LwlynSmithQELCCPXSec.cxx

Go to the documentation of this file.

//____________________________________________________________________________
/*
 Copyright (c) 2003-2019, The GENIE Collaboration
 For the full text of the license visit http://copyright.genie-mc.org
 or see $GENIE/LICENSE

 Author: Costas Andreopoulos <costas.andreopoulos \at stfc.ac.uk>
         University of Liverpool & STFC Rutherford Appleton Lab

 For the class documentation see the corresponding header file.

 Important revisions after version 2.0.0 :
 @ Sep 19, 2009 - CA
   Renamed QELPXSec -> LwlynSmithQELCCPXSec
 @ Mar 18, 2016 - JJ (SD)
   Moved code to average over initial nucleons from QELXSec to the Integral()
   method here. For each nucleon, generate a struck nucleon position, then a
   momentum, then integrate.
 @ 2015 - AF
   Added FullDifferentialXSec method to work with QELEventGenerator
*/
//____________________________________________________________________________

#include <TMath.h>

#include "Framework/Algorithm/AlgConfigPool.h"
#include "Physics/XSectionIntegration/XSecIntegratorI.h"
#include "Physics/QuasiElastic/XSection/QELFormFactors.h"
#include "Physics/QuasiElastic/XSection/QELFormFactorsModelI.h"
#include "Framework/Conventions/GBuild.h"
#include "Framework/Conventions/Constants.h"
#include "Framework/Conventions/RefFrame.h"
#include "Framework/Conventions/KineVar.h"
#include "Framework/Conventions/Units.h"
#include "Physics/Common/VertexGenerator.h"
#include "Framework/GHEP/GHepParticle.h"
#include "Physics/QuasiElastic/XSection/LwlynSmithQELCCPXSec.h"

#include "Physics/NuclearState/NuclearModelI.h"
#include "Framework/Messenger/Messenger.h"
#include "Framework/ParticleData/PDGCodes.h"
#include "Framework/ParticleData/PDGLibrary.h"
#include "Framework/ParticleData/PDGUtils.h"
#include "Framework/Numerical/MathUtils.h"
#include "Framework/Utils/KineUtils.h"
#include "Physics/NuclearState/NuclearUtils.h"
#include "Physics/QuasiElastic/XSection/QELUtils.h"

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

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

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

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

}
//____________________________________________________________________________
double LwlynSmithQELCCPXSec::XSec(
   const Interaction * interaction, KinePhaseSpace_t kps) const
{
  if(! this -> ValidProcess    (interaction) ) {LOG("LwlynSmith",pWARN) << "not a valid process"; return 0.;}
  if(! this -> ValidKinematics (interaction) ) {LOG("LwlynSmith",pWARN) << "not valid kinematics"; return 0.;}

  // If computing the full differential cross section, then all four momentum
  // four-vectors (probe, hit nucleon, final lepton, and final nucleon) should
  // have been set already, with the hit nucleon off-shell as appropriate.
  if (kps == kPSQELEvGen) {
    return this->FullDifferentialXSec(interaction);
  }

  // Get kinematics & init-state parameters
  const Kinematics &   kinematics = interaction -> Kine();
  const InitialState & init_state = interaction -> InitState();
  const Target & target = init_state.Tgt();

  double E  = init_state.ProbeE(kRfHitNucRest);
  double E2 = TMath::Power(E,2);
  double ml = interaction->FSPrimLepton()->Mass();
  double M  = target.HitNucMass();
  double q2 = kinematics.q2();

  // One of the xsec terms changes sign for antineutrinos
  bool is_neutrino = pdg::IsNeutrino(init_state.ProbePdg());
  int sign = (is_neutrino) ? -1 : 1;

  // Calculate the QEL form factors
  fFormFactors.Calculate(interaction);

  double F1V   = fFormFactors.F1V();
  double xiF2V = fFormFactors.xiF2V();
  double FA    = fFormFactors.FA();
  double Fp    = fFormFactors.Fp();

#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
  LOG("LwlynSmith", pDEBUG) << "\n" << fFormFactors;
#endif

