Double differential resonance cross section for P33 according to the Paschos, Lalakulich model. More...

#include <P33PaschosLalakulichPXSec.h>

Inheritance diagram for genie::P33PaschosLalakulichPXSec:

Collaboration diagram for genie::P33PaschosLalakulichPXSec:

Public Member Functions
	P33PaschosLalakulichPXSec ()

	P33PaschosLalakulichPXSec (string name)

virtual	~P33PaschosLalakulichPXSec ()

double	XSec (const Interaction *i, KinePhaseSpace_t k) const
	Compute the cross section for the input interaction. More...

double	Integral (const Interaction *i) const

bool	ValidProcess (const Interaction *i) const
	Can this cross section algorithm handle the input process? More...

void	Configure (const Registry &config)

void	Configure (string config)

Public Member Functions inherited from genie::XSecAlgorithmI
virtual	~XSecAlgorithmI ()

virtual bool	ValidKinematics (const Interaction *i) const
	Is the input kinematical point a physically allowed one? More...

Public Member Functions inherited from genie::Algorithm
virtual	~Algorithm ()

virtual void	FindConfig (void)

virtual const Registry &	GetConfig (void) const

Registry *	GetOwnedConfig (void)

virtual const AlgId &	Id (void) const
	Get algorithm ID. More...

virtual AlgStatus_t	GetStatus (void) const
	Get algorithm status. More...

virtual bool	AllowReconfig (void) const

virtual AlgCmp_t	Compare (const Algorithm *alg) const
	Compare with input algorithm. More...

virtual void	SetId (const AlgId &id)
	Set algorithm ID. More...

virtual void	SetId (string name, string config)

const Algorithm *	SubAlg (const RgKey &registry_key) const

void	AdoptConfig (void)

void	AdoptSubstructure (void)

virtual void	Print (ostream &stream) const
	Print algorithm info. More...

Private Member Functions
void	LoadConfig (void)

double	Pauli (double Q2, double W, double MN) const
	Pauli suppression for D2. More...

double	Nu (double Q2, double W, double MN) const
	kinematic variables More...

double	NuStar (double Q2, double W, double MN) const
	... More...

double	PPiStar (double W, double MN) const
	... More...

Private Attributes
const XSecIntegratorI *	fXSecIntegrator

double	fFermiConstant2

double	fMa

double	fMv

double	fCos28c

bool	fTurnOnPauliCorrection

Additional Inherited Members
Static Public Member Functions inherited from genie::Algorithm
static string	BuildParamVectKey (const std::string &comm_name, unsigned int i)

static string	BuildParamVectSizeKey (const std::string &comm_name)

static string	BuildParamMatKey (const std::string &comm_name, unsigned int i, unsigned int j)

static string	BuildParamMatRowSizeKey (const std::string &comm_name)

static string	BuildParamMatColSizeKey (const std::string &comm_name)

Protected Member Functions inherited from genie::XSecAlgorithmI
	XSecAlgorithmI ()

	XSecAlgorithmI (string name)

	XSecAlgorithmI (string name, string config)

Protected Member Functions inherited from genie::Algorithm
	Algorithm ()

	Algorithm (string name)

	Algorithm (string name, string config)

void	Initialize (void)

void	DeleteConfig (void)

void	DeleteSubstructure (void)

Registry *	ExtractLocalConfig (const Registry &in) const

Registry *	ExtractLowerConfig (const Registry &in, const string &alg_key) const
	Split an incoming configuration Registry into a block valid for the sub-algo identified by alg_key. More...

template<class T >
bool	GetParam (const RgKey &name, T &p, bool is_top_call=true) const

template<class T >
bool	GetParamDef (const RgKey &name, T &p, const T &def) const

template<class T >
int	GetParamVect (const std::string &comm_name, std::vector< T > &v, bool is_top_call=true) const
	Handle to load vectors of parameters. More...

int	GetParamVectKeys (const std::string &comm_name, std::vector< RgKey > &k, bool is_top_call=true) const

template<class T >
int	GetParamMat (const std::string &comm_name, TMatrixT< T > &mat, bool is_top_call=true) const
	Handle to load matrix of parameters. More...

template<class T >
int	GetParamMatSym (const std::string &comm_name, TMatrixTSym< T > &mat, bool is_top_call=true) const

int	GetParamMatKeys (const std::string &comm_name, std::vector< RgKey > &k, bool is_top_call=true) const

int	AddTopRegistry (Registry *rp, bool owns=true)
	add registry with top priority, also update ownership More...

int	AddLowRegistry (Registry *rp, bool owns=true)
	add registry with lowest priority, also update ownership More...

int	MergeTopRegistry (const Registry &r)

int	AddTopRegisties (const vector< Registry * > &rs, bool owns=false)
	Add registries with top priority, also udated Ownerships. More...

