameIndex == "Pole3" )
_kmatrix_index = 3;
else if ( nameIndex == "Pole4" )
_kmatrix_index = 4;
else if ( nameIndex == "Pole5" )
_kmatrix_index = 5;
else if ( nameIndex == "f11prod" )
_kmatrix_index = 6;
else
assert( 0 );
}
// LASS parameterization
EvtDalitzReso::EvtDalitzReso( const EvtDalitzPlot& dp, Pair pairRes, double m0,
double g0, double a, double r, double B,
double phiB, double R, double phiR, double cutoff,
bool scaleByMOverQ ) :
_dp( dp ),
_pairRes( pairRes ),
_typeN( LASS ),
_m0( m0 ),
_g0( g0 ),
_massFirst( dp.m( first( pairRes ) ) ),
_massSecond( dp.m( second( pairRes ) ) ),
_m0_mix( -1. ),
_g0_mix( 0. ),
_delta_mix( 0. ),
_amp_mix( 0., 0. ),
_g1( -1. ),
_g2( -1. ),
_coupling2( Undefined ),
_f_b( 0.0 ),
_f_d( 1.5 ),
_kmatrix_index( -1 ),
_fr12prod( 0., 0. ),
_fr13prod( 0., 0. ),
_fr14prod( 0., 0. ),
_fr15prod( 0., 0. ),
_s0prod( 0. ),
_a( a ),
_r( r ),
_Blass( B ),
_phiB( phiB ),
_R( R ),
_phiR( phiR ),
_cutoff( cutoff ),
_scaleByMOverQ( scaleByMOverQ ),
_alpha( 0. )
{
_spin = EvtSpinType::SCALAR;
_vd = EvtTwoBodyVertex( _massFirst, _massSecond, _m0, _spin );
_vd.set_f( 1.5 ); // Default values for Blatt-Weisskopf factors.
}
//Flatte
EvtDalitzReso::EvtDalitzReso( const EvtDalitzPlot& dp, EvtCyclic3::Pair pairRes,
double m0 ) :
_dp( dp ),
_pairRes( pairRes ),
_typeN( FLATTE ),
_m0( m0 ),
_g0( 0. ),
_massFirst( dp.m( first( pairRes ) ) ),
_massSecond( dp.m( second( pairRes ) ) ),
_m0_mix( -1. ),
_g0_mix( 0. ),
_delta_mix( 0. ),
_amp_mix( 0., 0. ),
_g1( -1. ),
_g2( -1. ),
_coupling2( Undefined ),
_f_b( 0. ),
_f_d( 0. ),
_kmatrix_index( -1 ),
_fr12prod( 0., 0. ),
_fr13prod( 0., 0. ),
_fr14prod( 0., 0. ),
_fr15prod( 0., 0. ),
_s0prod( 0. ),
_a( 0. ),
_r( 0. ),
_Blass( 0. ),
_phiB( 0. ),
_R( 0. ),
_phiR( 0. ),
_cutoff( -1. ),
_scaleByMOverQ( false ),
_alpha( 0. )
{
_spin = EvtSpinType::SCALAR;
}
EvtComplex EvtDalitzReso::evaluate( const EvtDalitzPoint& x )
{
double m = sqrt( x.q( _pairRes ) );
if ( _typeN == NON_RES )
return EvtComplex( 1.0, 0.0 );
if ( _typeN == NON_RES_LIN )
return m * m;
if ( _typeN == NON_RES_EXP )
return exp( -_alpha * m * m );
// do use always hash table (speed up fitting)
if ( _typeN == K_MATRIX || _typeN == K_MATRIX_I || _typeN == K_MATRIX_II )
return Fvector( m * m, _kmatrix_index );
if ( _typeN == LASS )
return lass( m * m );
if ( _typeN == FLATTE )
return flatte( m );
EvtComplex amp( 1.0, 0.0 );
if ( fabs( _dp.bigM() - x.bigM() ) > 0.000001 ) {
_vb = EvtTwoBodyVertex( _m0, _dp.m( EvtCyclic3::other( _pairRes ) ),
x.bigM(), _spin );
_vb.set_f( _f_b );
}
EvtTwoBodyKine vb( m, x.m( EvtCyclic3::other( _pairRes ) ), x.bigM() );
EvtTwoBodyKine vd( _massFirst, _massSecond, m );
EvtComplex prop( 0, 0 );
