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ChristyBosted.cpp
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ChristyBosted.cpp
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#include "ChristyBosted.h"
namespace CepGen
{
namespace SF
{
double
ChristyBosted::resmod507( char sf, double w2, double q2 ) const
{
const double mp = Constants::mp, mp2 = mp*mp,
mpi = Constants::mpi, mpi2 = mpi*mpi,
meta = Particle::massFromPDGId( Particle::Eta ), meta2 = meta*meta;
const double w = sqrt( w2 );
const double xb = q2/( q2+w2-mp2 );
double m0 = 0., q20 = 0.;
if ( sf == 'T' ) { // transverse
m0 = 0.125;
q20 = 0.05;
}
else if ( sf == 'L' ) {
m0 = params_.m0;
q20 = 0.125;
}
else {
InError( "Invalid direction retrieved! Aborting." )
return 0.;
}
const double norm_q2 = 1./0.330/0.330;
const double t = log( log( ( q2+m0 )*norm_q2 )/log( m0*norm_q2 ) );
//--- calculate kinematics needed for threshold relativistic B-W
// equivalent photon energies
const double k = 0.5 * ( w2-mp2 )/mp;
const double kcm = 0.5 * ( w2-mp2 )/w;
const double epicm = 0.5 * ( w2+mpi2-mp2 )/w, ppicm = sqrt( std::max( 0., epicm*epicm-mpi2 ) );
const double epi2cm = 0.5 * ( w2 + 4.*mpi2 - mp2 )/w, ppi2cm = sqrt( std::max( 0., epi2cm*epi2cm-4*mpi2 ) );
const double eetacm = 0.5 * ( w2 + meta2 - mp2 )/w, petacm = sqrt( std::max( 0., eetacm*eetacm-meta2 ) );
std::array<double,7> width, height, pgam;
for ( unsigned short i = 0; i < 7; ++i ) {
const Parameterisation::ResonanceParameters& res = params_.resonances[i];
width[i] = res.width;
//--- calculate partial widths
//----- 1-pion decay mode
const double x02 = res.x0*res.x0;
const double partial_width_singlepi = pow( ppicm /res.pcmr( mpi2 ), 2.*res.angular_momentum+1. )
* pow( ( res.pcmr( mpi2 )*res.pcmr( mpi2 )+x02 )/( ppicm *ppicm +x02 ), res.angular_momentum );
//----- 2-pion decay mode
const double partial_width_doublepi = pow( ppi2cm/res.pcmr( 4.*mpi2 ), 2.*( res.angular_momentum+2. ) )
* pow( ( res.pcmr( 4.*mpi2 )*res.pcmr( 4.*mpi2 )+x02 )/( ppi2cm*ppi2cm+x02 ), res.angular_momentum+2 )
* w / res.mass;
//----- eta decay mode (only for S11's)
const double partial_width_eta = ( res.br.eta == 0. ) ? 0. :
pow( petacm/res.pcmr( meta2 ), 2.*res.angular_momentum+1. )
* pow( ( res.pcmr( meta2 )*res.pcmr( meta2 )+x02 )/( petacm*petacm+x02 ), res.angular_momentum );
// virtual photon width
pgam[i] = res.width * pow( kcm/res.kcmr(), 2 ) * ( res.kcmr()*res.kcmr()+x02 )/( kcm*kcm+x02 );
width[i] = ( partial_width_singlepi * res.br.singlepi
+ partial_width_doublepi * res.br.doublepi
+ partial_width_eta * res.br.eta ) * res.width;
//std::cout << i << "\t" << width[i] << "\t" << partial_width_doublepi << "\t" << pow( ppi2cm/res.pcmr( 4.*mpi2 ), 2.*( res.angular_momentum+2. ) ) << std::endl;
//--- resonance Q^2 dependence calculations
if ( sf == 'T' ) height[i] = res.A0_T*( 1.+res.fit_parameters[0]*q2/( 1.+res.fit_parameters[1]*q2 ) )/pow( 1.+q2/0.91, res.fit_parameters[2] );
