BergerSehgalFMCOHPiPXSec2015.cxx

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//____________________________________________________________________________
/*
   Copyright (c) 2003-2020, The GENIE Collaboration
   For the full text of the license visit http://copyright.genie-mc.org

   G. Perdue, H. Gallagher, D. Cherdack
*/
//____________________________________________________________________________

#include <TMath.h>

#include "Framework/Algorithm/AlgConfigPool.h"
#include "Physics/XSectionIntegration/XSecIntegratorI.h"
#include "Framework/Conventions/GBuild.h"
#include "Framework/Conventions/Constants.h"
#include "Framework/Conventions/Units.h"
#include "Framework/Conventions/RefFrame.h"
#include "Framework/Messenger/Messenger.h"
#include "Framework/ParticleData/PDGCodes.h"
#include "Framework/ParticleData/PDGUtils.h"
#include "Physics/Coherent/XSection/BergerSehgalFMCOHPiPXSec2015.h"
#include "Framework/Utils/HadXSUtils.h"
#include "Framework/Utils/KineUtils.h"

using namespace genie;
using namespace genie::constants;
using namespace genie::utils;

//____________________________________________________________________________
BergerSehgalFMCOHPiPXSec2015::BergerSehgalFMCOHPiPXSec2015() :
    XSecAlgorithmI("genie::BergerSehgalFMCOHPiPXSec2015")
{

}
//____________________________________________________________________________
BergerSehgalFMCOHPiPXSec2015::BergerSehgalFMCOHPiPXSec2015(string config) :
    XSecAlgorithmI("genie::BergerSehgalFMCOHPiPXSec2015", config)
{

}
//____________________________________________________________________________
BergerSehgalFMCOHPiPXSec2015::~BergerSehgalFMCOHPiPXSec2015()
{

}
//____________________________________________________________________________
double BergerSehgalFMCOHPiPXSec2015::XSec(
        const Interaction * interaction, KinePhaseSpace_t /*kps*/) const
{
    // Here we are following PRD 79, 053003 (2009) by Berger and Sehgal
    // This method computes the differential cross section represented
    // in Eq.'s 6 (CC) and 7 (NC) from that paper.

    // We have additionally modified the formulae to account for a
    // non-infinite mass for the target nucleus

    if(! this -> ValidProcess    (interaction) ) return 0.;
    if(! this -> ValidKinematics (interaction) ) return 0.;

    const Kinematics &   kinematics = interaction -> Kine();
    const InitialState & init_state = interaction -> InitState();

    bool pionIsCharged = interaction->ProcInfo().IsWeakCC();
    double xsec = 0.0;

    double E      = init_state.ProbeE(kRfLab);        // nu E
    double Q2     = kinematics.Q2();
    double y      = kinematics.y();                   // inelasticity
    double t      = kinematics.t();                   // fun exists?
    assert(E > 0.);
    assert(y > 0.);
    assert(y < 1.);
    double ppistar = PionCOMAbsMomentum(interaction); // |Center of Mass Momentum|
    if (ppistar <= 0.0) {
        LOG("BergerSehgalFMCohPi", pDEBUG) <<
            "Pion COM momentum negative for Q2 = " << Q2 <<
            " y = " << y;
        return 0.0;
    }
    double front  = ExactKinematicTerm(interaction);
    if (front <= 0.0) {
        LOG("BergerSehgalFMCohPi", pDEBUG) << "Exact kin. form = " << front <<
            " E = " << E << " Q2 = " << Q2 << " y = " << y;
        return 0.0;
    }

    double A      = (double) init_state.Tgt().A();   // mass number
    double A2     = TMath::Power(A, 2.);
    double A_3    = TMath::Power(A, 1./3.);
    double M      = init_state.Tgt().Mass();
    double M_pi   = pionIsCharged ? kPionMass : kPi0Mass;
    double M_pi2  = M_pi * M_pi;
    double Epi    = y * E - t / (2 * M);
    double Epi2   = Epi * Epi;
    double ma2    = fMa * fMa;
    double Ga     = ma2 / (ma2 + Q2);
    double Ga2    = Ga * Ga;
    double Ro2    = TMath::Power(fRo * units::fermi, 2.);
    double ppi2   = Epi2 - M_pi2;
    double ppi    = ppi2 > 0.0 ? sqrt(ppi2) : 0.0;
    // double fp     = 0.93 * kPionMass;  // unused  // pion decay constant

    double costheta = (t - Q2 - M_pi * M_pi) / (2 * ( (y *E - Epi) * Epi -
                ppi * sqrt(TMath::Power(y * E - Epi, 2.) + t) ) );

    if ((costheta > 1.0) || (costheta < -1.0)) return 0.0;