if ( _typeN == NBW ) {
prop = propBreitWigner( _m0, _g0, m );
} else if ( _typeN == GAUSS_CLEO || _typeN == GAUSS_CLEO_ZEMACH ) {
prop = propGauss( _m0, _g0, m );
} else {
if ( _coupling2 == Undefined ) {
// single BW
double g = ( _g0 <= 0. || _vd.pD() <= 0. )
? -_g0
: _g0 * _vd.widthFactor( vd ); // running width
if ( _typeN == GS_CLEO || _typeN == GS_CLEO_ZEMACH ) {
// Gounaris-Sakurai (GS)
prop = propGounarisSakurai( _m0, fabs( _g0 ), _vd.pD(), m, g,
vd.p() );
} else {
// standard relativistic BW
prop = propBreitWignerRel( _m0, g, m );
}
} else {
// coupled width BW
EvtComplex G1, G2;
switch ( _coupling2 ) {
case PicPic: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mPic = EvtPDL::getMass( EvtPDL::getId( "pi+" ) );
G2 = _g2 * _g2 * psFactor( mPic, mPic, m );
break;
}
case PizPiz: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mPiz = EvtPDL::getMass( EvtPDL::getId( "pi0" ) );
G2 = _g2 * _g2 * psFactor( mPiz, mPiz, m );
break;
}
case PiPi: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mPic = EvtPDL::getMass( EvtPDL::getId( "pi+" ) );
static double mPiz = EvtPDL::getMass( EvtPDL::getId( "pi0" ) );
G2 = _g2 * _g2 * psFactor( mPic, mPic, mPiz, mPiz, m );
break;
}
case KcKc: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mKc = EvtPDL::getMass( EvtPDL::getId( "K+" ) );
G2 = _g2 * _g2 * psFactor( mKc, mKc, m );
break;
}
case KzKz: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mKz = EvtPDL::getMass( EvtPDL::getId( "K0" ) );
G2 = _g2 * _g2 * psFactor( mKz, mKz, m );
break;
}
case KK: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mKc = EvtPDL::getMass( EvtPDL::getId( "K+" ) );
static double mKz = EvtPDL::getMass( EvtPDL::getId( "K0" ) );
G2 = _g2 * _g2 * psFactor( mKc, mKc, mKz, mKz, m );
break;
}
case EtaPic: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mEta = EvtPDL::getMass( EvtPDL::getId( "eta" ) );
static double mPic = EvtPDL::getMass( EvtPDL::getId( "pi+" ) );
G2 = _g2 * _g2 * psFactor( mEta, mPic, m );
break;
}
case EtaPiz: {
G1 = _g1 * _g1 * psFactor( _massFirst, _massSecond, m );
static double mEta = EvtPDL::getMass( EvtPDL::getId( "eta" ) );
static double mPiz = EvtPDL::getMass( EvtPDL::getId( "pi0" ) );
G2 = _g2 * _g2 * psFactor( mEta, mPiz, m );
break;
}
case PicPicKK: {
static double mPic = EvtPDL::getMass( EvtPDL::getId( "pi+" ) );
//G1 = _g1*_g1*psFactor(mPic,mPic,m);
G1 = _g1 * psFactor( mPic, mPic, m );
static double mKc = EvtPDL::getMass( EvtPDL::getId( "K+" ) );
static double mKz = EvtPDL::getMass( EvtPDL::getId( "K0" ) );
//G2 = _g2*_g2*psFactor(mKc,mKc,mKz,mKz,m);
G2 = _g2 * psFactor( mKc, mKc, mKz, mKz, m );
break;
}
default:
std::cout
<< "EvtDalitzReso:evaluate(): PANIC, wrong coupling2 state."
