genie::Born Class Reference

Born level nu-electron cross section. More...

#include <Born.h>

Public Member Functions
	Born ()
virtual	~Born ()
double	GetReAlpha (void)
double	PXSecCCR (double s, double t, double mlin, double mlout)
double	PXSecCCV (double s, double t, double mlin, double mlout)
double	PXSecCCRNC (double s, double t, double mlin, double mlout)
double	PXSecCCVNC (double s, double t, double mlin, double mlout)
double	PXSecNCVnu (double s, double t, double mlin, double mlout)
double	PXSecNCVnubar (double s, double t, double mlin, double mlout)
double	PXSecPhoton (double s, double t, double mlout2)
double	PXSecPhoton_T (double s12, double s13, double Q2, double ml2)
double	PXSecPhoton_L (double s12, double s13, double Q2, double ml2)
double	GetS (double mlin, double Enuin)
double	GetT (double mlin, double mlout, double s, double costhCM)
double	GetU (double mlin, double mlout, double s, double t)
bool	IsInPhaseSpace (double mlin, double mlout, double Enuin, double Enuout)
double	Lambda (double a, double b, double c)

Private Attributes
double	fGw
double	fGz
TComplex	falpha
TComplex	fsw2
TComplex	fcw2
TComplex	fmw2c
TComplex	fmz2c
TComplex	fgae
TComplex	fgbe
TComplex	fgav

Detailed Description

Born level nu-electron cross section.

Author

Alfonso Garcia <aagarciasoto km3net.de> IFIC & Harvard University

Created:

Dec 8, 2021

License:

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

Definition at line 26 of file Born.h.

Constructor & Destructor Documentation

Born::Born

(

)

Definition at line 24 of file Born.cxx.

References genie::PDGLibrary::Find(), genie::PDGLibrary::Instance(), genie::constants::kGF, genie::constants::kMw, genie::constants::kMw2, genie::constants::kMz, genie::constants::kMz2, genie::kPdgWM, genie::kPdgZ0, and genie::constants::kPi.

{

  fGw      = PDGLibrary::Instance()->Find(kPdgWM)->Width();
  fGz      = PDGLibrary::Instance()->Find(kPdgZ0)->Width();
  fmw2c    = TComplex(kMw2,fGw*kMw);
  fmz2c    = TComplex(kMz2,fGz*kMz);
  TComplex rat = fmw2c/fmz2c;
  fsw2     = TComplex(1.-rat.Re(),-rat.Im());
  fcw2     = 1.-fsw2;
  falpha   = TMath::Sqrt(2.)*kGF/kPi * fmw2c * fsw2;
  
  fgae = -1./2. + 2.*fsw2;
  fgbe = -1./2.;
  fgav = 1./2.;

}

Born::~Born ( )

virtual

Definition at line 42 of file Born.cxx.

{

/*
Make sure the p3 is always the charged lepton:

nu (p1) + lp (p2) -> lp (p3) + nu (p4)

  s-channel       t-channel        u-channel
1 \      / 3    1 --------- 3    1 ------\ / 3
   ------             |                |  X
2 /      \ 4    2 --------- 4    2 ------/ \ 4
*/

}

Member Function Documentation

double genie::Born::GetReAlpha ( void  )

inline

Definition at line 32 of file Born.h.

References falpha.

Referenced by genie::HENuElGenerator::ProcessEventRecord(), genie::GLRESGenerator::ProcessEventRecord(), genie::HENuElPXSec::XSec(), genie::PhotonCOHPXSec::XSec(), and genie::GLRESPXSec::XSec().

{ return falpha.Re(); }

double Born::GetS	(	double	mlin,
		double	Enuin
	)

Definition at line 195 of file Born.cxx.

Referenced by genie::HENuElGenerator::ProcessEventRecord(), genie::PhotonRESGenerator::ProcessEventRecord(), genie::GLRESGenerator::ProcessEventRecord(), genie::HENuElPXSec::XSec(), genie::GLRESPXSec::XSec(), and genie::PhotonRESPXSec::XSec().

{
  return 2. * mlin * Enuin + mlin*mlin;
}

double Born::GetT	(	double	mlin,
		double	mlout,
		double	s,
		double	costhCM
	)

Definition at line 200 of file Born.cxx.

Referenced by genie::HENuElGenerator::ProcessEventRecord(), genie::GLRESGenerator::ProcessEventRecord(), genie::HENuElPXSec::XSec(), genie::PhotonRESPXSec::XSec(), and genie::GLRESPXSec::XSec().