    // tot. pi+N xsec
    double sTot   =
        utils::hadxs::berger::TotalPionNucleonXSec(Epi, pionIsCharged);
    double sTot2  = sTot * sTot;
    // inel. pi+N xsec
    double sInel  =
        utils::hadxs::berger::InelasticPionNucleonXSec(Epi, pionIsCharged);

    // Fabs (F_{abs}) describes the average attenuation of a pion emerging
    // from a sphere of nuclear matter with radius = R_0 A^{1/3}. it is
    // Eq. 13 in Berger-Sehgal PRD 79, 053003
    double Fabs_input = (9.0 * A_3) / (16.0 * kPi * Ro2);
    double Fabs       = TMath::Exp( -1.0 * Fabs_input * sInel);

    // A_RS for BS version of RS, and/or Tpi>1.0
    //double RS_factor = (A2 * Fabs) / (16.0 * kPi) * (sTot2);
    double R         = fRo * A_3 * units::fermi; // nuclear radius
    double R2        = R * R;                    //
    double b         = 0.33333 * R2;             // Eq. 12 in BS
    double expbt     = TMath::Exp( -b * t );
    double dsigEldt  = sTot2 / (16. * kPi);           // Eq. 11 in BS
    double dsigpiNdt = A2 * dsigEldt * expbt * Fabs;  // Eq. 10 in BS

    double tpilow    = 0.0;
    double siglow    = 0.0;
    double tpihigh   = 0.0;
    double sighigh   = 0.0;
    double dsigdt    = 0.0;
    double tpi       = 0.0;
    int    xsec_stat = 0;

    // differential cross section for pion-nucleus in t (ds/dt term from
    // Eq. 7 in BS. we will initially set the value to a "Rein-Sehgal style"
    // computation and update to use the Berger-Sehgal pion-nucleus cross
    // section where appropriate.
    double edep_dsigpiNdt = dsigpiNdt;

    // c.o.m.
    tpi       = Epi - M_pi;

    if (tpi <= 1.0 && fRSPionXSec == false) {
        // use the Berger-Sehgal pion-nucleus cross section. note we're only
        // checking on the pion energy and the conditional flag - is it really
        // reasonable to ever use this value for non-Carbon targets?
        xsec_stat =
            utils::hadxs::berger::PionNucleusXSec(
                    tpi, ppistar, t, A,
                    tpilow, siglow,
                    tpihigh, sighigh);
        if (xsec_stat != 0)
            LOG("BergerSehgalFMCohPi", pWARN) <<
                "Unable to retrieve pion-nucleus cross section with A = " <<
                A << ", t_pi = " << tpi;
        dsigdt = siglow + (sighigh - siglow) * (tpi - tpilow) / (tpihigh - tpilow);
        dsigdt = dsigdt / (2.0 * ppistar * ppistar) * units::mb;
        edep_dsigpiNdt = dsigdt;
    }

    // complete calculation of Eq. 7 in BS paper
    xsec = front * Ga2 * edep_dsigpiNdt;

    // Correction for finite final state lepton mass.
    // Lepton mass modification is part of Berger-Sehgal and is not optional.
    if (pionIsCharged) {
        double C = 1.;
        // First, we need to remove the leading G_{A}^2 which is required for NC.
        xsec /= Ga2;
        // Next, \cos^2 \theta_{Cabibbo} appears in the CC xsec, but not the NC.
        xsec *= fCos8c2;
        double ml    = interaction->FSPrimLepton()->Mass();
        double ml2   = TMath::Power(ml,2);
        double Q2min = ml2 * y/(1-y);
        if(Q2 > Q2min) {
            double C1 = TMath::Power(Ga - 0.5 * Q2min / (Q2 + kPionMass2), 2);
            double C2 = 0.25 * y * Q2min * (Q2 - Q2min) /
                TMath::Power(Q2 + kPionMass2, 2);
            C = C1 + C2;
        } else {
            C = 0.;
        }
        xsec *= (2. * C); // *2 is for CC vs NC in BS
    }

#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
    LOG("BergerSehgalFMCohPi", pDEBUG)
        << "\n momentum transfer .............. Q2    = " << Q2
        << "\n mass number .................... A     = " << A
        << "\n pion energy .................... Epi   = " << Epi
        << "\n propagator term ................ propg = " << propg
        << "\n Re/Im of fwd pion scat. ampl. .. Re/Im = " << fReIm
        << "\n total pi+N cross section ....... sigT  = " << sTot
        << "\n inelastic pi+N cross section ... sigI  = " << sInel
        << "\n nuclear size scale ............. Ro    = " << fRo
        << "\n pion absorption factor ......... Fabs  = " << Fabs
        << "\n t integration factor ........... tint  = " << tint;
    LOG("BergerSehgalFMCohPi", pINFO)
        << "d3xsec/dQ2dydt[COHPi] (x= " << x << ", y="
        << y << ", E=" << E << ") = "<< xsec;
#endif