<< std::endl;
assert( 0 );
break;
}
// calculate standard couple BW propagator
if ( _coupling2 != WA76 )
prop = _g1 * propBreitWignerRelCoupled( _m0, G1, G2, m );
}
}
amp *= prop;
// Compute form-factors (Blatt-Weisskopf penetration factor)
amp *= _vb.formFactor( vb );
amp *= _vd.formFactor( vd );
// Compute numerator (angular distribution)
amp *= numerator( x, vb, vd );
// Compute electromagnetic mass mixing factor
if ( _m0_mix > 0. ) {
EvtComplex prop_mix;
if ( _typeN == NBW ) {
prop_mix = propBreitWigner( _m0_mix, _g0_mix, m );
} else {
assert( _g1 < 0. ); // running width only
double g_mix = _g0_mix * _vd.widthFactor( vd );
prop_mix = propBreitWignerRel( _m0_mix, g_mix, m );
}
amp *= mixFactor( prop, prop_mix );
}
return amp;
}
EvtComplex EvtDalitzReso::psFactor( double& ma, double& mb, double& m )
{
if ( m > ( ma + mb ) ) {
EvtTwoBodyKine vd( ma, mb, m );
return EvtComplex( 0, 2 * vd.p() / m );
} else {
// analytical continuation
double s = m * m;
double phaseFactor_analyticalCont =
-0.5 * ( sqrt( 4 * ma * ma / s - 1 ) + sqrt( 4 * mb * mb / s - 1 ) );
return EvtComplex( phaseFactor_analyticalCont, 0 );
}
}
EvtComplex EvtDalitzReso::psFactor( double& ma1, double& mb1, double& ma2,
double& mb2, double& m )
{
return 0.5 * ( psFactor( ma1, mb1, m ) + psFactor( ma2, mb2, m ) );
}
EvtComplex EvtDalitzReso::propGauss( const double& m0, const double& s0,
const double& m )
{
// Gaussian
double gauss = 1. / sqrt( EvtConst::twoPi ) / s0 *
exp( -( m - m0 ) * ( m - m0 ) / 2. / ( s0 * s0 ) );
return EvtComplex( gauss, 0. );
}
EvtComplex EvtDalitzReso::propBreitWigner( const double& m0, const double& g0,
const double& m )
{
// non-relativistic BW
return sqrt( g0 / EvtConst::twoPi ) / ( m - m0 - EvtComplex( 0.0, g0 / 2. ) );
}
EvtComplex EvtDalitzReso::propBreitWignerRel( const double& m0,
const double& g0, const double& m )
{
// relativistic BW with real width
return 1. / ( m0 * m0 - m * m - EvtComplex( 0., m0 * g0 ) );
}
EvtComplex EvtDalitzReso::propBreitWignerRel( const double& m0,
const EvtComplex& g0,
const double& m )
{
// relativistic BW with complex width
return 1. / ( m0 * m0 - m * m - EvtComplex( 0., m0 ) * g0 );
}
EvtComplex EvtDalitzReso::propBreitWignerRelCoupled( const double& m0,
const EvtComplex& g1,
const EvtComplex& g2,
const double& m )
{
// relativistic coupled BW
return 1. / ( m0 * m0 - m * m - ( g1 + g2 ) );
}
EvtComplex EvtDalitzReso::propGounarisSakurai( const double& m0, const double& g0,
const double& k0, const double& m,
const double& g, const double& k )
{
// Gounaris-Sakurai parameterization of pi+pi- P wave. PRD, Vol61, 112002. PRL, Vol21, 244.
// Expressions taken from BAD637v4, after fixing the imaginary part of the BW denominator: i M_R Gamma_R(s) --> i sqrt(s) Gamma_R(s)
return ( 1. + GS_d( m0, k0 ) * g0 / m0 ) /
( m0 * m0 - m * m - EvtComplex( 0., m * g ) +
GS_f( m0, g0, k0, m, k ) );
}
inline double EvtDalitzReso::GS_f( const double& m0, const double& g0,
const double& k0, const double& m,
const double& k )
{
// m: sqrt(s)
// m0: nominal resonance mass
// k: momentum of pion in resonance rest frame (at m)
