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 \at km3net.de> IFIC & Harvard University

Created:\n Dec 8, 2021

License:\n Copyright (c) 2003-2025, 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::Born ( )

Definition at line 24 of file Born.cxx.

{
 
  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.;
 
}

References falpha, fcw2, fgae, fgav, fgbe, fGw, fGz, genie::PDGLibrary::Find(), fmw2c, fmz2c, fsw2, 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.

◆ ~Born()

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

◆ GetReAlpha()

double genie::Born::GetReAlpha ( void )

inline

Definition at line 32 of file Born.h.

32{ return falpha.Re(); }

References falpha.

◆ GetS()

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

Definition at line 195 of file Born.cxx.

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

◆ GetT()

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

Definition at line 200 of file Born.cxx.

{
  //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.;
}

References Lambda().

◆ GetU()

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;
}

Referenced by PXSecCCRNC(), PXSecCCVNC(), PXSecNCVnu(), and PXSecNCVnubar().

◆ IsInPhaseSpace()

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

Definition at line 212 of file Born.cxx.

{
 
  //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;
 
}

◆ Lambda()

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

Definition at line 190 of file Born.cxx.

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

References a.

Referenced by GetT().

◆ PXSecCCR()

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

Definition at line 58 of file Born.cxx.

{
 
  TComplex prop = falpha/fsw2/(s-fmw2c);
 
  return (t-mlout*mlout)*(t-mlin*mlin) * prop.Rho2();
 
}

References falpha, fmw2c, and fsw2.

◆ PXSecCCRNC()

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

Definition at line 76 of file Born.cxx.

{
 
  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() );
 
}

References a, falpha, fcw2, fgae, fgav, fgbe, fmw2c, fmz2c, fsw2, and GetU().

◆ PXSecCCV()

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

Definition at line 67 of file Born.cxx.

{
 
  TComplex prop = falpha/fsw2/(t-fmw2c);
 
  return (s-mlout*mlout)*(s-mlin*mlin) * prop.Rho2();
 
}

References falpha, fmw2c, and fsw2.

◆ PXSecCCVNC()

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

Definition at line 87 of file Born.cxx.

{
 
  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() );
 
}

References a, falpha, fcw2, fgae, fgav, fgbe, fmw2c, fmz2c, fsw2, and GetU().

◆ PXSecNCVnu()

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

Definition at line 98 of file Born.cxx.

{
 
  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() );
 
}

References a, falpha, fcw2, fgae, fgav, fgbe, fmz2c, fsw2, and GetU().

◆ PXSecNCVnubar()

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

Definition at line 109 of file Born.cxx.

{
 
  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() );
 
}

References a, falpha, fcw2, fgae, fgav, fgbe, fmz2c, fsw2, and GetU().

◆ PXSecPhoton()

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

Definition at line 120 of file Born.cxx.

{
 
  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);
 
}

References falpha, fsw2, genie::constants::kMw2, and genie::constants::kPi2.

◆ PXSecPhoton_L()

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

Definition at line 163 of file Born.cxx.

{
  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);        
}

References falpha, fsw2, genie::constants::kMw2, and genie::constants::kPi2.

◆ PXSecPhoton_T()

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

Definition at line 135 of file Born.cxx.

{
  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);
}

References falpha, fsw2, genie::constants::kMw2, and genie::constants::kPi2.

Member Data Documentation

◆ falpha

TComplex genie::Born::falpha

private

Definition at line 53 of file Born.h.

Referenced by Born(), GetReAlpha(), PXSecCCR(), PXSecCCRNC(), PXSecCCV(), PXSecCCVNC(), PXSecNCVnu(), PXSecNCVnubar(), PXSecPhoton(), PXSecPhoton_L(), and PXSecPhoton_T().

◆ fcw2

TComplex genie::Born::fcw2

private

Definition at line 55 of file Born.h.

Referenced by Born(), PXSecCCRNC(), PXSecCCVNC(), PXSecNCVnu(), and PXSecNCVnubar().

◆ fgae

TComplex genie::Born::fgae

private

Definition at line 58 of file Born.h.

Referenced by Born(), PXSecCCRNC(), PXSecCCVNC(), PXSecNCVnu(), and PXSecNCVnubar().

◆ fgav

TComplex genie::Born::fgav

private

Definition at line 60 of file Born.h.

Referenced by Born(), PXSecCCRNC(), PXSecCCVNC(), PXSecNCVnu(), and PXSecNCVnubar().

◆ fgbe

TComplex genie::Born::fgbe

private

Definition at line 59 of file Born.h.

Referenced by Born(), PXSecCCRNC(), PXSecCCVNC(), PXSecNCVnu(), and PXSecNCVnubar().

◆ fGw

double genie::Born::fGw

private

Definition at line 50 of file Born.h.

Referenced by Born().

◆ fGz

double genie::Born::fGz

private

Definition at line 51 of file Born.h.

Referenced by Born().

◆ fmw2c

TComplex genie::Born::fmw2c

private

Definition at line 56 of file Born.h.

Referenced by Born(), PXSecCCR(), PXSecCCRNC(), PXSecCCV(), and PXSecCCVNC().

◆ fmz2c

TComplex genie::Born::fmz2c

private

Definition at line 57 of file Born.h.

Referenced by Born(), PXSecCCRNC(), PXSecCCVNC(), PXSecNCVnu(), and PXSecNCVnubar().

◆ fsw2

TComplex genie::Born::fsw2

private

Definition at line 54 of file Born.h.

Referenced by Born(), PXSecCCR(), PXSecCCRNC(), PXSecCCV(), PXSecCCVNC(), PXSecNCVnu(), PXSecNCVnubar(), PXSecPhoton(), PXSecPhoton_L(), and PXSecPhoton_T().

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

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Born()

◆ ~Born()

Member Function Documentation

◆ GetReAlpha()

◆ GetS()

◆ GetT()

◆ GetU()

◆ IsInPhaseSpace()

◆ Lambda()

◆ PXSecCCR()

◆ PXSecCCRNC()

◆ PXSecCCV()

◆ PXSecCCVNC()

◆ PXSecNCVnu()

◆ PXSecNCVnubar()

◆ PXSecPhoton()

◆ PXSecPhoton_L()

◆ PXSecPhoton_T()

Member Data Documentation

◆ falpha

◆ fcw2

◆ fgae

◆ fgav

◆ fgbe

◆ fGw

◆ fGz

◆ fmw2c

◆ fmz2c

◆ fsw2