Protected Attributes inherited from genie::Algorithm
bool	fAllowReconfig

bool	fOwnsSubstruc
	true if it owns its substructure (sub-algs,...) More...

AlgId	fID
	algorithm name and configuration set More...

vector< Registry * >	fConfVect

vector< bool >	fOwnerships
	ownership for every registry in fConfVect More...

AlgStatus_t	fStatus
	algorithm execution status More...

AlgMap *	fOwnedSubAlgMp
	local pool for owned sub-algs (taken out of the factory pool) More...

Detailed Description

Double differential resonance cross section for P33 according to the Paschos, Lalakulich model.

      Is a concrete implementation of the XSecAlgorithmI interface.

References:: O.Lalakulich and E.A.Paschos, Resonance Production by Neutrinos: I. J=3/2 Resonances, hep-ph/0501109

Author: Costas Andreopoulos <c.andreopoulos cern.ch> University of Liverpool

based on code written by the model authors (Olga Lalakulich).

Created:: February 22, 2005

License:: Copyright (c) 2003-2024, The GENIE Collaboration For the full text of the license visit http://copyright.genie-mc.org

Definition at line 35 of file P33PaschosLalakulichPXSec.h.

Constructor & Destructor Documentation

P33PaschosLalakulichPXSec::P33PaschosLalakulichPXSec ( )

Definition at line 33 of file P33PaschosLalakulichPXSec.cxx.

                                                      :
 XSecAlgorithmI("genie::P33PaschosLalakulichPXSec")
 {
 
 }

P33PaschosLalakulichPXSec::P33PaschosLalakulichPXSec ( string name )

Definition at line 39 of file P33PaschosLalakulichPXSec.cxx.

                                                                   :
 XSecAlgorithmI("genie::P33PaschosLalakulichPXSec", config)
 {
 
 }

P33PaschosLalakulichPXSec::~P33PaschosLalakulichPXSec ( )

virtual

Definition at line 45 of file P33PaschosLalakulichPXSec.cxx.

 {
 
 }

Member Function Documentation

void P33PaschosLalakulichPXSec::Configure ( const Registry & config )

virtual

Configure the algorithm with an external registry The registry is merged with the top level registry if it is owned, Otherwise a copy of it is added with the highest priority

Reimplemented from genie::Algorithm.

Definition at line 275 of file P33PaschosLalakulichPXSec.cxx.

References genie::Algorithm::Configure(), and LoadConfig().

 {
   Algorithm::Configure(config);
   this->LoadConfig();
 }

void P33PaschosLalakulichPXSec::Configure ( string config )

virtual

Configure the algorithm from the AlgoConfigPool based on param_set string given in input An algorithm contains a vector of registries coming from different xml configuration files, which are loaded according a very precise prioriy This methods will load a number registries in order of priority: 1) "Tunable" parameter set from CommonParametes. This is loaded with the highest prioriry and it is designed to be used for tuning procedure Usage not expected from the user. 2) For every string defined in "CommonParame" the corresponding parameter set will be loaded from CommonParameter.xml 3) parameter set specified by the config string and defined in the xml file of the algorithm 4) if config is not "Default" also the Default parameter set from the same xml file will be loaded Effectively this avoids the repetion of a parameter when it is not changed in the requested configuration

Reimplemented from genie::Algorithm.

Definition at line 281 of file P33PaschosLalakulichPXSec.cxx.

References genie::Algorithm::Configure(), and LoadConfig().

 {
   Algorithm::Configure(config);
   this->LoadConfig();
 }

double P33PaschosLalakulichPXSec::Integral ( const Interaction * i ) const

virtual

Integrate the model over the kinematic phase space available to the input interaction (kinematical cuts can be included)

Implements genie::XSecAlgorithmI.