// k0: momentum of pion in resonance rest frame (at nominal resonance mass)
return g0 * m0 * m0 / ( k0 * k0 * k0 ) *
( k * k * ( GS_h( m, k ) - GS_h( m0, k0 ) ) +
( m0 * m0 - m * m ) * k0 * k0 * GS_dhods( m0, k0 ) );
}
inline double EvtDalitzReso::GS_h( const double& m, const double& k )
{
return 2. / EvtConst::pi * k / m *
log( ( m + 2. * k ) / ( 2. * _massFirst ) );
}
inline double EvtDalitzReso::GS_dhods( const double& m0, const double& k0 )
{
return GS_h( m0, k0 ) * ( 0.125 / ( k0 * k0 ) - 0.5 / ( m0 * m0 ) ) +
0.5 / ( EvtConst::pi * m0 * m0 );
}
inline double EvtDalitzReso::GS_d( const double& m0, const double& k0 )
{
return 3. / EvtConst::pi * _massFirst * _massFirst / ( k0 * k0 ) *
log( ( m0 + 2. * k0 ) / ( 2. * _massFirst ) ) +
m0 / ( 2. * EvtConst::pi * k0 ) -
_massFirst * _massFirst * m0 / ( EvtConst::pi * k0 * k0 * k0 );
}
EvtComplex EvtDalitzReso::numerator( const EvtDalitzPoint& x,
const EvtTwoBodyKine& vb,
const EvtTwoBodyKine& vd )
{
EvtComplex ret( 0., 0. );
// 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 );
}
// Standard relativistic Zemach propagator
else if ( RBW_ZEMACH2 == _typeN ) {
ret = _vd.phaseSpaceFactor( vd, EvtTwoBodyKine::AB ) *
_vb.phaseSpaceFactor( vb, EvtTwoBodyKine::AB ) * angDep( x );
if ( _spin == EvtSpinType::VECTOR ) {
ret *= -4.;
} else if ( _spin == EvtSpinType::TENSOR ) {
ret *= 16. / 3.;
} else if ( _spin != EvtSpinType::SCALAR )
assert( 0 );
}
// Kuehn-Santamaria normalization:
else if ( RBW_KUEHN == _typeN ) {
ret = _m0 * _m0 * angDep( x );
}
// CLEO amplitude
else if ( ( RBW_CLEO == _typeN ) || ( GS_CLEO == _typeN ) ||
( RBW_CLEO_ZEMACH == _typeN ) || ( GS_CLEO_ZEMACH == _typeN ) ||
( GAUSS_CLEO == _typeN ) || ( GAUSS_CLEO_ZEMACH == _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 M2 = M * M;
double m02 = ( ( RBW_CLEO_ZEMACH == _typeN ) ||
( GS_CLEO_ZEMACH == _typeN ) ||
( GAUSS_CLEO_ZEMACH == _typeN ) )
? qAB
: _m0 * _m0;
double mA2 = mA * mA;
double mB2 = mB * mB;
double mC2 = mC * mC;
if ( _spin == EvtSpinType::SCALAR )
ret = EvtComplex( 1., 0. );
else if ( _spin == EvtSpinType::VECTOR ) {
ret = qCA - qBC + ( M2 - mC2 ) * ( mB2 - mA2 ) / m02;
} else if ( _spin == EvtSpinType::TENSOR ) {
double x1 = qBC - qCA + ( M2 - mC2 ) * ( mA2 - mB2 ) / m02;
double x2 = M2 - mC2;
double x3 = qAB - 2 * M2 - 2 * mC2 + x2 * x2 / m02;
double x4 = mA2 - mB2;
double x5 = qAB - 2 * mB2 - 2 * mA2 + x4 * x4 / m02;
ret = x1 * x1 - x3 * x5 / 3.;
} else
assert( 0 );
}
return ret;
}
double EvtDalitzReso::angDep( const EvtDalitzPoint& x )
{
// Angular dependece for factorizable amplitudes
// unphysical cosines indicate we are in big trouble
double cosTh = x.cosTh(
_pairAng, _pairRes ); // angle between common(reso,ang) and other(reso)
if ( fabs( cosTh ) > 1. ) {
EvtGenReport( EVTGEN_INFO, "EvtGen" ) << "cosTh " << cosTh << std::endl;
assert( 0 );
}
// in units of half-spin
return EvtdFunction::d( EvtSpinType::getSpin2( _spin ), 2 * 0, 2 * 0,
acos( cosTh ) );
}
EvtComplex EvtDalitzReso::mixFactor( EvtComplex prop, EvtComplex prop_mix )
{
double Delta = _delta_mix * ( _m0 + _m0_mix );
return 1 / ( 1 - Delta * Delta * prop * prop_mix ) *