    //----- The algorithm computes d^3xsec/dQ^2dydt
    //      Check whether Jacobian tranformation is needed...

    return xsec;
}
//____________________________________________________________________________
double BergerSehgalFMCOHPiPXSec2015::ExactKinematicTerm(
        const Interaction * interaction) const
{
    // This function is a bit inefficient but is being encapsulated as
    // such in order to possibly migrate into a general kinematics check.
    const Kinematics &   kinematics = interaction -> Kine();
    const InitialState & init_state = interaction -> InitState();

    bool   pionIsCharged = interaction->ProcInfo().IsWeakCC();
    double M_pi          = pionIsCharged ? kPionMass : kPi0Mass;
    double E             = init_state.ProbeE(kRfLab);        // nu E
    double Q2            = kinematics.Q2();
    double y             = kinematics.y();                   // inelasticity
    double fp2           = (0.93 * M_pi)*(0.93 * M_pi);

    double term = ((kGF2 * fp2) / (4.0 * kPi2)) *
        ((E * (1.0 - y)) / sqrt(y*E * y*E + Q2)) *
        (1.0 - Q2 / (4.0 * E*E * (1.0 - y)));
    return term;
}
//____________________________________________________________________________
double BergerSehgalFMCOHPiPXSec2015::PionCOMAbsMomentum(
        const Interaction * interaction) const
{
    // This function is a bit inefficient but is being encapsulated as
    // such in order to possibly migrate into a general kinematics check.
    const Kinematics &   kinematics = interaction -> Kine();
    const InitialState & init_state = interaction -> InitState();

    bool   pionIsCharged = interaction->ProcInfo().IsWeakCC();
    double M_pi          = pionIsCharged ? kPionMass : kPi0Mass;
    double E             = init_state.ProbeE(kRfLab);        // nu E
    double Q2            = kinematics.Q2();
    double y             = kinematics.y();                   // inelasticity
    double MT            = init_state.Tgt().Mass();

    double W2      = MT * MT - Q2 + 2.0 * y * E * MT;
    double arg     = (2.0 * MT * (y * E - M_pi) - Q2 - M_pi * M_pi) *
        (2.0 * MT * (y * E + M_pi) - Q2 - M_pi * M_pi);
    if (arg < 0) return arg;
    double ppistar = TMath::Sqrt(arg) / 2.0 / TMath::Sqrt(W2);

    return ppistar;
}
//____________________________________________________________________________
double BergerSehgalFMCOHPiPXSec2015::Integral(const Interaction * interaction) const
{
    double xsec = fXSecIntegrator->Integrate(this,interaction);
    return xsec;
}
//____________________________________________________________________________
bool BergerSehgalFMCOHPiPXSec2015::ValidProcess(const Interaction * interaction) const
{
    if(interaction->TestBit(kISkipProcessChk)) return true;

    const InitialState & init_state = interaction->InitState();
    const ProcessInfo &  proc_info  = interaction->ProcInfo();
    const Target &       target     = init_state.Tgt();

    int nu = init_state.ProbePdg();

    if (!proc_info.IsCoherentProduction())  return false;
    if (!proc_info.IsWeak())      return false;
    if (target.HitNucIsSet())     return false;
    if (!(target.A()>1))          return false;
    if (!pdg::IsNeutrino(nu) && !pdg::IsAntiNeutrino(nu)) return false;

    return true;
}
//____________________________________________________________________________
void BergerSehgalFMCOHPiPXSec2015::Configure(const Registry & config)
{
    Algorithm::Configure(config);
    this->LoadConfig();
}
//____________________________________________________________________________
void BergerSehgalFMCOHPiPXSec2015::Configure(string config)
{
    Algorithm::Configure(config);
    this->LoadConfig();
}
//____________________________________________________________________________
void BergerSehgalFMCOHPiPXSec2015::LoadConfig(void)
{
        GetParam( "COH-Ma",fMa ) ;
    GetParam( "COH-Ro", fRo ) ;

    double thc ;
    GetParam( "CabibboAngle", thc ) ;
    fCos8c2     = TMath::Power(TMath::Cos(thc), 2);

    // fRSPionXSec => Do not use the pion-nucleus cross section from Table 1 in PRD 79, 053003
    // Instead, use the Rein-Sehgal "style" pion-nucleon cross section and scale by A
    // for all pion energies.
    GetParam( "COH-UseRSPionXSec", fRSPionXSec ) ;

    //-- load the differential cross section integrator
    fXSecIntegrator =
        dynamic_cast<const XSecIntegratorI *> (this->SubAlg("XSec-Integrator"));
    assert(fXSecIntegrator);
}
//____________________________________________________________________________