GSLXSecFunc.cxx

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//____________________________________________________________________________
/*
 Copyright (c) 2003-2025, The GENIE Collaboration
 For the full text of the license visit http://copyright.genie-mc.org
 
 Costas Andreopoulos <c.andreopoulos \at cern.ch>
 University of Liverpool
 
 Changes required to implement the GENIE Boosted Dark Matter module
 were installed by Josh Berger (Univ. of Wisconsin)
 
 Changes required to implement the GENIE Dark Neutrino module
 were installed by Iker de Icaza (Univ. of Sussex)
*/
//____________________________________________________________________________
 
#include <cassert>
 
#include <TMath.h>
 
#include "Framework/EventGen/XSecAlgorithmI.h"
#include "Framework/Conventions/Constants.h"
#include "Framework/Conventions/GBuild.h"
#include "Framework/Conventions/Units.h"
#include "Framework/Conventions/KineVar.h"
#include "Framework/Conventions/KinePhaseSpace.h"
#include "Physics/XSectionIntegration/GSLXSecFunc.h"
#include "Framework/Interaction/Interaction.h"
#include "Framework/Messenger/Messenger.h"
#include "Framework/Numerical/MathUtils.h"
#include "Framework/Utils/KineUtils.h"
#include "Framework/Numerical/GSLUtils.h"
 
using namespace genie;
 
//____________________________________________________________________________
genie::utils::gsl::dXSec_dQ2_E::dXSec_dQ2_E(
    const XSecAlgorithmI * m, const Interaction * i, double scale) :
ROOT::Math::IBaseFunctionOneDim(),
fModel(m),
fInteraction(i),
fScale(scale)
{
 
}
genie::utils::gsl::dXSec_dQ2_E::~dXSec_dQ2_E()
{
 
}
unsigned int genie::utils::gsl::dXSec_dQ2_E::NDim(void) const
{
  return 1;
}
double genie::utils::gsl::dXSec_dQ2_E::DoEval(double xin) const
{
// inputs:
//    Q2 [GeV^2]
// outputs:
//   differential cross section [10^-38 cm^2 / GeV^2]
//
  double Q2 = xin;
  fInteraction->KinePtr()->SetQ2(Q2);
  double xsec = fModel->XSec(fInteraction, kPSQ2fE);
#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
  LOG("GSLXSecFunc", pDEBUG) << "xsec(Q2 = " << Q2 << ") = " << xsec;
#endif
  return fScale*xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionOneDim *
   genie::utils::gsl::dXSec_dQ2_E::Clone() const
{
  return
    new genie::utils::gsl::dXSec_dQ2_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::dXSec_dy_E::dXSec_dy_E(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionOneDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::dXSec_dy_E::~dXSec_dy_E()
{
 
}
unsigned int genie::utils::gsl::dXSec_dy_E::NDim(void) const
{
  return 1;
}
double genie::utils::gsl::dXSec_dy_E::DoEval(double xin) const
{
// inputs:
//    y [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  double y = xin;
  fInteraction->KinePtr()->Sety(y);
  double xsec = fModel->XSec(fInteraction, kPSyfE);
#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
  LOG("GXSecFunc", pDEBUG) << "xsec(y = " << y << ") = " << xsec;
#endif
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionOneDim *
   genie::utils::gsl::dXSec_dy_E::Clone() const
{
  return
    new genie::utils::gsl::dXSec_dy_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::dXSec_dEDNu_E::dXSec_dEDNu_E(
  const XSecAlgorithmI * m, const Interaction * i,
  double DNuMass, double scale) :
  ROOT::Math::IBaseFunctionOneDim(),
  fModel(m),
  fInteraction(i),
  fDNuMass(DNuMass),
  fScale(scale)
{
 
}
genie::utils::gsl::dXSec_dEDNu_E::~dXSec_dEDNu_E()
{
 
}
unsigned int genie::utils::gsl::dXSec_dEDNu_E::NDim(void) const
{
  return 1;
}
double genie::utils::gsl::dXSec_dEDNu_E::DoEval(double xin) const
{
// inputs:
//    DNuEnergy [GeV]
// outputs:
//   differential cross section [10^-38 cm^2 / GeV]
//
 
  double DNuEnergy = xin;
  double fDNuMass2 = fDNuMass*fDNuMass;
 
  Kinematics * kinematics = fInteraction->KinePtr();
  const TLorentzVector * P4_nu = fInteraction->InitStatePtr()->GetProbeP4(kRfLab);
  double E_nu = P4_nu->E();
  double M_target = fInteraction->InitState().Tgt().Mass();
 
  double ETimesM = E_nu * M_target;
  double EPlusM  = E_nu + M_target;
 
  double p_DNu = TMath::Sqrt(DNuEnergy*DNuEnergy - fDNuMass2);
  double cos_theta_DNu = (DNuEnergy*(EPlusM) - ETimesM - 0.5*fDNuMass2) / (E_nu * p_DNu);
  double theta_DNu = TMath::ACos(cos_theta_DNu);
  TVector3 DNu_3vector = TVector3(0,0,0);
  DNu_3vector.SetMagThetaPhi(p_DNu, theta_DNu, 0.);
  TLorentzVector P4_DNu = TLorentzVector(DNu_3vector, DNuEnergy);
  kinematics->SetFSLeptonP4(P4_DNu);
 