  // Calculate auxiliary parameters
  double ml2     = TMath::Power(ml,    2);
  double M2      = TMath::Power(M,     2);
  double M4      = TMath::Power(M2,    2);
  double FA2     = TMath::Power(FA,    2);
  double Fp2     = TMath::Power(Fp,    2);
  double F1V2    = TMath::Power(F1V,   2);
  double xiF2V2  = TMath::Power(xiF2V, 2);
  double Gfactor = M2*kGF2*fCos8c2 / (8*kPi*E2);
  double s_u     = 4*E*M + q2 - ml2;
  double q2_M2   = q2/M2;

  // Compute free nucleon differential cross section
  double A = (0.25*(ml2-q2)/M2) * (
              (4-q2_M2)*FA2 - (4+q2_M2)*F1V2 - q2_M2*xiF2V2*(1+0.25*q2_M2)
              -4*q2_M2*F1V*xiF2V - (ml2/M2)*(
               (F1V2+xiF2V2+2*F1V*xiF2V)+(FA2+4*Fp2+4*FA*Fp)+(q2_M2-4)*Fp2));
  double B = -1 * q2_M2 * FA*(F1V+xiF2V);
  double C = 0.25*(FA2 + F1V2 - 0.25*q2_M2*xiF2V2);

  double xsec = Gfactor * (A + sign*B*s_u/M2 + C*s_u*s_u/M4);

  // Apply given scaling factor
  xsec *= fXSecScale;

#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
  LOG("LwlynSmith", pDEBUG)
     << "dXSec[QEL]/dQ2 [FreeN](E = "<< E << ", Q2 = "<< -q2 << ") = "<< xsec;
  LOG("LwlynSmith", pDEBUG)
                 << "A(Q2) = " << A << ", B(Q2) = " << B << ", C(Q2) = " << C;
#endif

  //----- The algorithm computes dxsec/dQ2
  //      Check whether variable tranformation is needed
  if(kps!=kPSQ2fE) {
    double J = utils::kinematics::Jacobian(interaction,kPSQ2fE,kps);

#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
    LOG("LwlynSmith", pDEBUG)
     << "Jacobian for transformation to: "
                  << KinePhaseSpace::AsString(kps) << ", J = " << J;
#endif
    xsec *= J;
  }

  //----- if requested return the free nucleon xsec even for input nuclear tgt
  if( interaction->TestBit(kIAssumeFreeNucleon) ) return xsec;

  //----- compute nuclear suppression factor
  //      (R(Q2) is adapted from NeuGEN - see comments therein)
  double R = nuclear::NuclQELXSecSuppression("Default", 0.5, interaction);

  //----- number of scattering centers in the target
  int nucpdgc = target.HitNucPdg();
  int NNucl = (pdg::IsProton(nucpdgc)) ? target.Z() : target.N();

#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
  LOG("LwlynSmith", pDEBUG)
       << "Nuclear suppression factor R(Q2) = " << R << ", NNucl = " << NNucl;
#endif

  xsec *= (R*NNucl); // nuclear xsec

  return xsec;
}
//____________________________________________________________________________
double LwlynSmithQELCCPXSec::FullDifferentialXSec(const Interaction*  interaction)
  const
{
  // First we need access to all of the particles in the interaction
  // The particles were stored in the lab frame
  const Kinematics&   kinematics = interaction -> Kine();
  const InitialState& init_state = interaction -> InitState();

  const Target& tgt = init_state.Tgt();

  const TLorentzVector leptonMom = kinematics.FSLeptonP4();
  const TLorentzVector outNucleonMom = kinematics.HadSystP4();

  // Apply Pauli blocking if enabled
  if ( fDoPauliBlocking && tgt.IsNucleus() && !interaction->TestBit(kIAssumeFreeNucleon) ) {
    int final_nucleon_pdg = interaction->RecoilNucleonPdg();
    double kF = fPauliBlocker->GetFermiMomentum(tgt, final_nucleon_pdg,
      tgt.HitNucPosition());
    double pNf = outNucleonMom.P();
    if ( pNf < kF ) return 0.;
  }

  // Note that GetProbeP4 defaults to returning the probe 4-momentum in the
  // struck nucleon rest frame, so we have to explicitly ask for the lab frame
  // here
  TLorentzVector * tempNeutrino = init_state.GetProbeP4(kRfLab);
  TLorentzVector neutrinoMom = *tempNeutrino;
  delete tempNeutrino;
  TLorentzVector * inNucleonMom = init_state.TgtPtr()->HitNucP4Ptr();

  // *** CALCULATION OF "q" and "qTilde" ***
  // According to the de Forest prescription for handling the off-shell
  // initial struck nucleon, the cross section calculation should proceed
  // as if for a free nucleon, except that an effective value of the 4-momentum
  // transfer qTilde should be used in which the difference between the on-
  // and off-shell energies of the hit nucleon has been subtracted from the
  // energy transfer q0.

