Computes the double differential cross section for CC & NC coherent pion production according to the Berger-Sehgal model. v(vbar)A->v(vbar)Api0, vA->l-Api+, vbarA->l+Api-. More...

#include <BergerSehgalCOHPiPXSec2015.h>

Inheritance diagram for genie::BergerSehgalCOHPiPXSec2015:

Public Member Functions
	BergerSehgalCOHPiPXSec2015 ()

	BergerSehgalCOHPiPXSec2015 (string config)

virtual	~BergerSehgalCOHPiPXSec2015 ()

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	ExactKinematicTerm (const Interaction *i) const

double	PionCOMAbsMomentum (const Interaction *i) const

Private Attributes
double	fMa
	axial mass More...

double	fRo
	nuclear size scale parameter More...

double	fCos8c2
	cos^2(Cabibbo angle) More...

bool	fRSPionXSec
	Use Rein-Sehgal "style" pion-nucleon xsecs. More...

const XSecIntegratorI *	fXSecIntegrator

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)

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

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

Computes the double differential cross section for CC & NC coherent pion production according to the Berger-Sehgal model. v(vbar)A->v(vbar)Api0, vA->l-Api+, vbarA->l+Api-.

The t-dependence of the triple differential cross (d^3xsec/dxdydt) is integrated out.

Is a concrete implementation of the XSecAlgorithmI interface.

PRD 79, 053003 (2009) by Berger and Sehgal

Author: G. Perdue, H. Gallagher, D. Cherdack

2014

Definition at line 35 of file BergerSehgalCOHPiPXSec2015.h.

Constructor & Destructor Documentation

BergerSehgalCOHPiPXSec2015::BergerSehgalCOHPiPXSec2015 ( )

Definition at line 30 of file BergerSehgalCOHPiPXSec2015.cxx.

                                                        :
   XSecAlgorithmI("genie::BergerSehgalCOHPiPXSec2015")
 {
 
 }

BergerSehgalCOHPiPXSec2015::BergerSehgalCOHPiPXSec2015 ( string config )

Definition at line 36 of file BergerSehgalCOHPiPXSec2015.cxx.

                                                                     :
   XSecAlgorithmI("genie::BergerSehgalCOHPiPXSec2015", config)
 {
 
 }

BergerSehgalCOHPiPXSec2015::~BergerSehgalCOHPiPXSec2015 ( )

virtual

Definition at line 42 of file BergerSehgalCOHPiPXSec2015.cxx.

 {
 
 }

Member Function Documentation

void BergerSehgalCOHPiPXSec2015::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 285 of file BergerSehgalCOHPiPXSec2015.cxx.

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

void BergerSehgalCOHPiPXSec2015::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 291 of file BergerSehgalCOHPiPXSec2015.cxx.

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

double BergerSehgalCOHPiPXSec2015::ExactKinematicTerm ( const Interaction * i ) const

private

Definition at line 218 of file BergerSehgalCOHPiPXSec2015.cxx.

 {
   // 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 BergerSehgalCOHPiPXSec2015::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 260 of file BergerSehgalCOHPiPXSec2015.cxx.

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

void BergerSehgalCOHPiPXSec2015::LoadConfig ( void )

private

Definition at line 297 of file BergerSehgalCOHPiPXSec2015.cxx.

 {
   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);
 }

double BergerSehgalCOHPiPXSec2015::PionCOMAbsMomentum ( const Interaction * i ) const

private

Definition at line 238 of file BergerSehgalCOHPiPXSec2015.cxx.

 {
   // 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;
 }

bool BergerSehgalCOHPiPXSec2015::ValidProcess ( const Interaction * i ) const

virtual

Can this cross section algorithm handle the input process?

Implements genie::XSecAlgorithmI.

Definition at line 266 of file BergerSehgalCOHPiPXSec2015.cxx.

 {
   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;
 }

double BergerSehgalCOHPiPXSec2015::XSec	(	const Interaction *	i,
		KinePhaseSpace_t	k
	)		const

virtual

Compute the cross section for the input interaction.

Implements genie::XSecAlgorithmI.

Definition at line 47 of file BergerSehgalCOHPiPXSec2015.cxx.

 {
   // 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.
 
   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 x      = kinematics.x();
   assert(E > 0.);
   assert(y > 0.);
   assert(y < 1.);
   double ppistar = PionCOMAbsMomentum(interaction); // |Center of Mass Momentum|
   if (ppistar <= 0.0) {
     LOG("BergerSehgalCohPi", pDEBUG) << "Pion COM momentum negative for Q2 = " << Q2 <<
       " x = " << x << " y = " << y;
     return 0.0;
   }
   double front  = ExactKinematicTerm(interaction);
   if (front <= 0.0) {
     LOG("BergerSehgalCohPi", pDEBUG) << "Exact kin. form = " << front <<
       " E = " << E << " Q2 = " << Q2 << " y = " << y << " x = " << x;
     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 Epi    = y*E;                             // ~pion energy
   double ma2    = TMath::Power(fMa, 2);            // "axial mass" squared
   double Ga     = ma2 / (ma2 + Q2);
   double Ga2    = TMath::Power(Ga, 2.);            // propagator term
   double Ro2    = TMath::Power(fRo * units::fermi, 2.);
 