else if ( sf == 'L' ) height[i] = res.A0_L/( 1.+res.fit_parameters[3]*q2 )*q2*exp( -q2*res.fit_parameters[4] );
//std::cout << sf << "//////" << height[i] << "\t" << res.fit_parameters[4] << std::endl;
height[i] = height[i]*height[i];
}
//--- calculate Breit-Wigners for all resonances
double sig_res = 0.;
for ( unsigned short i = 0; i < 7; ++i ) {
const Parameterisation::ResonanceParameters res = params_.resonances[i];
const double mass2 = res.mass*res.mass, width2 = width[i]*width[i];
const double sigr = height[i]*res.kr()/k*res.kcmr()/kcm/res.width * ( width[i]*pgam[i] / ( pow( w2-mass2, 2 ) + mass2*width2 ) );
sig_res += sigr;
}
sig_res *= w;
//--- finish resonances / start non-res background calculation
const double xpr = 1./( 1.+( w2-pow( mp+mpi, 2 ) )/( q2+q20 ) );
double sig_nr = 0.;
if ( sf == 'T' ) { // transverse
const double wdif = w - ( mp + mpi );
for ( unsigned short i = 0; i < 2; ++i ) {
const double expo = params_.continuum.transverse[i].fit_parameters[1]
+ params_.continuum.transverse[i].fit_parameters[2]*q2
+ params_.continuum.transverse[i].fit_parameters[3]*q2*q2;
sig_nr += params_.continuum.transverse[i].sig0 / pow( q2+params_.continuum.transverse[i].fit_parameters[0], expo ) * pow( wdif, i+1.5 );
}
sig_nr *= xpr;
}
else if ( sf == 'L' ) { // longitudinal
for ( unsigned short i = 0; i < 1; ++i ) {
const double expo = params_.continuum.longitudinal[i].fit_parameters[0]
+ params_.continuum.longitudinal[i].fit_parameters[1];
sig_nr += params_.continuum.longitudinal[i].sig0
* pow( 1.-xpr, expo )/( 1.-xb )
* pow( q2/( q2+q20 ), params_.continuum.longitudinal[i].fit_parameters[2] )/( q2+q20 )
* pow( xpr, params_.continuum.longitudinal[i].fit_parameters[3]+params_.continuum.longitudinal[i].fit_parameters[4]*t );
}
}
return sig_res + sig_nr;
}
ChristyBosted::Parameterisation
ChristyBosted::Parameterisation::standard()
{
Parameterisation params;
params.m0 = 4.2802;
params.continuum.transverse = {
ContinuumParameters::DirectionParameters( 246.06, { 0.067469, 1.3501, 0.12054, -0.0038495 } ),
ContinuumParameters::DirectionParameters( -89.360, { 0.20977, 1.5715, 0.090736, 0.010362 } )
};
params.continuum.longitudinal = {
ContinuumParameters::DirectionParameters( 86.746, { 0., 4.0294, 3.1285, 0.33403, 4.9623 } )
};
//--- P33(1232)
ResonanceParameters p33;
p33.br = ResonanceParameters::BranchingRatios( 1., 0., 0. );
p33.angular_momentum = 1.;
//p33.x0 = 0.15;
p33.x0 = 0.14462;
p33.mass = 1.2298;
p33.width = 0.13573;
p33.fit_parameters = { 4.2291, 1.2598, 2.1242, 19.910, 0.22587 };
p33.A0_T = 7.7805;
p33.A0_L = 29.414;
params.resonances.emplace_back( p33 );
//--- S11(1535)
ResonanceParameters s11_1535;
s11_1535.br = ResonanceParameters::BranchingRatios( 0.45, 0.1, 0.45 );
s11_1535.angular_momentum = 0.;
s11_1535.x0 = 0.215;
s11_1535.mass = 1.5304;
s11_1535.width = 0.220;
s11_1535.fit_parameters = { 6823.2, 33521., 2.5686, 0., 0. };
s11_1535.A0_T = 6.3351;
s11_1535.A0_L = 0.;