{
  //http://edu.itp.phys.ethz.ch/hs10/ppp1/PPP1_2.pdf [Sec 2.2.1]
  double sum = mlin*mlin+mlout*mlout;
  return ( (TMath::Sqrt(Lambda(s,0.,mlin*mlin)*Lambda(s,mlout*mlout,0.))*costhCM+mlin*mlin*mlout*mlout)/s + sum - s ) /2.;
}

double Born::GetU	(	double	mlin,
		double	mlout,
		double	s,
		double	t
	)

Definition at line 207 of file Born.cxx.

{
    return mlin*mlin+mlout*mlout-s-t;
}

bool Born::IsInPhaseSpace	(	double	mlin,
		double	mlout,
		double	Enuin,
		double	Enuout
	)

Definition at line 212 of file Born.cxx.

Referenced by genie::GLRESPXSec::XSec(), and genie::HENuElPXSec::XSec().

{

  //https://arxiv.org/pdf/2007.14426.pdf [section 2.2]
  double frac = Enuout/Enuin;
  if      ( frac < mlin/(mlin+2.*Enuin)+(mlout*mlout-mlin*mlin)/2./Enuin/(mlin+2.*Enuin)  ) return false;
  else if ( frac > 1.-(mlout*mlout-mlin*mlin)/2./Enuin/mlin ) return false;

  return true;

}

double Born::Lambda	(	double	a,
		double	b,
		double	c
	)

Definition at line 190 of file Born.cxx.

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

{
  return a*a + b*b + c*c - 2*a*b - 2*a*c - 2*b*c;
}

double Born::PXSecCCR	(	double	s,
		double	t,
		double	mlin,
		double	mlout
	)

Definition at line 58 of file Born.cxx.

Referenced by genie::GLRESPXSec::XSec(), and genie::PhotonRESPXSec::XSec().

{

  TComplex prop = falpha/fsw2/(s-fmw2c);

  return (t-mlout*mlout)*(t-mlin*mlin) * prop.Rho2();

}

double Born::PXSecCCRNC	(	double	s,
		double	t,
		double	mlin,
		double	mlout
	)

Definition at line 76 of file Born.cxx.

References a, and genie::units::b.

Referenced by genie::GLRESPXSec::XSec(), and genie::PhotonRESPXSec::XSec().

{

  double u = GetU(mlin,mlout,s,t);
  
  TComplex a = fgav*(fgae-fgbe)/(u-fmz2c)/fcw2/fsw2;
  TComplex b = fgav*(fgae+fgbe)/(u-fmz2c)/fcw2/fsw2 + 1./(s-fmw2c)/fsw2;
  return falpha.Rho2() * ( (t-mlout*mlout)*(t-mlin*mlin)*b.Rho2() + (s-mlout*mlout)*(s-mlin*mlin)*a.Rho2() );

}

double Born::PXSecCCV	(	double	s,
		double	t,
		double	mlin,
		double	mlout
	)

Definition at line 67 of file Born.cxx.

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

{

  TComplex prop = falpha/fsw2/(t-fmw2c);

  return (s-mlout*mlout)*(s-mlin*mlin) * prop.Rho2();

}

double Born::PXSecCCVNC	(	double	s,
		double	t,
		double	mlin,
		double	mlout
	)

Definition at line 87 of file Born.cxx.

References a, and genie::units::b.

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

{

  double u = GetU(mlin,mlout,s,t);
  
  TComplex a = fgav*(fgae+fgbe)/(u-fmz2c)/fcw2/fsw2 + 1./(t-fmw2c)/fsw2;
  TComplex b = fgav*(fgae-fgbe)/(u-fmz2c)/fcw2/fsw2;
  return falpha.Rho2() * ( (t-mlout*mlout)*(t-mlin*mlin)*b.Rho2() + (s-mlout*mlout)*(s-mlin*mlin)*a.Rho2() );

}

double Born::PXSecNCVnu	(	double	s,
		double	t,
		double	mlin,
		double	mlout
	)

Definition at line 98 of file Born.cxx.

References a, and genie::units::b.

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

{

  double u = GetU(mlin,mlout,s,t);
  
  TComplex a = fgav*(fgae+fgbe)/(u-fmz2c)/fcw2/fsw2;
  TComplex b = fgav*(fgae-fgbe)/(u-fmz2c)/fcw2/fsw2;
  return falpha.Rho2() * ( (t-mlout*mlout)*(t-mlin*mlin)*b.Rho2() + (s-mlout*mlout)*(s-mlin*mlin)*a.Rho2() );

}

double Born::PXSecNCVnubar	(	double	s,
		double	t,
		double	mlin,
		double	mlout
	)

Definition at line 109 of file Born.cxx.