Definition at line 261 of file P33PaschosLalakulichPXSec.cxx.

References fXSecIntegrator, and genie::XSecIntegratorI::Integrate().

 {
   double xsec = fXSecIntegrator->Integrate(this,interaction);
   return xsec;
 }

void P33PaschosLalakulichPXSec::LoadConfig ( void )

private

Definition at line 287 of file P33PaschosLalakulichPXSec.cxx.

References fCos28c, fFermiConstant2, fMa, fMv, fTurnOnPauliCorrection, fXSecIntegrator, genie::Algorithm::GetParam(), genie::Algorithm::GetParamDef(), and genie::Algorithm::SubAlg().

Referenced by Configure().

 {
   double fermi_constant ;
   GetParam( "FermiConstant", fermi_constant ) ;
   fFermiConstant2 = fermi_constant * fermi_constant ;
 
   GetParam( "RES-Ma", fMa ) ;
   GetParam( "RES-Mv", fMv ) ;
 
   double thc ;
   GetParam( "CabibboAngle", thc ) ;
   fCos28c = TMath::Power( TMath::Cos(thc), 2 );
 
   GetParamDef( "TurnOnPauliSuppr", fTurnOnPauliCorrection, false ) ;
 
   //-- load the differential cross section integrator
   fXSecIntegrator =
       dynamic_cast<const XSecIntegratorI *> (this->SubAlg("XSec-Integrator"));
   assert(fXSecIntegrator);
 }

double P33PaschosLalakulichPXSec::Nu	(	double	Q2,
		double	W,
		double	MN
	)		const

private

kinematic variables

Definition at line 353 of file P33PaschosLalakulichPXSec.cxx.

Referenced by XSec().

 {
   return (TMath::Power(W,2) - TMath::Power(MN,2) + Q2)/2/MN;
 }

double P33PaschosLalakulichPXSec::NuStar	(	double	Q2,
		double	W,
		double	MN
	)		const

private

...

Definition at line 367 of file P33PaschosLalakulichPXSec.cxx.

References genie::utils::kinematics::W().

Referenced by Pauli().

 {
   return (TMath::Power(W,2) - TMath::Power(MN,2) - Q2)/2/W;
 }

double P33PaschosLalakulichPXSec::Pauli	(	double	Q2,
		double	W,
		double	MN
	)		const

private

Pauli suppression for D2.

Definition at line 308 of file P33PaschosLalakulichPXSec.cxx.

References NuStar(), and PPiStar().

Referenced by XSec().

 {
 // Pauli suppression for deuterium with Fermi momentum 0.160 GeV
 
   // ---remove--- this value from here & ask GENIE for D2 Fermi momentum
   double qF=0.160; /* 0.160 deuterium */
 
   double Paulii = 0;
 
   double p_pi_star = this->PPiStar(W,MN);
   double nu_star   = this->NuStar(Q2,W,MN);
 
   double p_pi_star_2 = TMath::Power(p_pi_star,   2);
   double p_pi_star_4 = TMath::Power(p_pi_star_2, 2);
   double nu_star_2   = TMath::Power(nu_star,     2);
 
   double q3  = TMath::Sqrt(Q2+nu_star_2);
   double q6  = TMath::Power(q3,2);
   double q12 = TMath::Power(q6,2);
 
   double qF2 = TMath::Power(qF,2);
   double qF3 = TMath::Power(qF,3);
 
   if ( q3+p_pi_star < 2*qF )
   {
      Paulii = ( (3*q6 + p_pi_star_2)/2/qF
                -(5*q12+p_pi_star_4 + 10*q6*p_pi_star_2)/40/qF3
               )/2/q3;
   }
   if ( (q3+p_pi_star > 2*qF) && (q3-p_pi_star < 2*qF) )
   {
      double tmp1 = TMath::Power( q3+p_pi_star, 2 );
      double tmp2 = TMath::Power( q3-p_pi_star, 3 );
      double tmp3 = TMath::Power( q3-p_pi_star, 5 );
 
      Paulii = (tmp1-4.0*qF2/5.0 - tmp2/2/qF + tmp3/40/qF3)/4/p_pi_star/q3;
   }
   if ( q3-p_pi_star > 2*qF )
   {
      Paulii = 1;
   }
 
   return Paulii;
 }

double P33PaschosLalakulichPXSec::PPiStar	(	double	W,
		double	MN
	)		const

private

...