( 1 + _amp_mix * Delta * prop_mix );
}
EvtComplex EvtDalitzReso::Fvector( double s, int index )
{
assert( index >= 1 && index <= 6 );
//Define the complex coupling constant
//The convection is as follow
//i=0 --> pi+ pi-
//i=1 --> KK
//i=2 --> 4pi
//i=3 --> eta eta
//i=4 --> eta eta'
//The first index is the resonace-pole index
double g[5][5]; // Coupling constants. The first index is the pole index. The second index is the decay channel
double ma[5]; // Pole masses. The unit is in GeV
int solution = ( _typeN == K_MATRIX )
? 3
: ( ( _typeN == K_MATRIX_I )
? 1
: ( ( _typeN == K_MATRIX_II ) ? 2 : 0 ) );
if ( solution == 0 ) {
std::cout << "EvtDalitzReso::Fvector() error. Kmatrix solution incorrectly chosen ! "
<< std::endl;
abort();
}
if ( solution == 3 ) {
// coupling constants
//pi+pi- channel
g[0][0] = 0.22889;
g[1][0] = 0.94128;
g[2][0] = 0.36856;
g[3][0] = 0.33650;
g[4][0] = 0.18171;
//K+K- channel
g[0][1] = -0.55377;
g[1][1] = 0.55095;
g[2][1] = 0.23888;
g[3][1] = 0.40907;
g[4][1] = -0.17558;
//4pi channel
g[0][2] = 0;
g[1][2] = 0;
g[2][2] = 0.55639;
g[3][2] = 0.85679;
g[4][2] = -0.79658;
//eta eta channel
g[0][3] = -0.39899;
g[1][3] = 0.39065;
g[2][3] = 0.18340;
g[3][3] = 0.19906;
g[4][3] = -0.00355;
//eta eta' channel
g[0][4] = -0.34639;
g[1][4] = 0.31503;
g[2][4] = 0.18681;
g[3][4] = -0.00984;
g[4][4] = 0.22358;
// Pole masses
ma[0] = 0.651;
ma[1] = 1.20360;
ma[2] = 1.55817;
ma[3] = 1.21000;
ma[4] = 1.82206;
} else if ( solution == 1 ) { // solnI.txt
// coupling constants
//pi+pi- channel
g[0][0] = 0.31896;
g[1][0] = 0.85963;
g[2][0] = 0.47993;
g[3][0] = 0.45121;
g[4][0] = 0.39391;
//K+K- channel
g[0][1] = -0.49998;
g[1][1] = 0.52402;
g[2][1] = 0.40254;
g[3][1] = 0.42769;
g[4][1] = -0.30860;
//4pi channel
g[0][2] = 0;
g[1][2] = 0;
g[2][2] = 1.0;
g[3][2] = 1.15088;
g[4][2] = 0.33999;
//eta eta channel
g[0][3] = -0.21554;
g[1][3] = 0.38093;
g[2][3] = 0.21811;
g[3][3] = 0.22925;
g[4][3] = 0.06919;
//eta eta' channel
g[0][4] = -0.18294;
g[1][4] = 0.23788;
g[2][4] = 0.05454;
g[3][4] = 0.06444;
g[4][4] = 0.32620;
// Pole masses
ma[0] = 0.7369;
ma[1] = 1.24347;
ma[2] = 1.62681;
ma[3] = 1.21900;
ma[4] = 1.74932;
} else if ( solution == 2 ) { // solnIIa.txt
// coupling constants
//pi+pi- channel
g[0][0] = 0.26014;
g[1][0] = 0.95289;
g[2][0] = 0.46244;
g[3][0] = 0.41848;
g[4][0] = 0.01804;
//K+K- channel
g[0][1] = -0.57849;
g[1][1] = 0.55887;
g[2][1] = 0.31712;
g[3][1] = 0.49910;
g[4][1] = -0.28430;
//4pi channel
g[0][2] = 0;
g[1][2] = 0;
g[2][2] = 0.70340;
g[3][2] = 0.96819;
g[4][2] = -0.90100;
//eta eta channel
g[0][3] = -0.32936;
g[1][3] = 0.39910;
g[2][3] = 0.22963;
g[3][3] = 0.24415;
g[4][3] = -0.07252;
//eta eta' channel
g[0][4] = -0.30906;
g[1][4] = 0.31143;
g[2][4] = 0.19802;
g[3][4] = -0.00522;
g[4][4] = 0.17097;
// Pole masses
ma[0] = 0.67460;
ma[1] = 1.21094;
ma[2] = 1.57896;
ma[3] = 1.21900;
ma[4] = 1.86602;
}
//Now define the K-matrix pole
double rho1sq, rho2sq, rho4sq, rho5sq;
EvtComplex rho[5];
double f[5][5];
//Initalize the mass of the resonance
double mpi = 0.13957;
double mK = 0.493677; //using charged K value
double meta = 0.54775; //using PDG value