  TVector3 target_3vector = P4_nu->Vect() - DNu_3vector;
  double E_target = E_nu + M_target - DNuEnergy;
  TLorentzVector P4_target = TLorentzVector(target_3vector , E_target);
  kinematics->SetHadSystP4(P4_target);
  kinematics->SetQ2(2.*M_target*(E_target-M_target));
 
  delete P4_nu;
  double xsec = fModel->XSec(fInteraction, kPSEDNufE);
#ifdef __GENIE_LOW_LEVEL_MESG_ENABLED__
  LOG("GSLXSecFunc", pDEBUG) << "xsec(DNuEnergy = " << DNuEnergy << ") = " << xsec;
#endif
 
  return fScale*xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionOneDim *
genie::utils::gsl::dXSec_dEDNu_E::Clone() const
{
  return
    new genie::utils::gsl::dXSec_dEDNu_E(fModel, fInteraction, fDNuMass);
}
Range1D_t genie::utils::gsl::dXSec_dEDNu_E::IntegrationRange() const
{
  // look at valid angles section at tech note
  const double E  = fInteraction->InitState().ProbeE(kRfLab);
  const double M = fInteraction->InitState().Tgt().Mass();
  const double M2 = M * M;
  double fDNuMass2 = fDNuMass*fDNuMass;
 
  const double A = M2 +  2.*M*E;
  const double B = (M+E) * (E*M + 0.5*fDNuMass2);
  const double C = E*E *(M2 + fDNuMass2) + E*M*fDNuMass2 + 0.25*fDNuMass2*fDNuMass2;
  const double D = sqrt(B*B - A*C);
  // Range1D_t DNuEnergy((B - D)/A, (B + D)/A);
  // 12_04_2025 applying an upper bound on Ttarget at 1 GeV^2/2M --> lower bound on the integration range
  //            Otherwise the integral does funny things. 
  const double Tmax = std::min(E - ((B - D) / A), (1. / (2 * M)));
  Range1D_t DNuEnergy(E - Tmax, (B + D) / A);
  return DNuEnergy;
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dxdy_E::d2XSec_dxdy_E(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::d2XSec_dxdy_E::~d2XSec_dxdy_E()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dxdy_E::NDim(void) const
{
  return 2;
}
double genie::utils::gsl::d2XSec_dxdy_E::DoEval(const double * xin) const
{
// inputs:
//    x [-]
//    y [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  double x = xin[0];
  double y = xin[1];
  fInteraction->KinePtr()->Setx(x);
  fInteraction->KinePtr()->Sety(y);
  kinematics::UpdateWQ2FromXY(fInteraction);
  double xsec = fModel->XSec(fInteraction, kPSxyfE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d2XSec_dxdy_E::Clone() const
{
  return
    new genie::utils::gsl::d2XSec_dxdy_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dQ2dy_E::d2XSec_dQ2dy_E(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::d2XSec_dQ2dy_E::~d2XSec_dQ2dy_E()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dQ2dy_E::NDim(void) const
{
  return 2;
}
double genie::utils::gsl::d2XSec_dQ2dy_E::DoEval(const double * xin) const
{
// inputs:
//   Q2 [-]
//    y [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  double Q2 = xin[0];
  double  y = xin[1];
  fInteraction->KinePtr()->SetQ2(Q2);
  fInteraction->KinePtr()->Sety(y);
  kinematics::UpdateXFromQ2Y(fInteraction);
  double xsec = fModel->XSec(fInteraction, kPSQ2yfE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d2XSec_dQ2dy_E::Clone() const
{
  return
    new genie::utils::gsl::d2XSec_dQ2dy_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dlog10xdlog10Q2_E::d2XSec_dlog10xdlog10Q2_E(
     const XSecAlgorithmI * m, const Interaction * i, double scale) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i),
fScale(scale)
{
  