Definition at line 358 of file P33PaschosLalakulichPXSec.cxx.

References a, genie::units::b, genie::constants::kPionMass, and genie::utils::kinematics::W().

Referenced by Pauli(), and XSec().

 {
   double W2 = TMath::Power(W,2);
   double a  = TMath::Power(MN+kPionMass,2);
   double b  = TMath::Power(MN-kPionMass,2);
 
   return TMath::Sqrt( (W2-a)*(W2-b) )/2/W;
 }

bool P33PaschosLalakulichPXSec::ValidProcess ( const Interaction * i ) const

virtual

Can this cross section algorithm handle the input process?

Implements genie::XSecAlgorithmI.

Definition at line 268 of file P33PaschosLalakulichPXSec.cxx.

References genie::kISkipProcessChk.

Referenced by XSec().

 {
   if(interaction->TestBit(kISkipProcessChk)) return true;
   return true;
 }

double P33PaschosLalakulichPXSec::XSec	(	const Interaction *	i,
		KinePhaseSpace_t	k
	)		const

virtual

Compute the cross section for the input interaction.

Implements genie::XSecAlgorithmI.

Definition at line 50 of file P33PaschosLalakulichPXSec.cxx.

References fCos28c, fFermiConstant2, fMa, fMv, fTurnOnPauliCorrection, genie::Algorithm::GetConfig(), genie::Registry::GetString(), genie::Target::HitNucMass(), genie::Target::HitNucPdg(), genie::pdg::IsProton(), genie::utils::mec::J(), genie::utils::kinematics::Jacobian(), genie::kIAssumeFreeNucleon, genie::constants::kMuonMass2, genie::kP33_1232, genie::constants::kPi, genie::constants::kPionMass2, genie::kPSWQ2fE, genie::kRfHitNucRest, LOG, genie::utils::res::Mass(), genie::Target::N(), Nu(), Pauli(), pDEBUG, PPiStar(), genie::InitialState::ProbeE(), genie::Kinematics::Q2(), genie::utils::kinematics::Q2(), genie::InitialState::Tgt(), genie::XSecAlgorithmI::ValidKinematics(), ValidProcess(), genie::Kinematics::W(), genie::utils::kinematics::W(), genie::utils::res::Width(), and genie::Target::Z().

 {
   if(! this -> ValidProcess    (interaction) ) return 0.;
   if(! this -> ValidKinematics (interaction) ) return 0.;
 
   //-- Get initial state and kinematic variables
   const InitialState & init_state = interaction -> InitState();
   const Kinematics &   kinematics = interaction -> Kine();
   const Target &       target     = init_state.Tgt();
 
   double E    = init_state.ProbeE(kRfHitNucRest);
   double E2   = TMath::Power(E,2);
   double Q2   = kinematics.Q2();
   double W    = kinematics.W();
   double MN   = target.HitNucMass();
   double MN2  = TMath::Power(MN,2);
   double Mmu2 = kMuonMass2;
   double Mpi2 = kPionMass2;
 
   LOG("PaschLal", pDEBUG) << "Input kinematics: W = " << W << ", Q2 = " << Q2;
 
   //-- Retrieve P33(1232) information
   double Gamma_R0  = utils::res::Width (kP33_1232);
   double MR        = utils::res::Mass  (kP33_1232);
   double MR2      = TMath::Power(MR,2);
   double MR3      = TMath::Power(MR,3);
 
   //-- Auxiliary params
 
   const double kPlRes_f3_P1232_V =  1.95/MN;
   const double kPlRes_f4_P1232_V = -1.95/MN;
   const double kPlRes_f5_P1232_V =  0;
   const double kPlRes_f5_P1232_A =  1.2;
   const double kPlRes_f4_P1232_A = -0.3/MN2;
   const double kPlRes_f3_P1232_A =  0;
   const double kPlRes_f6_P1232_A =  kPlRes_f5_P1232_A;
 
