genie::utils::phys Namespace Reference

Various physics formulas & utilities. More...

Functions
double	FormationZone (double m, const TLorentzVector &p, const TVector3 &p3hadr, double ct0, double K)
double	R99118 (double x, double Q2)
	PRL 98, 142301, 2007. More...
double	RWhitlow (double x, double Q2)

Detailed Description

Various physics formulas & utilities.

Author

Costas Andreopoulos <constantinos.andreopoulos cern.ch> University of Liverpool & STFC Rutherford Appleton Laboratory

January 22, 2008

Copyright (c) 2003-2020, The GENIE Collaboration For the full text of the license visit http://copyright.genie-mc.org

Function Documentation

double genie::utils::phys::FormationZone	(	double	m,
		const TLorentzVector &	p,
		const TVector3 &	p3hadr,
		double	ct0,
		double	K
	)

Definition at line 18 of file PhysUtils.cxx.

{
// m -> hadon mass (on-shell)
// p -> hadron momentum 4-vector (Lab)
// p3hadr -> hadronic-system momentum 3-vector (Lab)

  TVector3 p3  = p4.Vect();            // hadron's: p (px,py,pz)
  double   m2  = m*m;                  //           m^2
  double   P   = p4.P();               //           |p|
  double   Pt  = p3.Pt(p3hadr);        //           pT
  double   Pt2 = Pt*Pt;                //           pT^2
  double   fz  = P*ct0*m/(m2+K*Pt2);   //           formation zone, in fm

  LOG("PhysUtil", pNOTICE)
      << "Formation zone(|P| = " << P << " GeV, Pt = " << Pt
      << " GeV, ct0 = " << ct0 << " fm, K = " << K << ") = " << fz << " fm";

  return fz;
}

double genie::utils::phys::R99118	(	double	x,
		double	Q2
	)

PRL 98, 142301, 2007.

Definition at line 40 of file PhysUtils.cxx.

{
// Adapted from fortran code sent by V.Tvaskis
// PRL 98, 142301, 2007
//
    double A[3] = { .06723, .46714, 1.89794 };
    double B[3] = { .06347, .57468, -.35342 };
    double C[3] = { .05992, .50885, 2.10807 };

    double consq2=2.;  // Joining point of r1990 and re99118
    double R=0;

    if(Q2 >= consq2) {
       double FAC   = 1+12.*(Q2/(1.+Q2))*(.125*.125/(x*x+.125*.125));
       double RLOG  = FAC/TMath::Log(Q2/.04);
       double Q2thr = 5.*TMath::Power(1.-x,5);
       double R_A   = A[0]*RLOG + A[1] / TMath::Sqrt( TMath::Sqrt( TMath::Power(Q2,4)+TMath::Power(A[2],4) ));
       double R_B   = B[0]*RLOG + B[1]/Q2 + B[2]/( TMath::Power(Q2,2) + TMath::Power(.3,2) );
       double R_C   = C[0]*RLOG + C[1]/TMath::Sqrt( TMath::Power(Q2-Q2thr,2) + TMath::Power(C[2],2) );
       R = (R_A+R_B+R_C)/3.;
    }

    if(Q2 < consq2) {
       double FAC   = 1+12.*(consq2/(1.+consq2))*(.125*.125/(x*x+.125*.125));
       double RLOG  = FAC/TMath::Log(consq2/.04);
       double Q2thr = 5.*TMath::Power(1.-x,5);
       double R_A   = A[0]*RLOG + A[1]/TMath::Sqrt(TMath::Sqrt( TMath::Power(consq2,4)+TMath::Power(A[2],4) ));
       double R_B   = B[0]*RLOG + B[1]/consq2 + B[2]/( TMath::Power(consq2,2) + TMath::Power(.3,2) );
       double R_C   = C[0]*RLOG + C[1]/TMath::Sqrt( TMath::Power(consq2-Q2thr,2) + TMath::Power(C[2],2) );
       double norm=(R_A+R_B+R_C)/3.;
       R=norm*(1.0-TMath::Exp(-Q2*9.212));
   }
   return R;
}

double genie::utils::phys::RWhitlow	(	double	x,
		double	Q2
	)

Definition at line 75 of file PhysUtils.cxx.

{
// Adapted from NeuGEN's rmodel_mod()
//
// Hugh's comments in original code:
//   from NuTeV code provided by Donna Naples, May 2005
//   added form for R below qsq=.35 GEV**2 from hep-ex/030807
//
// NuTEV comments:
//
//C  Revised to make HTWIST select between more than two different
//C  values of R.
//C
//C     HTWIST = 'F'     ==> RQCD   - WITH LIMIT R > (2MX)**2/Q2
//C     HTWIST = 'T'     ==> RSLAC  - WITH LIMIT R > (2MX)**2/Q2
//C     HTWIST = '0'     ==> R = 0 (NOT TRUE, BUT USEFUL FOR STUDIES)
//C     HTWIST = '2'     ==> R =.2 (NOT TRUE, BUT USEFUL FOR STUDIES)
//C     HTWIST = 'C'     ==> R-CALLAN-GROSS = (2MX)**2/Q2
//C
//C     HTWIST = 'W'     ==> R PARAMETERIZATION FROM WHITLOW'S THESIS
//C     HTWIST = '+'     ==> R PARAMETRIZATION FROM WHITLOW +15%
//C     HTWIST = 'P'     ==> R PARAMETRIZATION FROM WHITLOW +0.03
//C     HTWIST = 'M'     ==> R PARAMETRIZATION FROM WHITLOW -0.03
//C
//C  22-DEC-92 WGS
//
  const double C2 = TMath::Power(0.125, 2);
  const double B1 =  0.0635;
  const double B2 =  0.5747;
  const double B3 = -0.3534;

  double Q2R   = TMath::Max(Q2, 0.35);
  double ss    = TMath::Log(Q2R/.04);

  double x2    = TMath::Power(x,   2.);
  double Q4R   = TMath::Power(Q2R, 2.);
  double Q4    = TMath::Power(Q2,  2.);

  double theta = 1. + (12.*Q2R/(Q2R+1.)) * (C2/(C2+x2));
  double R     = (B1/ss)*theta + B2/Q2R + B3/(Q4R+.09);

  R = TMath::Max(R,0.);

  if(Q2 < 0.35)  {
      R *= ( 3.207*(Q2/(Q4+1.)) );
  }
  return R;
}