params.resonances.emplace_back( s11_1535 );
//--- D13(1520)
ResonanceParameters d13;
d13.br = ResonanceParameters::BranchingRatios( 0.65, 0.35, 0. );
d13.angular_momentum = 2.;
d13.x0 = 0.215;
d13.mass = 1.5057;
d13.width = 0.082956;
d13.fit_parameters = { 21.240, 0.055746, 2.4886, 97.046, 0.31042 };
d13.A0_T = 0.60347;
d13.A0_L = 157.92;
params.resonances.emplace_back( d13 );
//--- F15(1680)
ResonanceParameters f15;
f15.br = ResonanceParameters::BranchingRatios( 0.65, 0.35, 0. );
f15.angular_momentum = 3.;
f15.x0 = 0.215;
f15.mass = 1.6980;
f15.width = 0.095782;
f15.fit_parameters = { -0.28789, 0.18607, 0.063534, 0.038200, 1.2182 };
f15.A0_T = 2.3305;
f15.A0_L = 4.2160;
params.resonances.emplace_back( f15 );
//--- S11(1650)
ResonanceParameters s11_1650;
s11_1650.br = ResonanceParameters::BranchingRatios( 0.4, 0.5, 0.1 );
s11_1650.angular_momentum = 0.;
s11_1650.x0 = 0.215;
s11_1650.mass = 1.6650;
s11_1650.width = 0.10936;
s11_1650.fit_parameters = { -0.56175, 0.38964, 0.54883, 0.31393, 2.9997 };
s11_1650.A0_T = 1.9790;
s11_1650.A0_L = 13.764;
params.resonances.emplace_back( s11_1650 );
//--- P11(1440) roper
ResonanceParameters p11;
p11.br = ResonanceParameters::BranchingRatios( 0.65, 0.35, 0. );
p11.angular_momentum = 1.;
p11.x0 = 0.215;
p11.mass = 1.4333;
p11.width = 0.37944;
p11.fit_parameters = { 46.213, 0.19221, 1.9141, 0.053743, 1.3091 };
p11.A0_T = 0.022506;
p11.A0_L = 5.5124;
params.resonances.emplace_back( p11 );
//--- F37(1950)
ResonanceParameters f37;
f37.br = ResonanceParameters::BranchingRatios( 0.5, 0.5, 0. );
f37.angular_momentum = 3.;
f37.x0 = 0.215;
f37.mass = 1.9341;
f37.width = 0.380;
f37.fit_parameters = { 0., 0., 1., 1.8951, 0.51376 };
f37.A0_T = 3.4187;
f37.A0_L = 1.8951;
params.resonances.emplace_back( f37 );
return params;
}
StructureFunctions
ChristyBosted::operator()( double q2, double xbj ) const
{
const double mp2 = Constants::mp*Constants::mp;
const double w2 = mp2 + q2*( 1.-xbj )/xbj;
const double w_min = Constants::mp+Constants::mpi;
StructureFunctions cb;
if ( sqrt( w2 ) < w_min ) return cb;
//-----------------------------
// modification of Christy-Bosted at large q2 as described in the LUXqed paper
//-----------------------------
const double q21 = 30., q20 = 8.;
const double delq2 = q2 - q20;
const double qq = q21 - q20;
const double prefac = 1./( 4.*M_PI*M_PI*Constants::alphaEM ) * ( 1.-xbj );
//------------------------------
double q2_eff = q2, w2_eff = w2;
if ( q2 > q20 ) {
q2_eff = q20 + delq2/( 1.+delq2/qq );
w2_eff = mp2 + q2_eff*( 1.-xbj )/xbj;
}
const double tau = 4.*xbj*xbj*mp2/q2_eff;
const double sigT = resmod507( 'T', w2_eff, q2_eff ), sigL = resmod507( 'L', w2_eff, q2_eff );
cb.F2 = prefac * q2_eff / ( 1+tau ) * ( sigT+sigL ) / Constants::GeV2toBarn * 1.e6;
if ( q2 > q20 ) cb.F2 *= q21/( q21 + delq2 );
const double R = sigL/sigT;
cb.FL = cb.F2*( 1+tau )*R/( 1.+R );
return cb;
}
}
}

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