   double MA2    = TMath::Power( fMa, 2 );
   double MV2    = TMath::Power( fMv, 2 );
   double ftmp1a = TMath::Power( 1 + Q2/MA2, 2 );
   double ftmp1v = TMath::Power( 1 + Q2/MA2, 2 );
   double ftmp2a = 1 + Q2/3/MA2;
   double ftmp2v = 1 + Q2/4/MV2;
   double f3A    = kPlRes_f3_P1232_A/ftmp1a/ftmp2a;
   double f4A    = kPlRes_f4_P1232_A/ftmp1a/ftmp2a;
   double f5A    = kPlRes_f5_P1232_A/ftmp1a/ftmp2a;
   double f6A    = kPlRes_f6_P1232_A/ftmp1a/ftmp2a/(Q2+Mpi2);
   double f3V    = kPlRes_f3_P1232_V/ftmp1v/ftmp2v;
   double f4V    = kPlRes_f4_P1232_V/ftmp1v/ftmp2v/W;
   double f5V    = kPlRes_f5_P1232_V/ftmp1v/ftmp2v;
   double f3V4A  = f3V*f4A;
   double f3V5A  = f3V*f5A;
   double f4V4A  = f4V*f4A;
   double f4V5A  = f4V*f5A;
   double f3A2   = TMath::Power( f3A, 2 );
   double f4A2   = TMath::Power( f4A, 2 );
   double f5A2   = TMath::Power( f5A, 2 );
   double f6A2   = TMath::Power( f6A, 2 );
   double f3V2   = TMath::Power( f3V, 2 );
   double f4V2   = TMath::Power( f4V, 2 );
   double f5V2   = TMath::Power( f5V, 2 );
 
   //-- move these running gamma definitions into GENIE's breit-wigner
   //   functions so that they can be directly used here
 
   // model of the running Gamma from Paschos [default]
   double Gamma_R=Gamma_R0*pow((this->PPiStar(W,MN)/this->PPiStar(MR,MN)),3);
 
   // check for other option
   if ( GetConfig().Exists("running-gamma") ) {
 
      string gamma_model = GetConfig().GetString("running-gamma");
 
      if ( gamma_model.find("Hagiwara") != string::npos )
      {
          // model of the running Gamma from Hagiwara et. al.
          Gamma_R = Gamma_R0*MR/W*pow((this->PPiStar(W,MN)/this->PPiStar(MR,MN)),1);
      } else
      if ( gamma_model.find("Galster") != string::npos )
      {
          // model of the running Gamma similar to Galster-1972
          double gtmp1 = TMath::Power( this->PPiStar(W,MN) / this->PPiStar(MR,MN), 3);
          double gtmp2 = TMath::Power( this->PPiStar(W,MN) / this->PPiStar(MR,MN), 2);
          Gamma_R = Gamma_R0*gtmp1/(1+gtmp2);
      }
   }
   double Breit_Wigner = TMath::Power(W*W-MR2,2) + MR2 * TMath::Power(Gamma_R,2);
 
   //-- Include Pauli suppression [if the option was turned on by the user]
   double pauli = 1.;
   if(fTurnOnPauliCorrection) pauli = this->Pauli(Q2,W,MN);
 
   //-- Kinematic variables
   double nu  = this->Nu(Q2,W,MN);
   double pq  = MN*nu;
   double qk  = -(Q2+Mmu2)/2.;
   double pk  = MN*E;
   double pq2 = TMath::Power(pq,2);
   double pq3 = TMath::Power(pq,3);
   double Q4  = TMath::Power(Q2,2);
 
   //-- Compute Wi's, i=1-5
   double W1=0, W2=0, W3=0, W4=0, W5=0;
 