  // HitNucMass() looks up the PDGLibrary (on-shell) value for the initial
  // struck nucleon
  double mNi = init_state.Tgt().HitNucMass();

  // Hadronic matrix element for CC neutrino interactions should really use
  // the "nucleon mass," i.e., the mean of the proton and neutrino masses.
  // This expression would also work for NC and EM scattering (since the
  // initial and final on-shell nucleon masses would be the same)
  double mNucleon = ( mNi + interaction->RecoilNucleon()->Mass() ) / 2.;

  // Ordinary 4-momentum transfer
  TLorentzVector qP4 = neutrinoMom - leptonMom;

  // Initial struck nucleon 4-momentum in which it is forced to be on-shell
  double inNucleonOnShellEnergy = std::sqrt( std::pow(mNi, 2)
    + std::pow(inNucleonMom->P(), 2) );
  TLorentzVector inNucleonMomOnShell( inNucleonMom->Vect(), inNucleonOnShellEnergy );

  // Effective 4-momentum transfer (according to the deForest prescription) for
  // use in computing the hadronic tensor
  TLorentzVector qTildeP4 = outNucleonMom - inNucleonMomOnShell;

  double Q2 = -1. * qP4.Mag2();
  double Q2tilde = -1. * qTildeP4.Mag2();

  // If the binding energy correction causes an unphysical value
  // of q0Tilde or Q2tilde, just return 0.
  if ( qTildeP4.E() <= 0. && init_state.Tgt().IsNucleus() &&
    !interaction->TestBit(kIAssumeFreeNucleon) ) return 0.;
  if ( Q2tilde <= 0. ) return 0.;

  // Store Q2tilde in the kinematic variable representing Q2.
  // This will ensure that the form factors are calculated correctly
  // using the de Forest prescription (Q2tilde instead of Q2).
  interaction->KinePtr()->SetQ2(Q2tilde);

  // Calculate the QEL form factors
  fFormFactors.Calculate(interaction);

  double F1V   = fFormFactors.F1V();
  double xiF2V = fFormFactors.xiF2V();
  double FA    = fFormFactors.FA();
  double Fp    = fFormFactors.Fp();

  // Restore Q2 in the interaction's kinematic variables
  // now that the form factors have been computed
  interaction->KinePtr()->SetQ2( Q2 );

  // Overall factor in the differential cross section
  double Gfactor = kGF2*fCos8c2 / ( 8. * kPi * kPi * inNucleonOnShellEnergy
    * neutrinoMom.E() * outNucleonMom.E() * leptonMom.E() );

  // Now, we can calculate the cross section
  double tau = Q2tilde / (4 * std::pow(mNucleon, 2));
  double h1 = FA*FA*(1 + tau) + tau*(F1V + xiF2V)*(F1V + xiF2V);
  double h2 = FA*FA + F1V*F1V + tau*xiF2V*xiF2V;
  double h3 = 2.0 * FA * (F1V + xiF2V);
  double h4 = 0.25 * xiF2V*xiF2V *(1-tau) + 0.5*F1V*xiF2V + FA*Fp - tau*Fp*Fp;

  bool is_neutrino = pdg::IsNeutrino(init_state.ProbePdg());
  int sign = (is_neutrino) ? -1 : 1;
  double l1 = 2*neutrinoMom.Dot(leptonMom)*std::pow(mNucleon, 2);
  double l2 = 2*(neutrinoMom.Dot(inNucleonMomOnShell)) * (inNucleonMomOnShell.Dot(leptonMom)) - neutrinoMom.Dot(leptonMom)*std::pow(mNucleon, 2);
  double l3 = (neutrinoMom.Dot(inNucleonMomOnShell) * qTildeP4.Dot(leptonMom)) - (neutrinoMom.Dot(qTildeP4) * leptonMom.Dot(inNucleonMomOnShell));
  l3 *= sign;
  double l4 = neutrinoMom.Dot(leptonMom) * qTildeP4.Dot(qTildeP4) - 2*neutrinoMom.Dot(qTildeP4)*leptonMom.Dot(qTildeP4);
  double l5 = neutrinoMom.Dot(inNucleonMomOnShell) * leptonMom.Dot(qTildeP4) + leptonMom.Dot(inNucleonMomOnShell)*neutrinoMom.Dot(qTildeP4) - neutrinoMom.Dot(leptonMom)*inNucleonMomOnShell.Dot(qTildeP4);

  double LH = 2 *(l1*h1 + l2*h2 + l3*h3 + l4*h4 + l5*h2);

  double xsec = Gfactor * LH;