   // the xsec is d^3xsec/dQ^2dydt but the only t-dependent factor
   // is an exp(-bt) so it can be integrated analyticaly
   double Epi2   = TMath::Power(Epi, 2.);
   double R      = fRo * A_3 * units::fermi; // nuclear radius
   double R2     = TMath::Power(R, 2.);
   double b      = 0.33333 * R2;
   double MxEpi  = M * x / Epi;
   double mEpi2  = (M_pi * M_pi) / Epi2;
   double tA     = 1. + MxEpi - 0.5 * mEpi2;
   double tB     = TMath::Sqrt(1.0 + 2 * MxEpi) * TMath::Sqrt(1.0 - mEpi2);
   double tmin   = 2 * Epi2 * (tA - tB);
   double tmax   = 2 * Epi2 * (tA + tB);
   if (tmin < 1.0e-8) {
       tmin = 1.0e-8;
   }
 
   /* const KPhaseSpace & kphase = interaction->PhaseSpace(); */
   /* Range1D_t tl = kphase.TLim();   // TESTING! */
 
   double sigtot_pin  = utils::hadxs::berger::PionNucleonXSec(Epi, /* get_total = */ true, pionIsCharged);
   double sigel_pin   = utils::hadxs::berger::PionNucleonXSec(Epi, /* get_total = */ false, pionIsCharged);
   double siginel_pin = sigtot_pin - sigel_pin;
 
   // 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 * siginel_pin);
 
   // my old hackery to get things to work, A. Mislivec provided a better alt.
   // double factor      = 0.1; // to go from 10^-37 cm^2 -> 10^-38 cm^2
   // double RS_factor   = (units::mb*A2*fabs)/(16.0*kPi) * (sigtot_pin*sigtot_pin);
 
   // A_RS for BS version of RS, and/or Tpi>1.0
   double RS_factor = (A2 * fabs) / (16.0 * kPi) * (sigtot_pin * sigtot_pin);
 
   // get the pion-nucleus cross section on carbon, fold it into differential cross section
   double tpi         = (E * y) - M_pi - ((Q2 + M_pi * M_pi) / (2 * M));
   double tpilow      = 0.0;
   double siglow      = 0.0;
   double tpihigh     = 0.0;
   double sighigh     = 0.0;
   double dsigdzfit   = 0.0;
   double dsigdtfit   = 0.0;
   int    xsec_stat   = 0;
   double dsig        = 0.0;
   double tstep       = 100;
   double logt_step   = TMath::Abs(log(tmax) - log(tmin)) / tstep;
   double logt        = log(tmin) - logt_step/2.0;
   double t_itt       = TMath::Exp(logt);
   double t_width     = 0.0;
 
   for (double t_step = 0; t_step<tstep; t_step++) {
 
     logt = logt + logt_step;
     t_itt = TMath::Exp(logt);
     t_width = t_itt*logt_step;
 
     if (tpi <= 1.0 && fRSPionXSec == false) {
       xsec_stat =  utils::hadxs::berger::PionNucleusXSec(tpi, ppistar, t_itt, A, tpilow, siglow, tpihigh, sighigh);
       if(xsec_stat){
         LOG("BergerSehgalCohPi", pERROR) << "Call to PionNucleusXSec code failed - return xsec of 0.0";
         return 0.0;
       }
       dsigdzfit = siglow + (sighigh - siglow) * (tpi - tpilow) / (tpihigh - tpilow);
       dsigdtfit = dsigdzfit / (2.0 * ppistar * ppistar);
       // we are handed a cross section in mb, need to convert it to GeV^{-2}
       dsig +=   1.0  * front * Ga2 * t_width * dsigdtfit * units::mb;
     }
     else {
       dsig += /*factor **/ front * Ga2 * t_width * RS_factor * exp(-1.0*b*t_itt);
     }
 
   }
   xsec = dsig;
 
   // 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("BergerSehgalCohPi", pDEBUG)
     << "\n momentum transfer .............. Q2    = " << Q2
     << "\n mass number .................... A     = " << A
     << "\n pion energy .................... Epi   = " << Epi
     << "\n propagator term ................ Ga2   = " << Ga2
     << "\n total pi+N cross section ....... sigT  = " << sigtot_pin
     << "\n inelastic pi+N cross section ... sigI  = " << siginel_pin
     << "\n nuclear size scale ............. Ro    = " << fRo
     << "\n pion absorption factor ......... Fabs  = " << fabs
     << "\n t integration range ............ [" << tmin << "," << tmax << "]"
   LOG("BergerSehgalCohPi", pINFO)
     << "d2xsec/dQ2dy[COHPi] (Q2= " << Q2 << ", y="
     << y << ", E=" << E << ") = "<< xsec;
 #endif
 
   //----- The algorithm computes d^2xsec/dQ2dy
   // Check whether variable tranformation is needed? May be working with logs.
   // kPSlogQ2logyfE is possible - all others will not succeed
   if(kps != kPSQ2yfE) {
     double J = utils::kinematics::Jacobian(interaction,kPSQ2yfE, kps);
     xsec *= J;
   }
   return xsec;
 }