   W1 = 3.*(2*f5A2*MN2*MR2+2*f5A2*MN*MR3+2*f3A*f5A*MN2*MR*pq+2*f5A2*MR2*pq
        +4*f3A*f5A*MN*MR2*pq+4*f4A*f5A*MN2*MR2*pq+2*f3A*f5A*MR3*pq
        +4*f4A*f5A*MN*MR3*pq+2*f3A2*MN2*pq2+2*f3V2*MN2*pq2+2*f3A*f5A*MR*pq2
        +2*f3A*f4A*MN2*MR*pq2+2*f3V*f4V*MN2*MR*pq2+2*f3V*f5V*MN2*MR*pq2
        +2*f3A2*MR2*pq2+2*f3V2*MR2*pq2+4*f4A*f5A*MR2*pq2+4*f3A*f4A*MN*MR2*pq2
        -4*f3V*f4V*MN*MR2*pq2-4*f3V*f5V*MN*MR2*pq2+2*f4A2*MN2*MR2*pq2+2*f4V2*MN2*MR2*pq2
        +4*f4V*f5V*MN2*MR2*pq2+2*f5V2*MN2*MR2*pq2+2*f3A*f4A*MR3*pq2+2*f3V*f4V*MR3*pq2
        +2*f3V*f5V*MR3*pq2+2*f4A2*MN*MR3*pq2-2*f4V2*MN*MR3*pq2-4*f4V*f5V*MN*MR3*pq2
        -2*f5V2*MN*MR3*pq2+2*f3A2*pq3+2*f3V2*pq3+2*f3A*f4A*MR*pq3+2*f3V*f4V*MR*pq3
        +2*f3V*f5V*MR*pq3+2*f4A2*MR2*pq3+2*f4V2*MR2*pq3+4*f4V*f5V*MR2*pq3+2*f5V2*MR2*pq3
        -2*f3A*f5A*MN2*MR*Q2-4*f3A*f5A*MN*MR2*Q2+2*f3A2*MN2*MR2*Q2
        +2*f3V2*MN2*MR2*Q2-4*f4A*f5A*MN2*MR2*Q2-2*f3A2*MN*MR3*Q2+2*f3V2*MN*MR3*Q2
        -4*f4A*f5A*MN*MR3*Q2-4*f3A2*MN2*pq*Q2-4*f3V2*MN2*pq*Q2-2*f3A*f5A*MR*pq*Q2
        -4*f3A*f4A*MN2*MR*pq*Q2-4*f3V*f4V*MN2*MR*pq*Q2-2*f3V*f5V*MN2*MR*pq*Q2
        -4*f4A*f5A*MR2*pq*Q2-8*f3A*f4A*MN*MR2*pq*Q2+8*f3V*f4V*MN*MR2*pq*Q2
        +4*f3V*f5V*MN*MR2*pq*Q2-4*f4A2*MN2*MR2*pq*Q2-4*f4V2*MN2*MR2*pq*Q2
        -4*f4V*f5V*MN2*MR2*pq*Q2-2*f3A*f4A*MR3*pq*Q2-2*f3V*f4V*MR3*pq*Q2
        -4*f4A2*MN*MR3*pq*Q2+4*f4V2*MN*MR3*pq*Q2+4*f4V*f5V*MN*MR3*pq*Q2
        -4*f3A2*pq2*Q2-4*f3V2*pq2*Q2-4*f3A*f4A*MR*pq2*Q2-4*f3V*f4V*MR*pq2*Q2
        -2*f3V*f5V*MR*pq2*Q2-4*f4A2*MR2*pq2*Q2-4*f4V2*MR2*pq2*Q2-4*f4V*f5V*MR2*pq2*Q2
        +2*f3A2*MN2*Q4+2*f3V2*MN2*Q4+2*f3A*f4A*MN2*MR*Q4+2*f3V*f4V*MN2*MR*Q4
        +4*f3A*f4A*MN*MR2*Q4-4*f3V*f4V*MN*MR2*Q4+2*f4A2*MN2*MR2*Q4+2*f4V2*MN2*MR2*Q4
        +2*f4A2*MN*MR3*Q4-2*f4V2*MN*MR3*Q4+2*f3A2*pq*Q4+2*f3V2*pq*Q4+2*f3A*f4A*MR*pq*Q4
        +2*f3V*f4V*MR*pq*Q4+2*f4A2*MR2*pq*Q4+2*f4V2*MR2*pq*Q4)/(3.*MR2);
 