  // Apply the factor that arises from elimination of the energy-conserving
  // delta function
  xsec *= genie::utils::EnergyDeltaFunctionSolutionQEL( *interaction );

  // Apply given scaling factor
  xsec *= fXSecScale;

  // Number of scattering centers in the target
  const Target & target = init_state.Tgt();
  int nucpdgc = target.HitNucPdg();
  int NNucl = (pdg::IsProton(nucpdgc)) ? target.Z() : target.N();

#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
  LOG("LwlynSmith", pDEBUG)
    << "Nuclear suppression factor R(Q2) = " << R << ", NNucl = " << NNucl;
#endif

  xsec *= NNucl; // nuclear xsec

  return xsec;

}
//____________________________________________________________________________
double LwlynSmithQELCCPXSec::Integral(const Interaction * in) const
{
  // If we're using the new spline generation method (which integrates
  // over the kPSQELEvGen phase space used by QELEventGenerator) then
  // let the cross section integrator do all of the work. It's smart
  // enough to handle free nucleon vs. nuclear targets, different
  // nuclear models (including the local Fermi gas model), etc.
  // TODO: think about doing this in a better way
  if ( fXSecIntegrator->Id().Name() == "genie::NewQELXSec" ) {
    return fXSecIntegrator->Integrate(this, in);
  }

  // Otherwise, use the old integration method (kept for use with
  // the historical default G18_00x series of tunes)
  bool nuclear_target = in->InitState().Tgt().IsNucleus();
  if(!nuclear_target || !fDoAvgOverNucleonMomentum) {
    return fXSecIntegrator->Integrate(this,in);
  }

  double E = in->InitState().ProbeE(kRfHitNucRest);
  if(fLFG || E < fEnergyCutOff) {
    // clone the input interaction so as to tweak the
    // hit nucleon 4-momentum in the averaging loop
    Interaction in_curr(*in);

    // hit target
    Target * tgt = in_curr.InitState().TgtPtr();

    // get nuclear masses (init & final state nucleus)
    int nucleon_pdgc = tgt->HitNucPdg();
    bool is_p = pdg::IsProton(nucleon_pdgc);
    int Zi = tgt->Z();
    int Ai = tgt->A();
    int Zf = (is_p) ? Zi-1 : Zi;
    int Af = Ai-1;
    PDGLibrary * pdglib = PDGLibrary::Instance();
    TParticlePDG * nucl_i = pdglib->Find( pdg::IonPdgCode(Ai, Zi) );
    TParticlePDG * nucl_f = pdglib->Find( pdg::IonPdgCode(Af, Zf) );
    if(!nucl_f) {
      LOG("LwlynSmith", pFATAL)
        << "Unknwown nuclear target! No target with code: "
        << pdg::IonPdgCode(Af, Zf) << " in PDGLibrary!";
      exit(1);
    }
    double Mi  = nucl_i -> Mass(); // initial nucleus mass
    double Mf  = nucl_f -> Mass(); // remnant nucleus mass

    // throw nucleons with fermi momenta and binding energies
    // generated according to the current nuclear model for the
    // input target and average the cross section
    double xsec_sum = 0.;
    const int nnuc = 2000;
    // VertexGenerator for generating a position before generating
    // each nucleon
    VertexGenerator * vg = new VertexGenerator();
    vg->Configure("Default");
    for(int inuc=0;inuc<nnuc;inuc++){
      // Generate a position in the nucleus
      TVector3 nucpos = vg->GenerateVertex(&in_curr,tgt->A());
      tgt->SetHitNucPosition(nucpos.Mag());