References a, and genie::units::b.

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

{

  double u = GetU(mlin,mlout,s,t);
  
  TComplex a = fgav*(fgae-fgbe)/(u-fmz2c)/fcw2/fsw2;
  TComplex b = fgav*(fgae+fgbe)/(u-fmz2c)/fcw2;
  return falpha.Rho2() * ( (t-mlout*mlout)*(t-mlin*mlin)*b.Rho2()/fsw2.Rho2() + (s-mlout*mlout)*(s-mlin*mlin)*a.Rho2() );

}

double Born::PXSecPhoton	(	double	s,
		double	t,
		double	mlout2
	)

Definition at line 120 of file Born.cxx.

References genie::constants::kMw2, and genie::constants::kPi2.

{

  double u = kMw2 + mlout2 - s - t;
  
  double ME = 8*kPi2*falpha.Rho2()*s/kMw2/fsw2.Re()/TMath::Power(mlout2 - t,2)/TMath::Power(kMw2 - u,2)* 
        ( -2*(kMw2 - u)*TMath::Power(mlout2,3) - 2*TMath::Power(mlout2,2)*(-2*kMw2*u + u*(s + u) + TMath::Power(kMw2,2)) 
          + mlout2*(-(kMw2*u*(4*s + 5*u)) + (s + u)*TMath::Power(kMw2,2) + 3*TMath::Power(kMw2,3) + (s + u)*TMath::Power(u,2)) 
          + 2*kMw2*((3*s + u)*TMath::Power(kMw2,2) - TMath::Power(kMw2,3) + 4*u*TMath::Power(s,2) + 2*TMath::Power(s,3) + 3*s*TMath::Power(u,2) 
          + TMath::Power(u,3) - kMw2*TMath::Power(2*s + u,2)) );
  
  return TMath::Max(0.,ME);

}

double Born::PXSecPhoton_L	(	double	s12,
		double	s13,
		double	Q2,
		double	ml2
	)

Definition at line 163 of file Born.cxx.

References genie::constants::kMw2, and genie::constants::kPi2.