   W2 = 3.*(2*(f5A2*MN2
        +f5A2*MN*MR+f5A2*pq+f3A2*MN2*Q2+f3V2*MN2*Q2+f3A*f5A*MR*Q2+f3A*f4A*MN2*MR*Q2
        +f3V*f4V*MN2*MR*Q2+f3V*f5V*MN2*MR*Q2+f3A2*MR2*Q2+f3V2*MR2*Q2
        +2*f3A*f4A*MN*MR2*Q2-2*f3V*f4V*MN*MR2*Q2-2*f3V*f5V*MN*MR2*Q2
        +f4A2*MN2*MR2*Q2+f4V2*MN2*MR2*Q2+2*f4V*f5V*MN2*MR2*Q2+f5V2*MN2*MR2*Q2+f3A*f4A*MR3*Q2
        +f3V*f4V*MR3*Q2+f3V*f5V*MR3*Q2+f4A2*MN*MR3*Q2-f4V2*MN*MR3*Q2
        -2*f4V*f5V*MN*MR3*Q2-f5V2*MN*MR3*Q2+f3A2*pq*Q2+f3V2*pq*Q2+f3A*f4A*MR*pq*Q2
        +f3V*f4V*MR*pq*Q2+f3V*f5V*MR*pq*Q2+f4A2*MR2*pq*Q2+f4V2*MR2*pq*Q2
        +2*f4V*f5V*MR2*pq*Q2+f5V2*MR2*pq*Q2+f5V2*MN2*Q4+f3V*f5V*MR*Q4
        -f5V2*MN*MR*Q4+f5V2*pq*Q4))/(3.*MR2);
 
   W3 = 3.*((f3V4A*(Q2-pq)-f3V5A)*(2*MR2+2*MN*MR+Q2-pq)*4./3./MR
        -(Q2-pq)*(f4V4A*(Q2-pq)-f4V5A)*4./3.);
 
 
   W4 = 3.*(2*(f5A2*MN2+f5A2*MN*MR+f3A*f5A*MN2*MR
        +2*f3A*f5A*MN*MR2-f3A2*MN2*MR2-f3V2*MN2*MR2+2*f4A*f5A*MN2*MR2-2*f5A*f6A*MN2*MR2
        +f3A2*MN*MR3-f3V2*MN*MR3+2*f4A*f5A*MN*MR3-2*f5A*f6A*MN*MR3+f5A2*pq
        +2*f3A2*MN2*pq+2*f3V2*MN2*pq+2*f5A*f6A*MN2*pq+2*f3A*f5A*MR*pq
        +2*f5A*f6A*MN*MR*pq+2*f3A*f4A*MN2*MR*pq+2*f3V*f4V*MN2*MR*pq
        +f3V*f5V*MN2*MR*pq-f3A*f6A*MN2*MR*pq+2*f4A*f5A*MR2*pq
        -2*f5A*f6A*MR2*pq+4*f3A*f4A*MN*MR2*pq-4*f3V*f4V*MN*MR2*pq
        -2*f3V*f5V*MN*MR2*pq-2*f3A*f6A*MN*MR2*pq+2*f4A2*MN2*MR2*pq
        +2*f4V2*MN2*MR2*pq+2*f4V*f5V*MN2*MR2*pq-2*f4A*f6A*MN2*MR2*pq+f3A*f4A*MR3*pq
        +f3V*f4V*MR3*pq-f3A*f6A*MR3*pq+2*f4A2*MN*MR3*pq-2*f4V2*MN*MR3*pq
        -2*f4V*f5V*MN*MR3*pq-2*f4A*f6A*MN*MR3*pq+2*f3A2*pq2+2*f3V2*pq2
        +2*f5A*f6A*pq2+f5V2*MN2*pq2+f6A2*MN2*pq2+2*f3A*f4A*MR*pq2+2*f3V*f4V*MR*pq2
        +2*f3V*f5V*MR*pq2-f5V2*MN*MR*pq2+f6A2*MN*MR*pq2+2*f4A2*MR2*pq2+2*f4V2*MR2*pq2
        +2*f4V*f5V*MR2*pq2-2*f4A*f6A*MR2*pq2+f5V2*pq3+f6A2*pq3-f3A2*MN2*Q2-f3V2*MN2*Q2
        -2*f5A*f6A*MN2*Q2-2*f5A*f6A*MN*MR*Q2-f3A*f4A*MN2*MR*Q2
        -f3V*f4V*MN2*MR*Q2-2*f3A*f4A*MN*MR2*Q2+2*f3V*f4V*MN*MR2*Q2
        -f4A2*MN2*MR2*Q2-f4V2*MN2*MR2*Q2+f6A2*MN2*MR2*Q2-f4A2*MN*MR3*Q2+f4V2*MN*MR3*Q2
        +f6A2*MN*MR3*Q2-f3A2*pq*Q2-f3V2*pq*Q2-2*f5A*f6A*pq*Q2-2*f6A2*MN2*pq*Q2
        -f3A*f4A*MR*pq*Q2-f3V*f4V*MR*pq*Q2-f3A*f6A*MR*pq*Q2
        -2*f6A2*MN*MR*pq*Q2-f4A2*MR2*pq*Q2-f4V2*MR2*pq*Q2+f6A2*MR2*pq*Q2
        -2*f6A2*pq2*Q2+f6A2*MN2*Q4+f6A2*MN*MR*Q4+f6A2*pq*Q4))/(3.*MR2);
 