}
genie::utils::gsl::d2XSec_dlog10xdlog10Q2_E::~d2XSec_dlog10xdlog10Q2_E()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dlog10xdlog10Q2_E::NDim(void) const
{
  return 2;
}
double genie::utils::gsl::d2XSec_dlog10xdlog10Q2_E::DoEval(const double * xin) const
{
// inputs:  
//  log10(x) [-]
// log10(Q2) [-]
// outputs: 
//   differential cross section [10^-38 cm^2]
//
  fInteraction->KinePtr()->Setx(TMath::Power(10,xin[0]));
  fInteraction->KinePtr()->SetQ2(TMath::Power(10,xin[1]));
  kinematics::UpdateWYFromXQ2(fInteraction);
  double xsec = fModel->XSec(fInteraction, kPSlog10xlog10Q2fE);
  return fScale*xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionMultiDim * 
   genie::utils::gsl::d2XSec_dlog10xdlog10Q2_E::Clone() const
{
  return 
    new genie::utils::gsl::d2XSec_dlog10xdlog10Q2_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dQ2dydt_E::d2XSec_dQ2dydt_E(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::d2XSec_dQ2dydt_E::~d2XSec_dQ2dydt_E()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dQ2dydt_E::NDim(void) const
{
  return 3;
}
double genie::utils::gsl::d2XSec_dQ2dydt_E::DoEval(const double * xin) const
{
// inputs:
//   Q2 [-]
//    y [-]
//    t [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  //double  E = fInteraction->InitState().ProbeE(kRfLab);
  double Q2 = xin[0];
  double  y = xin[1];
  double  t = xin[2];
  fInteraction->KinePtr()->SetQ2(Q2);
  fInteraction->KinePtr()->Sety(y);
  fInteraction->KinePtr()->Sett(t);
  kinematics::UpdateXFromQ2Y(fInteraction);
  double xsec = fModel->XSec(fInteraction, kPSQ2yfE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d2XSec_dQ2dydt_E::Clone() const
{
  return
    new genie::utils::gsl::d2XSec_dQ2dydt_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::d3XSec_dxdydt_E::d3XSec_dxdydt_E(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::d3XSec_dxdydt_E::~d3XSec_dxdydt_E()
{
 
}
unsigned int genie::utils::gsl::d3XSec_dxdydt_E::NDim(void) const
{
  return 3;
}
double genie::utils::gsl::d3XSec_dxdydt_E::DoEval(const double * xin) const
{
// inputs:
//    x [-]
//    y [-]
//    t [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  //double  E = fInteraction->InitState().ProbeE(kRfLab);
  double  x = xin[0];
  double  y = xin[1];
  double  t = xin[2];
  fInteraction->KinePtr()->Setx(x);
  fInteraction->KinePtr()->Sety(y);
  fInteraction->KinePtr()->Sett(t);
  double xsec = fModel->XSec(fInteraction, kPSxytfE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d3XSec_dxdydt_E::Clone() const
{
  return
    new genie::utils::gsl::d3XSec_dxdydt_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dWdQ2_E::d2XSec_dWdQ2_E(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::d2XSec_dWdQ2_E::~d2XSec_dWdQ2_E()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dWdQ2_E::NDim(void) const
{
  return 2;
}
double genie::utils::gsl::d2XSec_dWdQ2_E::DoEval(const double * xin) const
{
// inputs:
//    W  [GeV]
//    Q2 [GeV^2]
// outputs:
//   differential cross section [10^-38 cm^2/GeV^3]
//
  double W  = xin[0];
  double Q2 = xin[1];
  fInteraction->KinePtr()->SetW(W);
  fInteraction->KinePtr()->SetQ2(Q2);
  if(fInteraction->ProcInfo().IsDeepInelastic() ||
     fInteraction->ProcInfo().IsDarkMatterDeepInelastic()) {
    double x=0,y=0;
    double E = fInteraction->InitState().ProbeE(kRfHitNucRest);
    double M = fInteraction->InitState().Tgt().HitNucP4Ptr()->M();
 
    kinematics::WQ2toXY(E,M,W,Q2,x,y);
    fInteraction->KinePtr()->Setx(x);
    fInteraction->KinePtr()->Sety(y);
  }
  double xsec = fModel->XSec(fInteraction, kPSWQ2fE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d2XSec_dWdQ2_E::Clone() const
{
  return
    new genie::utils::gsl::d2XSec_dWdQ2_E(fModel,fInteraction);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dxdy_Ex::d2XSec_dxdy_Ex(
     const XSecAlgorithmI * m, const Interaction * i, double x) :
ROOT::Math::IBaseFunctionOneDim(),
fModel(m),
fInteraction(i),
fx(x)
{
 
}
genie::utils::gsl::d2XSec_dxdy_Ex::~d2XSec_dxdy_Ex()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dxdy_Ex::NDim(void) const
{
  return 1;
}
double genie::utils::gsl::d2XSec_dxdy_Ex::DoEval(double xin) const
{
// inputs:
//    y [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  double y = xin;
  fInteraction->KinePtr()->Setx(fx);
  fInteraction->KinePtr()->Sety(y);
  double xsec = fModel->XSec(fInteraction, kPSxyfE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionOneDim *
   genie::utils::gsl::d2XSec_dxdy_Ex::Clone() const
{
  return
    new genie::utils::gsl::d2XSec_dxdy_Ex(fModel,fInteraction,fx);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dxdy_Ey::d2XSec_dxdy_Ey(
     const XSecAlgorithmI * m, const Interaction * i, double y) :
ROOT::Math::IBaseFunctionOneDim(),
fModel(m),
fInteraction(i),
fy(y)
{
 