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

{
  double ME2 = 0.0;
  ME2 = 2*falpha.Rho2()*Q2*TMath::Power(kMw2,-3)*kPi2*TMath::Power(s12,-2)*TMath::Power(ml2 - kMw2 + s13,-2)*TMath::Power(ml2 - kMw2 - s12 + s13,-2)*
 ((s12 - s13)*TMath::Power(ml2,5)*TMath::Power(s12,2) - 2*s12*TMath::Power(ml2,4)*(2*kMw2*TMath::Power(s12,2) - (Q2 - s12)*(-3*s12*s13 + TMath::Power(s12,2) + 2*TMath::Power(s13,2))) + 
   TMath::Power(ml2,3)*(-2*(s12 - s13)*TMath::Power(kMw2,2)*TMath::Power(s12,2) + 
      2*kMw2*s12*(Q2*(9*s12*s13 - 5*TMath::Power(s12,2) - 2*TMath::Power(s13,2)) + s12*(-11*s12*s13 + 3*TMath::Power(s12,2) + 4*TMath::Power(s13,2))) + 
      (s12 - s13)*(TMath::Power(Q2,2)*TMath::Power(s12 - 2*s13,2) + TMath::Power(s12,2)*(-6*s12*s13 + TMath::Power(s12,2) + 6*TMath::Power(s13,2)) - 
         2*Q2*s12*(-5*s12*s13 + TMath::Power(s12,2) + 6*TMath::Power(s13,2)))) + 
   2*TMath::Power(ml2,2)*(4*(2*s12 - s13)*TMath::Power(kMw2,3)*TMath::Power(s12,2) + 
      (Q2 - s12)*s13*(Q2*(s12 - 2*s13) + s12*(-s12 + s13))*(-3*s12*s13 + TMath::Power(s12,2) + 2*TMath::Power(s13,2)) + 
      s12*TMath::Power(kMw2,2)*(Q2*(-11*s12*s13 + 7*TMath::Power(s12,2) - 2*TMath::Power(s13,2)) + s12*(15*s12*s13 - 11*TMath::Power(s12,2) + 2*TMath::Power(s13,2))) - 
      kMw2*((s12 - s13)*TMath::Power(Q2,2)*TMath::Power(s12 - 2*s13,2) + TMath::Power(s12,2)*(-11*s13*TMath::Power(s12,2) + TMath::Power(s12,3) + 20*s12*TMath::Power(s13,2) - 8*TMath::Power(s13,3)) - 
         2*Q2*s12*(-10*s13*TMath::Power(s12,2) + TMath::Power(s12,3) + 17*s12*TMath::Power(s13,2) - 6*TMath::Power(s13,3)))) + 
   4*TMath::Power(kMw2,2)*TMath::Power(s12,2)*(-(s13*(Q2 - 7*s12 + 4*s13)*TMath::Power(kMw2,2)) + (s12 - 2*s13)*TMath::Power(kMw2,3) + kMw2*(2*Q2 - s12 - 2*s13)*TMath::Power(s13,2) + 
      (-Q2 + s12)*TMath::Power(s13,3)) + ml2*(-15*(s12 - s13)*TMath::Power(kMw2,4)*TMath::Power(s12,2) + 
      2*s12*TMath::Power(kMw2,3)*(Q2*(7*s12*s13 - 3*TMath::Power(s12,2) + 2*TMath::Power(s13,2)) + s12*(-21*s12*s13 + 9*TMath::Power(s12,2) + 4*TMath::Power(s13,2))) + 
      TMath::Power(kMw2,2)*((s12 - s13)*TMath::Power(Q2,2)*TMath::Power(s12 - 2*s13,2) + 
         TMath::Power(s12,2)*(-31*s13*TMath::Power(s12,2) + TMath::Power(s12,3) + 60*s12*TMath::Power(s13,2) - 14*TMath::Power(s13,3)) - 
         2*Q2*s12*(-14*s13*TMath::Power(s12,2) + TMath::Power(s12,3) + 27*s12*TMath::Power(s13,2) - 6*TMath::Power(s13,3))) - 
      2*kMw2*s13*((s12 - s13)*TMath::Power(Q2,2)*TMath::Power(s12 - 2*s13,2) + 
         TMath::Power(s12,2)*(-8*s13*TMath::Power(s12,2) + TMath::Power(s12,3) + 11*s12*TMath::Power(s13,2) - 4*TMath::Power(s13,3)) + 
         Q2*s12*(15*s13*TMath::Power(s12,2) - 2*TMath::Power(s12,3) - 25*s12*TMath::Power(s13,2) + 10*TMath::Power(s13,3))) + 
      (s12 - s13)*TMath::Power(s13,2)*TMath::Power(Q2*(s12 - 2*s13) + s12*(-s12 + s13),2)))/fsw2.Re();
  return TMath::Max(0.,ME2);        
}

double Born::PXSecPhoton_T	(	double	s12,
		double	s13,
		double	Q2,
		double	ml2
	)

Definition at line 135 of file Born.cxx.

References genie::constants::kMw2, and genie::constants::kPi2.

