genie::utils::bwfunc Namespace Reference

Breit Wigner functions. More...

Functions
double	BreitWignerLGamma (double W, int L, double mass, double width0, double norm)
double	BreitWignerL (double W, int L, double mass, double width0, double norm)
double	BreitWigner (double W, double mass, double width, double norm)

Detailed Description

Breit Wigner functions.

Author

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

Created:

November 22, 2004

License:

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

Function Documentation

double genie::utils::bwfunc::BreitWigner	(	double	W,
		double	mass,
		double	width,
		double	norm
	)

Definition at line 141 of file BWFunc.cxx.

References genie::constants::kPi.

{
//Inputs:
// - W:     Invariant mass (GeV)
// - mass:  Resonance mass (GeV)
// - width: Resonance width
// - norm:  Breit Wigner norm

  //-- sanity checks
  assert(mass  >  0);
  assert(width >  0);
  assert(norm  >  0);
  assert(W     >  0);

  //-- auxiliary parameters
  double width_2 = TMath::Power( width,  2);
  double W_m_2   = TMath::Power( W-mass, 2);

  //-- calculate the Breit Wigner function for the input W
  double bw = (0.5/kPi) * (width/norm) / (W_m_2 + 0.25*width_2);
  return bw;
}

double genie::utils::bwfunc::BreitWignerL	(	double	W,
		int	L,
		double	mass,
		double	width0,
		double	norm
	)

Definition at line 99 of file BWFunc.cxx.

References genie::constants::kNucleonMass, genie::constants::kPi, genie::constants::kPi0Mass, and genie::utils::kinematics::W().

Referenced by genie::utils::res::BWNorm(), main(), genie::ReinSehgalRESPXSec::XSec(), and genie::BSKLNBaseRESPXSec2014::XSec().

{
//Inputs:
// - W:      Invariant mass (GeV)
// - L:      Resonance orbital angular momentum
// - mass:   Resonance mass (GeV)
// - width0: Resonance width
// - norm:   Breit Wigner norm

  //-- sanity checks
  assert(mass   >  0);
  assert(width0 >  0);
  assert(norm   >  0);
  assert(W      >  0);
  assert(L      >= 0);

  //-- auxiliary parameters
  double mN    = kNucleonMass;
  double mPi   = kPi0Mass;
  double m_2   = TMath::Power(mass, 2);
  double mN_2  = TMath::Power(mN,   2);
  double mPi_2 = TMath::Power(mPi,  2);
  double W_2   = TMath::Power(W,    2);

  //-- calculate the L-dependent resonance width
  double qpW_2 = ( TMath::Power(W_2 - mN_2 - mPi_2, 2) - 4*mN_2*mPi_2 );
  double qpM_2 = ( TMath::Power(m_2 - mN_2 - mPi_2, 2) - 4*mN_2*mPi_2 );
  if(qpW_2 < 0) qpW_2 = 0;
  if(qpM_2 < 0) qpM_2 = 0;
  double qpW   = TMath::Sqrt(qpW_2) / (2*W);
  double qpM   = TMath::Sqrt(qpM_2) / (2*mass);
  double width = width0 * TMath::Power( qpW/qpM, 2*L+1 );

  //-- calculate the Breit Wigner function for the input W
  double width_2 = TMath::Power( width,  2);
  double W_m_2   = TMath::Power( W-mass, 2);

  double bw = (0.5/kPi) * (width/norm) / (W_m_2 + 0.25*width_2);
  return bw;
}

double genie::utils::bwfunc::BreitWignerLGamma	(	double	W,
		int	L,
		double	mass,
		double	width0,
		double	norm
	)

Definition at line 22 of file BWFunc.cxx.

References genie::constants::kNucleonMass, genie::constants::kPi, genie::constants::kPi0Mass, genie::units::m, and genie::utils::kinematics::W().

Referenced by genie::ReinSehgalRESPXSec::XSec().

{
//Inputs:
// - W:      Invariant mass (GeV)
// - L:      Resonance orbital angular momentum
// - mass:   Resonance mass (GeV)
// - width0: Resonance width
// - norm:   Breit Wigner norm

  //-- sanity checks
  assert(mass   >  0);
  assert(width0 >  0);
  assert(norm   >  0);
  assert(W      >  0);
  assert(L      >= 0);

  //-- auxiliary parameters
  double mN    = kNucleonMass;
  double mPi   = kPi0Mass;
  double m_2   = TMath::Power(mass, 2);
  double mN_2  = TMath::Power(mN,   2);
  double W_2   = TMath::Power(W,    2);

  double m=mass;
  //m_aux1 m_aux2
  double m_aux1= TMath::Power(mN+mPi, 2);
  double m_aux2= TMath::Power(mN-mPi, 2);

  double BRPi0    = 0.994; //Npi Branching Ratio
  double BRgamma0 = 0.006; //Ngamma Branching Ratio

  double widPi0   = width0*BRPi0;
  double widgamma0= width0*BRgamma0;

  //-- calculate the L-dependent resonance width
  double EgammaW= (W_2-mN_2)/(2*W);
  double Egammam= (m_2-mN_2)/(2*m);


  if(EgammaW<0) {
//  cout<< "Two small W!!! W is lower than one Nucleon Mass!!!!"<<endl;
  return 0;
  }
  //pPiW pion momentum
  double pPiW     = 0;
  //
  if(W_2>m_aux1) pPiW   = TMath::Sqrt((W_2-m_aux1)*(W_2-m_aux2))/(2*W);

  double pPim   = TMath::Sqrt((m_2-m_aux1)*(m_2-m_aux2))/(2*m);

  //double TPiW   = pPiW*TMath::Power(pPiW*rDelta, 2*L)/(1+TMath::Power(pPiW*rDelta, 2));
  //double TPim   = pPim*TMath::Power(pPim*rDelta, 2*L)/(1+TMath::Power(pPim*rDelta, 2));

  // Form factors
  //double fgammaW= 1/(TMath::Power(1+EgammaW*EgammaW/0.706, 2)*(1+EgammaW*EgammaW/3.519));
  //double fgammam= 1/(TMath::Power(1+Egammam*Egammam/0.706, 2)*(1+Egammam*Egammam/3.519));
  double fgammaW= 1/(TMath::Power(1+EgammaW*EgammaW/0.706, 2));
  double fgammam= 1/(TMath::Power(1+Egammam*Egammam/0.706, 2));


  double EgammaW_3=TMath::Power(EgammaW, 3);
  double Egammam_3=TMath::Power(Egammam, 3);
  double fgammaW_2=TMath::Power(fgammaW, 2);
  double fgammam_2=TMath::Power(fgammam, 2);

  //double width = widPi0*(TPiW/TPim)+widgamma0*(EgammaW_3*fgammaW_2/(Egammam_3*fgammam_2));
  double width = widPi0*TMath::Power((pPiW/pPim),3)+widgamma0*(EgammaW_3*fgammaW_2/(Egammam_3*fgammam_2));
  //-- calculate the Breit Wigner function for the input W
  double width_2 = TMath::Power( width,  2);
  double W_m_2   = TMath::Power( W-mass, 2);

  double bw = (0.5/kPi) * (width/norm) / (W_m_2 + 0.25*width_2);

  return bw;
}