      // Generate a nucleon
      fNuclModel->GenerateNucleon(*tgt, nucpos.Mag());
      TVector3 p3N = fNuclModel->Momentum3();
      double   EN  = Mi - TMath::Sqrt(p3N.Mag2() + Mf*Mf);
      TLorentzVector* p4N = tgt->HitNucP4Ptr();
      p4N->SetPx (p3N.Px());
      p4N->SetPy (p3N.Py());
      p4N->SetPz (p3N.Pz());
      p4N->SetE  (EN);

      double xsec = fXSecIntegrator->Integrate(this,&in_curr);
      xsec_sum += xsec;
    }
    double xsec_avg = xsec_sum / nnuc;
    delete vg;
    return xsec_avg;
  }else{
    return fXSecIntegrator->Integrate(this,in);
  }
}
//____________________________________________________________________________
bool LwlynSmithQELCCPXSec::ValidProcess(const Interaction * interaction) const
{
  if(interaction->TestBit(kISkipProcessChk)) return true;

  const InitialState & init_state = interaction->InitState();
  const ProcessInfo &  proc_info  = interaction->ProcInfo();

  if(!proc_info.IsQuasiElastic()) return false;

  int  nuc = init_state.Tgt().HitNucPdg();
  int  nu  = init_state.ProbePdg();

  bool isP   = pdg::IsProton(nuc);
  bool isN   = pdg::IsNeutron(nuc);
  bool isnu  = pdg::IsNeutrino(nu);
  bool isnub = pdg::IsAntiNeutrino(nu);

  bool prcok = proc_info.IsWeakCC() && ((isP&&isnub) || (isN&&isnu));
  if(!prcok) return false;

  return true;
}
//____________________________________________________________________________
void LwlynSmithQELCCPXSec::Configure(const Registry & config)
{
  Algorithm::Configure(config);
  this->LoadConfig();
}
//____________________________________________________________________________
void LwlynSmithQELCCPXSec::Configure(string config)
{
  Algorithm::Configure(config);
  this->LoadConfig();
}
//____________________________________________________________________________
void LwlynSmithQELCCPXSec::LoadConfig(void)
{
  // Cross section scaling factor
  GetParamDef( "QEL-CC-XSecScale", fXSecScale, 1. ) ;

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

   // load QEL form factors model
  fFormFactorsModel = dynamic_cast<const QELFormFactorsModelI *> (
                                             this->SubAlg("FormFactorsAlg"));
  assert(fFormFactorsModel);
  fFormFactors.SetModel(fFormFactorsModel); // <-- attach algorithm

   // load XSec Integrator
  fXSecIntegrator =
      dynamic_cast<const XSecIntegratorI *> (this->SubAlg("XSec-Integrator"));
  assert(fXSecIntegrator);

  // Get nuclear model for use in Integral()
  RgKey nuclkey = "IntegralNuclearModel";
  fNuclModel = dynamic_cast<const NuclearModelI *> (this->SubAlg(nuclkey));
  assert(fNuclModel);

  fLFG = fNuclModel->ModelType(Target()) == kNucmLocalFermiGas;

  bool average_over_nuc_mom ;
  GetParamDef( "IntegralAverageOverNucleonMomentum", average_over_nuc_mom, false ) ;
  // Always average over initial nucleons if the nuclear model is LFG
  fDoAvgOverNucleonMomentum = fLFG || average_over_nuc_mom ;

  fEnergyCutOff = 0.;

  // Get averaging cutoff energy
  GetParamDef("IntegralNuclearInfluenceCutoffEnergy", fEnergyCutOff, 2.0 ) ;

  // Method to use to calculate the binding energy of the initial hit nucleon when
  // generating splines
  std::string temp_binding_mode;
  GetParamDef( "IntegralNucleonBindingMode", temp_binding_mode, std::string("UseNuclearModel") );
  fIntegralNucleonBindingMode = genie::utils::StringToQELBindingMode( temp_binding_mode );

  // Get PauliBlocker for possible use in FullDifferentialXSec()
  GetParamDef( "IntegralNucleonBindingMode", temp_binding_mode, std::string("UseNuclearModel") );
  fPauliBlocker = dynamic_cast<const PauliBlocker*>( this->SubAlg("PauliBlockerAlg") );
  assert( fPauliBlocker );

  // Decide whether or not it should be used in FullDifferentialXSec
  GetParamDef( "DoPauliBlocking", fDoPauliBlocking, true );
}