   W5 = 3.*(2*f5A2*MN2
        +2*f5A2*MN*MR+f3A*f5A*MN2*MR+2*f3A*f5A*MN*MR2+2*f4A*f5A*MN2*MR2
        +f3A*f5A*MR3+2*f4A*f5A*MN*MR3+2*f5A2*pq+2*f3A2*MN2*pq+2*f3V2*MN2*pq
        +2*f5A*f6A*MN2*pq+2*f3A*f5A*MR*pq+2*f5A*f6A*MN*MR*pq
        +2*f3A*f4A*MN2*MR*pq+2*f3V*f4V*MN2*MR*pq+2*f3V*f5V*MN2*MR*pq
        +2*f3A2*MR2*pq+2*f3V2*MR2*pq+2*f4A*f5A*MR2*pq+4*f3A*f4A*MN*MR2*pq
        -4*f3V*f4V*MN*MR2*pq-4*f3V*f5V*MN*MR2*pq+2*f4A2*MN2*MR2*pq
        +2*f4V2*MN2*MR2*pq+4*f4V*f5V*MN2*MR2*pq+2*f5V2*MN2*MR2*pq+2*f3A*f4A*MR3*pq
        +2*f3V*f4V*MR3*pq+2*f3V*f5V*MR3*pq+2*f4A2*MN*MR3*pq-2*f4V2*MN*MR3*pq
        -4*f4V*f5V*MN*MR3*pq-2*f5V2*MN*MR3*pq+2*f3A2*pq2+2*f3V2*pq2+2*f5A*f6A*pq2
        +2*f3A*f4A*MR*pq2+2*f3V*f4V*MR*pq2+2*f3V*f5V*MR*pq2+2*f4A2*MR2*pq2
        +2*f4V2*MR2*pq2+4*f4V*f5V*MR2*pq2+2*f5V2*MR2*pq2-2*f5A*f6A*MN2*Q2+f3A*f5A*MR*Q2
        -2*f5A*f6A*MN*MR*Q2-f3A*f6A*MN2*MR*Q2-2*f3A*f6A*MN*MR2*Q2
        -2*f4A*f6A*MN2*MR2*Q2-f3A*f6A*MR3*Q2-2*f4A*f6A*MN*MR3*Q2
        -2*f5A*f6A*pq*Q2+2*f5V2*MN2*pq*Q2+2*f3V*f5V*MR*pq*Q2
        -2*f5V2*MN*MR*pq*Q2-2*f4A*f6A*MR2*pq*Q2+2*f5V2*pq2*Q2-f3A*f6A*MR*Q4)/(3.*MR2);
 
   double s1 =    W1 * (Q2+Mmu2)
                + W2 * (2*pk*pk-2*pq*pk+MN*qk)
                - W3 * (pq*qk+Q2*pk)
                + W4 * Mmu2*(Q2+Mmu2)/2.
                - W5 * 2*Mmu2*pk;
 
   double xsec = fFermiConstant2/4./kPi*fCos28c/MN2/E2*W*MR*Gamma_R/kPi/Breit_Wigner*pauli*s1;
 
   //-- The algorithm computes d^2xsec/dWdQ2
   //   Check whether variable tranformation is needed
   if(kps!=kPSWQ2fE) {
     double J = utils::kinematics::Jacobian(interaction,kPSWQ2fE,kps);
     xsec *= J;
   }
 
   //-- If requested return the free nucleon xsec even for input nuclear tgt
   if( interaction->TestBit(kIAssumeFreeNucleon) ) return xsec;
 
   //-- number of scattering centers in the target
   bool isp = pdg::IsProton(target.HitNucPdg());
   int NNucl = (isp) ? target.Z() : target.N();
 
   xsec*=NNucl; // nuclear xsec (no nuclear suppression factor)
 
   return xsec;
 }