double metap = 0.95778; //using PDG value
//Initialize the matrix to value zero
EvtComplex K[5][5];
for ( int i = 0; i < 5; i++ ) {
for ( int j = 0; j < 5; j++ ) {
K[i][j] = EvtComplex( 0, 0 );
f[i][j] = 0;
}
}
//Input the _f[i][j] scattering data
double s_scatt = 0.0;
if ( solution == 3 )
s_scatt = -3.92637;
else if ( solution == 1 )
s_scatt = -5.0;
else if ( solution == 2 )
s_scatt = -5.0;
double sa = 1.0;
double sa_0 = -0.15;
if ( solution == 3 ) {
f[0][0] = 0.23399; // f^scatt
f[0][1] = 0.15044;
f[0][2] = -0.20545;
f[0][3] = 0.32825;
f[0][4] = 0.35412;
} else if ( solution == 1 ) {
f[0][0] = 0.04214; // f^scatt
f[0][1] = 0.19865;
f[0][2] = -0.63764;
f[0][3] = 0.44063;
f[0][4] = 0.36717;
} else if ( solution == 2 ) {
f[0][0] = 0.26447; // f^scatt
f[0][1] = 0.10400;
f[0][2] = -0.35445;
f[0][3] = 0.31596;
f[0][4] = 0.42483;
}
f[1][0] = f[0][1];
f[2][0] = f[0][2];
f[3][0] = f[0][3];
f[4][0] = f[0][4];
//Now construct the phase-space factor
//For eta-eta' there is no difference term
rho1sq = 1. - pow( mpi + mpi, 2 ) / s; //pi+ pi- phase factor
if ( rho1sq >= 0 )
rho[0] = EvtComplex( sqrt( rho1sq ), 0 );
else
rho[0] = EvtComplex( 0, sqrt( -rho1sq ) );
rho2sq = 1. - pow( mK + mK, 2 ) / s;
if ( rho2sq >= 0 )
rho[1] = EvtComplex( sqrt( rho2sq ), 0 );
else
rho[1] = EvtComplex( 0, sqrt( -rho2sq ) );
//using the A&S 4pi phase space Factor:
//Shit, not continue
if ( s <= 1 ) {
double real = 1.2274 + .00370909 / ( s * s ) - .111203 / s -
6.39017 * s + 16.8358 * s * s - 21.8845 * s * s * s +
11.3153 * s * s * s * s;
double cont32 = sqrt( 1.0 - ( 16.0 * mpi * mpi ) );
rho[2] = EvtComplex( cont32 * real, 0 );
} else
rho[2] = EvtComplex( sqrt( 1. - 16. * mpi * mpi / s ), 0 );
rho4sq = 1. - pow( meta + meta, 2 ) / s;
if ( rho4sq >= 0 )
rho[3] = EvtComplex( sqrt( rho4sq ), 0 );
else
rho[3] = EvtComplex( 0, sqrt( -rho4sq ) );
rho5sq = 1. - pow( meta + metap, 2 ) / s;
if ( rho5sq >= 0 )
rho[4] = EvtComplex( sqrt( rho5sq ), 0 );
else
rho[4] = EvtComplex( 0, sqrt( -rho5sq ) );
double smallTerm = 1; // Factor to prevent divergences.
// Check if some pole may arise problems.
for ( int pole = 0; pole < 5; pole++ )
if ( fabs( pow( ma[pole], 2 ) - s ) < PRECISION )
smallTerm = pow( ma[pole], 2 ) - s;
//now sum all the pole
//equation (3) in the E791 K-matrix paper
for ( int i = 0; i < 5; i++ ) {
for ( int j = 0; j < 5; j++ ) {
for ( int pole_index = 0; pole_index < 5; pole_index++ ) {
double A = g[pole_index][i] * g[pole_index][j];
double B = ma[pole_index] * ma[pole_index] - s;
if ( fabs( B ) < PRECISION )
K[i][j] += EvtComplex( A, 0 );
else
K[i][j] += EvtComplex( A / B, 0 ) * smallTerm;
}
}
}
//now add the SVT part
for ( int i = 0; i < 5; i++ ) {
for ( int j = 0; j < 5; j++ ) {
double C = f[i][j] * ( 1.0 - s_scatt );
double D = ( s - s_scatt );
K[i][j] += EvtComplex( C / D, 0 ) * smallTerm;
}
}
//Fix the bug in the FOCUS paper
//Include the Alder zero term:
for ( int i = 0; i < 5; i++ ) {
for ( int j = 0; j < 5; j++ ) {
double E = ( s - ( sa * mpi * mpi * 0.5 ) ) * ( 1.0 - sa_0 );
double F = ( s - sa_0 );
K[i][j] *= EvtComplex( E / F, 0 );
}
}
//This is not correct!
