genie::utils::kinematics::electromagnetic Namespace Reference

Functions
Range1D_t	InelWLim (double El, double ml, double M)
Range1D_t	InelQ2Lim_W (double El, double ml, double M, double W)
Range1D_t	Inelq2Lim_W (double El, double ml, double M, double W)
Range1D_t	InelQ2Lim (double El, double ml, double M)
Range1D_t	Inelq2Lim (double El, double ml, double M)
Range1D_t	InelXLim (double El, double ml, double M)
Range1D_t	InelYLim (double El, double ml, double M)
Range1D_t	InelYLim_X (double El, double ml, double M, double x)

Variables
static const double	kMinQ2Limit = 0.02

Function Documentation

Range1D_t genie::utils::kinematics::electromagnetic::InelQ2Lim	(	double	El,
		double	ml,
		double	M
	)

Definition at line 606 of file KineUtils.cxx.

{
// Computes Q2 (>0) limits irrespective of W for inelastic em interactions

  Range1D_t Q2;
  Q2.min = -1;
  Q2.max = -1;

  Range1D_t W  = utils::kinematics::electromagnetic::InelWLim(El,ml,M);
  if(W.min<0) return Q2;

  Q2 = utils::kinematics::electromagnetic::InelQ2Lim_W(El,ml,M,W.min);
  return Q2;
}

Range1D_t genie::utils::kinematics::electromagnetic::Inelq2Lim	(	double	El,
		double	ml,
		double	M
	)

Definition at line 622 of file KineUtils.cxx.

{
// Computes Q2 (>0) limits irrespective of W for inelastic em interactions

  Range1D_t Q2 = utils::kinematics::electromagnetic::InelQ2Lim(El,ml,M);
  Range1D_t q2;
  q2.min = - Q2.max;
  q2.max = - Q2.min;
  return q2;
}

Range1D_t genie::utils::kinematics::electromagnetic::InelQ2Lim_W	(	double	El,
		double	ml,
		double	M,
		double	W
	)

Definition at line 556 of file KineUtils.cxx.

{
// Computes Q2 limits (>0) @ the input W for inelastic em interactions

  Range1D_t Q2;
  Q2.min = -1;
  Q2.max = -1;

  double M2  = TMath::Power(M,  2.);
  double ml2 = TMath::Power(ml, 2.);
  double W2  = TMath::Power(W,  2.);
  double s   = M2 + 2*M*El + ml2; // added lepton mass squared to be used in s calculation (non-negligible mass for em interactions)

  SLOG("KineLimits", pDEBUG) << "s  = " << s;
  SLOG("KineLimits", pDEBUG) << "El = " << El;
  assert (s>0);

  double auxC = 0.5*(s - M2 - ml2)/s; // subtract ml2 to account for the non-negligible mass of the incoming lepton
  double aux1 = s + ml2 - W2;
  double aux2 = aux1*aux1 - 4*s*ml2;

  (aux2 < 0) ? ( aux2 = 0 ) : ( aux2 = TMath::Sqrt(aux2) );

  Q2.max = -ml2 + auxC * (aux1 + aux2); // => 0
  Q2.min = -ml2 + auxC * (aux1 - aux2); // => 0

  // guard against overflows
  Q2.max = TMath::Max(0., Q2.max);
  Q2.min = TMath::Max(0., Q2.min);

  // limit the minimum Q2
  if(Q2.min < utils::kinematics::electromagnetic::kMinQ2Limit) {Q2.min = utils::kinematics::electromagnetic::kMinQ2Limit; } // use the relevant threshold for em scattering
  if(Q2.max < Q2.min   ) {Q2.min = -1; Q2.max = -1;}

  return Q2;
}

Range1D_t genie::utils::kinematics::electromagnetic::Inelq2Lim_W	(	double	El,
		double	ml,
		double	M,
		double	W
	)

Definition at line 594 of file KineUtils.cxx.

{
// Computes q2 (<0) limits @ the input W for inelastic em interactions

  Range1D_t Q2 = utils::kinematics::electromagnetic::InelQ2Lim_W(El,ml,M,W);
  Range1D_t q2;
  q2.min = - Q2.max;
  q2.max = - Q2.min;
  return q2;
}

Range1D_t genie::utils::kinematics::electromagnetic::InelWLim	(	double	El,
		double	ml,
		double	M
	)

Definition at line 534 of file KineUtils.cxx.