}
genie::utils::gsl::d2XSec_dxdy_Ey::~d2XSec_dxdy_Ey()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dxdy_Ey::NDim(void) const
{
  return 1;
}
double genie::utils::gsl::d2XSec_dxdy_Ey::DoEval(double xin) const
{
// inputs:
//    x [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  double x = xin;
  fInteraction->KinePtr()->Setx(x);
  fInteraction->KinePtr()->Sety(fy);
  double xsec = fModel->XSec(fInteraction, kPSxyfE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionOneDim *
   genie::utils::gsl::d2XSec_dxdy_Ey::Clone() const
{
  return
    new genie::utils::gsl::d2XSec_dxdy_Ey(fModel,fInteraction,fy);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dWdQ2_EW::d2XSec_dWdQ2_EW(
     const XSecAlgorithmI * m, const Interaction * i, double W) :
ROOT::Math::IBaseFunctionOneDim(),
fModel(m),
fInteraction(i),
fW(W)
{
 
}
genie::utils::gsl::d2XSec_dWdQ2_EW::~d2XSec_dWdQ2_EW()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dWdQ2_EW::NDim(void) const
{
  return 1;
}
double genie::utils::gsl::d2XSec_dWdQ2_EW::DoEval(double xin) const
{
// inputs:
//   Q2 [GeV^2]
// outputs:
//   differential cross section [10^-38 cm^2/GeV^3]
//
  double Q2 = xin;
  fInteraction->KinePtr()->SetW(fW);
  fInteraction->KinePtr()->SetQ2(Q2);
  double xsec = fModel->XSec(fInteraction, kPSWQ2fE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionOneDim *
   genie::utils::gsl::d2XSec_dWdQ2_EW::Clone(void) const
{
  return
    new genie::utils::gsl::d2XSec_dWdQ2_EW(fModel,fInteraction,fW);
}
//____________________________________________________________________________
genie::utils::gsl::d2XSec_dWdQ2_EQ2::d2XSec_dWdQ2_EQ2(
     const XSecAlgorithmI * m, const Interaction * i, double Q2) :
ROOT::Math::IBaseFunctionOneDim(),
fModel(m),
fInteraction(i),
fQ2(Q2)
{
 
}
genie::utils::gsl::d2XSec_dWdQ2_EQ2::~d2XSec_dWdQ2_EQ2()
{
 
}
unsigned int genie::utils::gsl::d2XSec_dWdQ2_EQ2::NDim(void) const
{
  return 1;
}
double genie::utils::gsl::d2XSec_dWdQ2_EQ2::DoEval(double xin) const
{
// inputs:
//   W [GeV]
// outputs:
//   differential cross section [10^-38 cm^2/GeV^3]
//
  double W = xin;
  fInteraction->KinePtr()->SetW(W);
  fInteraction->KinePtr()->SetQ2(fQ2);
  double xsec = fModel->XSec(fInteraction,kPSWQ2fE);
  return xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionOneDim *
   genie::utils::gsl::d2XSec_dWdQ2_EQ2::Clone() const
{
  return
   new genie::utils::gsl::d2XSec_dWdQ2_EQ2(fModel,fInteraction,fQ2);
}
//____________________________________________________________________________
//
//  This just returns the 5-D differential cross section
//
genie::utils::gsl::d5XSecAR::d5XSecAR(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i),
flip(false)
{
 
}
genie::utils::gsl::d5XSecAR::~d5XSecAR()
{
}
 
unsigned int genie::utils::gsl::d5XSecAR::NDim(void) const
{
  return 5;
}
double genie::utils::gsl::d5XSecAR::DoEval(const double * xin) const
{
// inputs:
//    x [-]
//    y [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
 
  Kinematics * kinematics = fInteraction->KinePtr();
  const TLorentzVector * P4_nu = fInteraction->InitStatePtr()->GetProbeP4(kRfLab);
  double E_nu       = P4_nu->E();
 
  double E_l       = xin[0];
  double theta_l   = xin[1];
  double phi_l     = xin[2];
  double theta_pi  = xin[3];
  double phi_pi    = xin[4];
 
  double E_pi= E_nu-E_l;
 
  double y = E_pi/E_nu;
 
  double m_l = fInteraction->FSPrimLepton()->Mass();
  if (E_l < m_l) {
    return 0.;
  }
 
  double m_pi;
  if ( fInteraction->ProcInfo().IsWeakCC() ) {
    m_pi = constants::kPionMass;
  }
  else {
    m_pi = constants::kPi0Mass;
  }
 