//(1-ipK) != (1-iKp)
static EvtMatrix<EvtComplex> mat;
mat.setRange(
5 ); // Try to do in only the first time. DEFINE ALLOCATION IN CONSTRUCTOR.
for ( int row = 0; row < 5; row++ )
for ( int col = 0; col < 5; col++ )
mat( row, col ) = ( row == col ) * smallTerm -
EvtComplex( 0., 1. ) * K[row][col] * rho[col];
EvtMatrix<EvtComplex>* matInverse =
mat.inverse(); //The 1st row of the inverse matrix. This matrix is {(I-iKp)^-1}_0j
vector<EvtComplex> U1j;
for ( int j = 0; j < 5; j++ )
U1j.push_back( ( *matInverse )[0][j] );
delete matInverse;
//this calculates final F0 factor
EvtComplex value( 0, 0 );
if ( index <= 5 ) {
//this calculates the beta_idx Factors
for ( int j = 0; j < 5; j++ ) { // sum for 5 channel
EvtComplex top = U1j[j] * g[index - 1][j];
double bottom = ma[index - 1] * ma[index - 1] - s;
if ( fabs( bottom ) < PRECISION )
value += top;
else
value += top / bottom * smallTerm;
}
} else {
//this calculates fprod Factors
value += U1j[0];
value += U1j[1] * _fr12prod;
value += U1j[2] * _fr13prod;
value += U1j[3] * _fr14prod;
value += U1j[4] * _fr15prod;
value *= ( 1 - _s0prod ) / ( s - _s0prod ) * smallTerm;
}
return value;
}
//replace Breit-Wigner with LASS
EvtComplex EvtDalitzReso::lass( double s )
{
EvtTwoBodyKine vd( _massFirst, _massSecond, sqrt( s ) );
double q = vd.p();
double GammaM = _g0 * _vd.widthFactor( vd ); // running width;
//calculate the background phase motion
double cot_deltaB = 1.0 / ( _a * q ) + 0.5 * _r * q;
double deltaB = atan( 1.0 / cot_deltaB );
double totalB = deltaB + _phiB;
//calculate the resonant phase motion
double deltaR = atan( ( _m0 * GammaM / ( _m0 * _m0 - s ) ) );
double totalR = deltaR + _phiR;
//sum them up
EvtComplex bkgB, resT;
bkgB = EvtComplex( _Blass * sin( totalB ), 0 ) *
EvtComplex( cos( totalB ), sin( totalB ) );
resT = EvtComplex( _R * sin( deltaR ), 0 ) *
EvtComplex( cos( totalR ), sin( totalR ) ) *
EvtComplex( cos( 2 * totalB ), sin( 2 * totalB ) );
EvtComplex T;
if ( _cutoff > 0 && sqrt( s ) > _cutoff )
T = resT;
else
T = bkgB + resT;
if ( _scaleByMOverQ )
T *= ( sqrt( s ) / q );
return T;
}
EvtComplex EvtDalitzReso::flatte( const double& m )
{
EvtComplex w;
for ( vector<EvtFlatteParam>::const_iterator param = _flatteParams.begin();
param != _flatteParams.end(); ++param ) {
double m1 = ( *param ).m1();
double m2 = ( *param ).m2();
double g = ( *param ).g();
w += ( g * g *
sqrtCplx( ( 1 - ( ( m1 - m2 ) * ( m1 - m2 ) ) / ( m * m ) ) *
( 1 - ( ( m1 + m2 ) * ( m1 + m2 ) ) / ( m * m ) ) ) );
}
EvtComplex denom = _m0 * _m0 - m * m - EvtComplex( 0, 1 ) * w;
return EvtComplex( 1.0, 0.0 ) / denom;
}

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