{
// Computes W limits for inelastic em interactions
//
  double M2 = TMath::Power(M,2);
  double ml2 = TMath::Power(ml,2); // added lepton mass squared to be used in s calculation
  double s  = M2 + 2*M*El + ml2; // non-negligible mass for em interactions
  assert (s>0);

  Range1D_t W;
  W.min  = kNeutronMass + kPhotontest;
  W.max  = TMath::Sqrt(s) - ml;
  if(W.max<=W.min) {
    W.min = -1;
    W.max = -1;
    return W;
  }
  W.min  += controls::kASmallNum;
  W.max  -= controls::kASmallNum;
  return W;
}

Range1D_t genie::utils::kinematics::electromagnetic::InelXLim	(	double	El,
		double	ml,
		double	M
	)

Definition at line 634 of file KineUtils.cxx.

{
// Computes Bjorken x limits for inelastic em interactions

  double M2  = TMath::Power(M, 2.);
  double ml2 = TMath::Power(ml,2.);
  double s   = M2 + 2*M*El + ml2; // added lepton mass squared to be used in s calculation (non-negligible mass for em interactions)

  SLOG("KineLimits", pDEBUG) << "s  = " << s;
  SLOG("KineLimits", pDEBUG) << "El = " << El;
  assert (s > M2 + ml2); // added lepton mass squared to be used in s calculation (non-negligible mass for em interactions)

  Range1D_t x;
  x.min = ml2/(s - M2 - ml2) + controls::kASmallNum; // subtracted lepton mass squared to be used in s calculation (non-negligible mass for em interactions)
  x.max = 1. - controls::kASmallNum;

  return x;
}

Range1D_t genie::utils::kinematics::electromagnetic::InelYLim	(	double	El,
		double	ml,
		double	M
	)

Definition at line 654 of file KineUtils.cxx.

{
// Computes y limits for inelastic v interactions

  Range1D_t y;
  y.min =  999;
  y.max = -999;

  Range1D_t xl = kinematics::electromagnetic::InelXLim(El,ml,M);
  assert(xl.min>0 && xl.max>0);

  const unsigned int N=100;
  const double logxmin = TMath::Log10(xl.min);
  const double logxmax = TMath::Log10(xl.max);
  const double dlogx   = (logxmax-logxmin) / (double)(N-1);

  for(unsigned int i=0; i<N; i++) {
    double x = TMath::Power(10, logxmin + i*dlogx);

    Range1D_t y_x = kinematics::electromagnetic::InelYLim_X(El,ml,M,x);
    if(y_x.min>=0 && y_x.min<=1) y.min = TMath::Min(y.min, y_x.min);
    if(y_x.max>=0 && y_x.max<=1) y.max = TMath::Max(y.max, y_x.max);
  }

  if(y.max >= 0 && y.max <= 1 && y.min >= 0 && y.min <= 1) {
    y.min = TMath::Max(y.min,     controls::kASmallNum);
    y.max = TMath::Min(y.max, 1 - controls::kASmallNum);
  } else {
    y.min = -1;
    y.max = -1;
  }
  SLOG("KineLimits", pDEBUG) << "y  = [" << y.min << ", " << y.max << "]";
  return y;
}

Range1D_t genie::utils::kinematics::electromagnetic::InelYLim_X	(	double	El,
		double	ml,
		double	M,
		double	x
	)

Definition at line 689 of file KineUtils.cxx.

{
// Computes y limits @ the input x for inelastic em interactions

  Range1D_t y;
  y.min = -1;
  y.max = -1;

  double El2 = TMath::Power(El,2);
  double ml2 = TMath::Power(ml,2);

  SLOG("KineLimits", pDEBUG) << "x  = " << x;
  SLOG("KineLimits", pDEBUG) << "El = " << El;

  assert (El>0);
  assert (x>0&&x<1);

  double a = 0.5 * ml2/(M*El*x);
  double b = ml2/El2;
  double c = 1 + 0.5*x*M/El;
  double d = TMath::Max(0., TMath::Power(1-a,2.) - b);

  double A = 0.5 * (1-a-0.5*b)/c;
  double B = 0.5 * TMath::Sqrt(d)/c;

  y.min = TMath::Max(0., A-B) + controls::kASmallNum;
  y.max = TMath::Min(1., A+B) - controls::kASmallNum;

  return y;
}

Variable Documentation

const double genie::utils::kinematics::electromagnetic::kMinQ2Limit = 0.02

static

Definition at line 114 of file KineUtils.h.