 
  double p_l = TMath::Sqrt(E_l*E_l - m_l*m_l);
  TVector3 lepton_3vector = TVector3(0,0,0);
  lepton_3vector.SetMagThetaPhi(p_l,theta_l,phi_l);
  TLorentzVector P4_lep    = TLorentzVector(lepton_3vector , E_l );
 
  double p_pi = TMath::Sqrt(E_pi*E_pi - m_pi*m_pi);
  TVector3 pion_3vector = TVector3(0,0,0);
  pion_3vector.SetMagThetaPhi(p_pi,theta_pi,phi_pi);
  TLorentzVector P4_pion   = TLorentzVector(pion_3vector   , E_pi);
 
  double Q2 = -(*P4_nu-P4_lep).Mag2();
 
  double x = Q2/(2*E_pi*constants::kNucleonMass);
 
  Range1D_t xlim = fInteraction->PhaseSpace().XLim();
 
  if ( x <  xlim.min || x > xlim.max ) {
    return 0.;
  }
 
  kinematics->Setx(x);
  kinematics->Sety(y);
  kinematics::UpdateWQ2FromXY(fInteraction);
 
  kinematics->SetFSLeptonP4(P4_lep );
  kinematics->SetHadSystP4 (P4_pion); // use Hadronic System variable to store pion momentum
 
  double xsec = fModel->XSec(fInteraction);
  if (xsec>0 && flip) {
    xsec = xsec*-1.0;
  }
  delete P4_nu;
  //return xsec/(1E-38 * units::cm2);
  return xsec;
}
 
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d5XSecAR::Clone() const
{
  return
    new genie::utils::gsl::d5XSecAR(fModel,fInteraction);
}
 
//____________________________________________________________________________
//
//  This is the original 5-D cross-section that Steve D coded
//
genie::utils::gsl::d5Xsec_dEldOmegaldOmegapi::d5Xsec_dEldOmegaldOmegapi(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::d5Xsec_dEldOmegaldOmegapi::~d5Xsec_dEldOmegaldOmegapi()
{
 
}
unsigned int genie::utils::gsl::d5Xsec_dEldOmegaldOmegapi::NDim(void) const
{
  return 5;
}
double genie::utils::gsl::d5Xsec_dEldOmegaldOmegapi::DoEval(const double * xin) const
{
// inputs:
//    x [-]
//    y [-]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  Kinematics * kinematics = fInteraction->KinePtr();
  const TLorentzVector * P4_nu = fInteraction->InitStatePtr()->GetProbeP4(kRfLab);
  double E_nu       = P4_nu->E();
 
  double E_l       = xin[0];
  double theta_l   = xin[1];
  double phi_l     = xin[2];
  double theta_pi  = xin[3];
  double phi_pi    = xin[4];
 
  double E_pi= E_nu-E_l;
 
  double y = E_pi/E_nu;
 
  double m_l = fInteraction->FSPrimLepton()->Mass();
  if (E_l < m_l) {
    return 0.;
  }
 
  double m_pi;
  if ( fInteraction->ProcInfo().IsWeakCC() ) {
    m_pi = constants::kPionMass;
  }
  else {
    m_pi = constants::kPi0Mass;
  }
 
  double p_l = TMath::Sqrt(E_l*E_l - m_l*m_l);
  TVector3 lepton_3vector = TVector3(0,0,0);
  lepton_3vector.SetMagThetaPhi(p_l,theta_l,phi_l);
  TLorentzVector P4_lep    = TLorentzVector(lepton_3vector , E_l );
 
  double p_pi = TMath::Sqrt(E_pi*E_pi - m_pi*m_pi);
  TVector3 pion_3vector = TVector3(0,0,0);
  pion_3vector.SetMagThetaPhi(p_pi,theta_pi,phi_pi);
  TLorentzVector P4_pion   = TLorentzVector(pion_3vector   , E_pi);
 
  double Q2 = -(*P4_nu-P4_lep).Mag2();
 
  double x = Q2/(2*E_pi*constants::kNucleonMass);
 
  Range1D_t xlim = fInteraction->PhaseSpace().XLim();
 
  if ( x <  xlim.min || x > xlim.max ) {
    return 0.;
  }
 
  kinematics->Setx(x);
  kinematics->Sety(y);
  kinematics::UpdateWQ2FromXY(fInteraction);
 
  kinematics->SetFSLeptonP4(P4_lep );
  kinematics->SetHadSystP4 (P4_pion); // use Hadronic System variable to store pion momentum
 
  delete P4_nu;
 
  double xsec = fModel->XSec(fInteraction)*TMath::Sin(theta_l)*TMath::Sin(theta_pi);
  return xsec/(1E-38 * units::cm2);
}
 
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d5Xsec_dEldOmegaldOmegapi::Clone() const
{
  return
    new genie::utils::gsl::d5Xsec_dEldOmegaldOmegapi(fModel,fInteraction);
}
 