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

{
  double ME2 = 0.0;
  ME2 = (4*falpha.Rho2()*kPi2*(TMath::Power(ml2,4)*s12*(2*TMath::Power(kMw2,2)*TMath::Power(s12,2) - 2*kMw2*Q2*s12*s13 + TMath::Power(Q2,2)*s13*(-s12 + s13)) + 
     TMath::Power(ml2,3)*(-2*TMath::Power(kMw2,3)*TMath::Power(s12,3) + TMath::Power(Q2,2)*(s12 - s13)*s13*(-(Q2*s12) + TMath::Power(s12,2) + Q2*s13 - 3*s12*s13) + 
        2*TMath::Power(kMw2,2)*TMath::Power(s12,2)*(3*Q2*s12 - 2*TMath::Power(s12,2) + 2*Q2*s13 + s12*s13) + 
        kMw2*Q2*s12*(Q2*TMath::Power(s12,2) - Q2*TMath::Power(s13,2) - 2*s12*TMath::Power(s13,2))) + 
     TMath::Power(ml2,2)*(-6*TMath::Power(kMw2,4)*TMath::Power(s12,3) + 2*kMw2*Q2*
         (-(Q2*s12*(s12 - 3*s13)) + TMath::Power(Q2,2)*(s12 - s13) + TMath::Power(s12,2)*(s12 - s13))*(s12 - s13)*s13 + 
        TMath::Power(Q2,2)*(s12 - s13)*TMath::Power(s13,2)*(-2*Q2*s12 + 2*TMath::Power(s12,2) + 2*Q2*s13 - 3*s12*s13) + 
        2*TMath::Power(kMw2,3)*TMath::Power(s12,2)*(2*TMath::Power(s12,2) - 3*Q2*(2*s12 + s13)) + 
        TMath::Power(kMw2,2)*s12*(2*TMath::Power(s12,2)*TMath::Power(s12 - s13,2) + TMath::Power(Q2,2)*(s12 - s13)*s13 - 
           2*Q2*s12*(TMath::Power(s12,2) - 8*s12*s13 - 2*TMath::Power(s13,2)))) - 
     2*TMath::Power(kMw2,2)*TMath::Power(s12,2)*(2*TMath::Power(kMw2,4)*s12 + TMath::Power(Q2,2)*TMath::Power(s13,2)*(-s12 + s13) - 
        2*TMath::Power(kMw2,3)*(2*TMath::Power(s12,2) - Q2*s13 + s12*s13) + 
        TMath::Power(kMw2,2)*(4*Q2*s12*(s12 - 2*s13) + TMath::Power(Q2,2)*(-s12 + s13) + 2*s12*TMath::Power(s12 + s13,2)) + 
        2*kMw2*s13*(TMath::Power(Q2,2)*(s12 - s13) - s12*(TMath::Power(s12,2) + TMath::Power(s13,2)) + Q2*(-TMath::Power(s12,2) + 2*s12*s13 + TMath::Power(s13,2)))) + 
     ml2*(10*TMath::Power(kMw2,5)*TMath::Power(s12,3) - TMath::Power(Q2,2)*(Q2 - s12)*TMath::Power(s12 - s13,2)*TMath::Power(s13,3) + 
        2*TMath::Power(kMw2,4)*TMath::Power(s12,2)*(3*Q2*s12 - 4*TMath::Power(s12,2) + 4*Q2*s13 - 3*s12*s13) + 
        kMw2*Q2*(s12 - s13)*TMath::Power(s13,2)*(2*TMath::Power(Q2,2)*(s12 - s13) + 2*TMath::Power(s12,2)*(s12 - s13) + Q2*s12*(-3*s12 + 5*s13)) + 
        TMath::Power(kMw2,3)*s12*(2*Q2*s12*(5*TMath::Power(s12,2) - 16*s12*s13 - TMath::Power(s13,2)) + 
           TMath::Power(Q2,2)*(-3*TMath::Power(s12,2) + 2*s12*s13 + TMath::Power(s13,2)) + 2*TMath::Power(s12,2)*(TMath::Power(s12,2) + 6*s12*s13 + TMath::Power(s13,2))) - 
        TMath::Power(kMw2,2)*s13*(TMath::Power(Q2,3)*TMath::Power(s12 - s13,2) - 2*TMath::Power(s12,3)*TMath::Power(s12 - s13,2) + 
           TMath::Power(Q2,2)*s12*(-5*TMath::Power(s12,2) + 8*s12*s13 - 3*TMath::Power(s13,2)) + 
           2*Q2*TMath::Power(s12,2)*(3*TMath::Power(s12,2) - 9*s12*s13 + 2*TMath::Power(s13,2))))))/(TMath::Power(kMw2,3)*TMath::Power(s12,2)*TMath::Power(ml2 - kMw2 + s13,2)*TMath::Power(ml2 - kMw2 - s12 + s13,2)*fsw2.Re());
  return TMath::Max(0.,ME2);
}

Member Data Documentation

TComplex genie::Born::falpha

private

Definition at line 53 of file Born.h.

Referenced by GetReAlpha().

TComplex genie::Born::fcw2

private

Definition at line 55 of file Born.h.

TComplex genie::Born::fgae

private

Definition at line 58 of file Born.h.

TComplex genie::Born::fgav

private

Definition at line 60 of file Born.h.

TComplex genie::Born::fgbe

private

Definition at line 59 of file Born.h.

double genie::Born::fGw

private

Definition at line 50 of file Born.h.

double genie::Born::fGz

private

Definition at line 51 of file Born.h.

TComplex genie::Born::fmw2c

private

Definition at line 56 of file Born.h.

TComplex genie::Born::fmz2c

private

Definition at line 57 of file Born.h.

TComplex genie::Born::fsw2

private

Definition at line 54 of file Born.h.

---

The documentation for this class was generated from the following files:

• Born.h
• Born.cxx