//____________________________________________________________________________
//
// This is the same as the 5d space that Steve D coded,
// But we remove the integration of phi_l
//
 
genie::utils::gsl::d4Xsec_dEldThetaldOmegapi::d4Xsec_dEldThetaldOmegapi(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i)
{
 
}
genie::utils::gsl::d4Xsec_dEldThetaldOmegapi::~d4Xsec_dEldThetaldOmegapi()
{
 
}
unsigned int genie::utils::gsl::d4Xsec_dEldThetaldOmegapi::NDim(void) const
{
  return 4;
}
double genie::utils::gsl::d4Xsec_dEldThetaldOmegapi::DoEval(const double * xin) const
{
// inputs:
//    El [GeV]
//    theta l [rad]
//    theta pi [rad]
//    phi pi [rad]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  Kinematics * kinematics = fInteraction->KinePtr();
  const TLorentzVector * P4_nu = fInteraction->InitStatePtr()->GetProbeP4(kRfLab);
  double E_nu       = P4_nu->E();
 
  double E_l       = xin[0];
  double theta_l   = xin[1];
  double phi_l     = 0.0;
  double theta_pi  = xin[2];
  double phi_pi    = xin[3];
 
  double sin_theta_l  = TMath::Sin(theta_l);
  double sin_theta_pi = TMath::Sin(theta_pi);
 
  double E_pi= E_nu-E_l;
 
  double y = E_pi/E_nu;
 
  double m_l = fInteraction->FSPrimLepton()->Mass();
  if (E_l < m_l) {
    return 0.;
  }
 
  double m_pi;
  if ( fInteraction->ProcInfo().IsWeakCC() ) {
    m_pi = constants::kPionMass;
  }
  else {
    m_pi = constants::kPi0Mass;
  }
 
  double p_l = TMath::Sqrt(E_l*E_l - m_l*m_l);
  TVector3 lepton_3vector = TVector3(0,0,0);
  lepton_3vector.SetMagThetaPhi(p_l,theta_l,phi_l);
  TLorentzVector P4_lep    = TLorentzVector(lepton_3vector , E_l );
 
  double p_pi = TMath::Sqrt(E_pi*E_pi - m_pi*m_pi);
  TVector3 pion_3vector = TVector3(0,0,0);
  pion_3vector.SetMagThetaPhi(p_pi,theta_pi,phi_pi);
  TLorentzVector P4_pion   = TLorentzVector(pion_3vector   , E_pi);
 
  double Q2 = -(*P4_nu-P4_lep).Mag2();
 
  double x = Q2/(2*E_pi*constants::kNucleonMass);
 
  Range1D_t xlim = fInteraction->PhaseSpace().XLim();
 
  if ( x <  xlim.min || x > xlim.max ) {
    return 0.;
  }
 
  kinematics->Setx(x);
  kinematics->Sety(y);
  kinematics::UpdateWQ2FromXY(fInteraction);
 
  kinematics->SetFSLeptonP4(P4_lep );
  kinematics->SetHadSystP4 (P4_pion); // use Hadronic System variable to store pion momentum
 
  delete P4_nu;
 
  double xsec = sin_theta_l * sin_theta_pi * fModel->XSec(fInteraction,kPSElOlTpifE);
  return fFactor * xsec/(1E-38 * units::cm2);
}
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d4Xsec_dEldThetaldOmegapi::Clone() const
{
  return
    new genie::utils::gsl::d4Xsec_dEldThetaldOmegapi(fModel,fInteraction);
}
void genie::utils::gsl::d4Xsec_dEldThetaldOmegapi::SetFactor(double factor)
{
  fFactor = factor;
}
double genie::utils::gsl::d4Xsec_dEldThetaldOmegapi::GetFactor(void) const
{
  return fFactor;
}
//____________________________________________________________________________
genie::utils::gsl::d3Xsec_dOmegaldThetapi::d3Xsec_dOmegaldThetapi(
     const XSecAlgorithmI * m, const Interaction * i) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i),
fElep(-1)
{
 
}
genie::utils::gsl::d3Xsec_dOmegaldThetapi::~d3Xsec_dOmegaldThetapi()
{
 
}
unsigned int genie::utils::gsl::d3Xsec_dOmegaldThetapi::NDim(void) const
{
  return 3;
}
double genie::utils::gsl::d3Xsec_dOmegaldThetapi::DoEval(const double * xin) const
{
// inputs:
//    theta l [rad]
//    phi_l   [rad]
//    phi pi  [rad]
// outputs:
//   differential cross section [10^-38 cm^2]
//
  Kinematics * kinematics = fInteraction->KinePtr();
  const TLorentzVector * P4_nu = fInteraction->InitStatePtr()->GetProbeP4(kRfLab);
  double E_nu = P4_nu->E();
 
  double E_l = fElep;
 
  double theta_l   = xin[0];
  double phi_l     = xin[1];
  double theta_pi  = xin[2];
  double phi_pi    = 0;
 
  double sin_theta_l  = TMath::Sin(theta_l);
  double sin_theta_pi = TMath::Sin(theta_pi);
 
  double E_pi= E_nu-E_l;
 
  double y = E_pi/E_nu;
 
  double m_l = fInteraction->FSPrimLepton()->Mass();
  if (E_l < m_l) {
    return 0.;
  }
 
  double m_pi;
  if ( fInteraction->ProcInfo().IsWeakCC() ) {
    m_pi = constants::kPionMass;
  }
  else {
    m_pi = constants::kPi0Mass;
  }
 
  double p_l = TMath::Sqrt(E_l*E_l - m_l*m_l);
  TVector3 lepton_3vector = TVector3(0,0,0);
  lepton_3vector.SetMagThetaPhi(p_l,theta_l,phi_l);
  TLorentzVector P4_lep    = TLorentzVector(lepton_3vector , E_l );
 
  double p_pi = TMath::Sqrt(E_pi*E_pi - m_pi*m_pi);
  TVector3 pion_3vector = TVector3(0,0,0);
  pion_3vector.SetMagThetaPhi(p_pi,theta_pi,phi_pi);
  TLorentzVector P4_pion   = TLorentzVector(pion_3vector   , E_pi);
 
  double Q2 = -(*P4_nu-P4_lep).Mag2();
 
  double x = Q2/(2*E_pi*constants::kNucleonMass);
 
  Range1D_t xlim = fInteraction->PhaseSpace().XLim();
 
  if ( x <  xlim.min || x > xlim.max ) {
    return 0.;
  }
 
  kinematics->Setx(x);
  kinematics->Sety(y);
  kinematics::UpdateWQ2FromXY(fInteraction);
 
  kinematics->SetFSLeptonP4(P4_lep );
  kinematics->SetHadSystP4 (P4_pion); // use Hadronic System variable to store pion momentum
 
  delete P4_nu;
 
  double xsec = (sin_theta_l * sin_theta_pi) * fModel->XSec(fInteraction,kPSElOlTpifE);
  return xsec/(1E-38 * units::cm2);
}
genie::utils::gsl::d3Xsec_dOmegaldThetapi *
   genie::utils::gsl::d3Xsec_dOmegaldThetapi::Clone() const
{
  d3Xsec_dOmegaldThetapi * out = new genie::utils::gsl::d3Xsec_dOmegaldThetapi(fModel,fInteraction);
  out->SetE_lep(fElep);
  return out;
}
//____________________________________________________________________________
void genie::utils::gsl::d3Xsec_dOmegaldThetapi::SetE_lep(double E_lepton) const
{
  fElep = E_lepton;
}
//____________________________________________________________________________
genie::utils::gsl::dXSec_dElep_AR::dXSec_dElep_AR(
    const XSecAlgorithmI * m, const Interaction * i,
    string gsl_nd_integrator_type, double gsl_relative_tolerance,
    unsigned int max_n_calls) :
ROOT::Math::IBaseFunctionOneDim(),
fModel(m),
fInteraction(i),
integrator(utils::gsl::IntegrationNDimTypeFromString(gsl_nd_integrator_type),1, gsl_relative_tolerance, max_n_calls),
fGSLIntegratorType(gsl_nd_integrator_type),
fGSLRelTol(gsl_relative_tolerance),
fGSLMaxCalls(max_n_calls)
{
  func = new utils::gsl::d3Xsec_dOmegaldThetapi(fModel, fInteraction);
 
  integrator.SetRelTolerance(gsl_relative_tolerance);
  integrator.SetFunction(*func);
 
  kine_min[0] = kine_min[1] = kine_min[2] = controls::kASmallNum;
 
  kine_max[0] = kine_max[2] = constants::kPi-controls::kASmallNum;
  kine_max[1] = 2 * constants::kPi-controls::kASmallNum;
}
genie::utils::gsl::dXSec_dElep_AR::~dXSec_dElep_AR()
{
  delete func;
}
double genie::utils::gsl::dXSec_dElep_AR::DoEval(double xin) const
{
  double Elep = xin;
  func->SetE_lep(Elep);
  double xsec = integrator.Integral(&kine_min[0], &kine_max[0]) ;
  LOG("GSLXSecFunc",pINFO) << "dXSec_dElep_AR >> "<<func->NDim()<<"d integral done. (Elep = " <<Elep<< " , dxsec/dElep = "<<xsec << ")";
  return xsec;
}
genie::utils::gsl::dXSec_dElep_AR *
   genie::utils::gsl::dXSec_dElep_AR::Clone() const
{
  return
    new genie::utils::gsl::dXSec_dElep_AR(fModel,fInteraction, fGSLIntegratorType, fGSLRelTol, fGSLMaxCalls);
}
//____________________________________________________________________________
genie::utils::gsl::dXSec_Log_Wrapper::dXSec_Log_Wrapper(
      const ROOT::Math::IBaseFunctionMultiDim * fn,
      bool * ifLog, double * mins, double * maxes) :
  fFn(fn),
  fIfLog(ifLog),
  fMins(mins),
  fMaxes(maxes)
{
}
genie::utils::gsl::dXSec_Log_Wrapper::~dXSec_Log_Wrapper()
{
}
//____________________________________________________________________________
 
// ROOT::Math::IBaseFunctionMultiDim interface
unsigned int genie::utils::gsl::dXSec_Log_Wrapper::NDim   (void) const
{
  return fFn->NDim();
}
//____________________________________________________________________________
double genie::utils::gsl::dXSec_Log_Wrapper::DoEval (const double * xin) const
{
  double * toEval = new double[this->NDim()];
  double a,b,x;
  for (unsigned int i = 0 ; i < this->NDim() ; i++ )
  {
    if (fIfLog[i]) {
      a = fMins[i];
      b = fMaxes[i];
      x = xin[i];
      toEval[i] = a + (b-a)/(constants::kNapierConst-1.) * (exp(x/(b-a)) - 1.);
    }
    else {
      toEval[i] = xin[i];
    }
  }
  double val = (*fFn)(toEval);
  delete[] toEval;
  return val;
}
ROOT::Math::IBaseFunctionMultiDim * genie::utils::gsl::dXSec_Log_Wrapper::Clone (void) const
{
  return new dXSec_Log_Wrapper(fFn,fIfLog,fMins,fMaxes);
}
 
//_____________________________________________________________________________
genie::utils::gsl::d2Xsec_dn1dn2_E::d2Xsec_dn1dn2_E(
     const XSecAlgorithmI * m, const Interaction * i, double scale) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i),
fScale(scale)
{
  
}
//____________________________________________________________________________
genie::utils::gsl::d2Xsec_dn1dn2_E::~d2Xsec_dn1dn2_E()
{
  
}   
//____________________________________________________________________________
unsigned int genie::utils::gsl::d2Xsec_dn1dn2_E::NDim(void) const
{
  return 2;
}
//____________________________________________________________________________
double genie::utils::gsl::d2Xsec_dn1dn2_E::DoEval(const double * xin) const
{
// inputs:
//    n1
//    n2
// outputs:
//   differential cross section (hbar=c=1 units)
//
 
  double n1 = xin[0];
  double n2 = xin[1];
 
  Kinematics * kinematics = fInteraction->KinePtr();
  kinematics->SetKV(kKVn1, n1);
  kinematics->SetKV(kKVn2, n2);
  
  double xsec = fModel->XSec(fInteraction, kPSn1n2fE); 
  return fScale*xsec/(1E-38 * units::cm2);
}
//____________________________________________________________________________
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d2Xsec_dn1dn2_E::Clone() const
{
  return
    new genie::utils::gsl::d2Xsec_dn1dn2_E(fModel,fInteraction);
}
//_____________________________________________________________________________
genie::utils::gsl::d2Xsec_dn1dn2dn3_E::d2Xsec_dn1dn2dn3_E(
     const XSecAlgorithmI * m, const Interaction * i, double scale) :
ROOT::Math::IBaseFunctionMultiDim(),
fModel(m),
fInteraction(i),
fScale(scale)
{
  
}
//____________________________________________________________________________
genie::utils::gsl::d2Xsec_dn1dn2dn3_E::~d2Xsec_dn1dn2dn3_E()
{
  
}   
//____________________________________________________________________________
unsigned int genie::utils::gsl::d2Xsec_dn1dn2dn3_E::NDim(void) const
{
  return 3;
}
//____________________________________________________________________________
double genie::utils::gsl::d2Xsec_dn1dn2dn3_E::DoEval(const double * xin) const
{
// inputs:
//    n1
//    n2
//    n3
// outputs:
//   differential cross section (hbar=c=1 units)
//
 
  double n1 = xin[0];
  double n2 = xin[1];
  double n3 = xin[2];
 
  Kinematics * kinematics = fInteraction->KinePtr();
  kinematics->SetKV(kKVn1, n1);
  kinematics->SetKV(kKVn2, n2);
  kinematics->SetKV(kKVn3, n3);
 
  double xsec = fModel->XSec(fInteraction, kPSn1n2n3fE); 
  return fScale*xsec/(1E-38 * units::cm2);
}
//____________________________________________________________________________
ROOT::Math::IBaseFunctionMultiDim *
   genie::utils::gsl::d2Xsec_dn1dn2dn3_E::Clone() const
{
  return
    new genie::utils::gsl::d2Xsec_dn1dn2dn3_E(fModel,fInteraction);
}