JPHYSICS::JGeanz Class Reference

Function object for longitudinal profile of EM-shower. More...

#include <JGeanz.hh>

Public Member Functions
	JGeanz (const double __a0, const double __a1, const double __b)
	constructor
double	getProbability (const double E, const double z) const
	Probability Density Function.
double	operator() (const double E, const double z) const
	Probability Density Function.
double	getIntegral (const double E, const double z) const
	Integral of PDF (starting from 0).
double	getLength (const double E, const double P, const double eps=1.0e-3) const
	Get shower length for a given integrated probability.
double	getMaximum (const double E) const
	Get depth of shower maximum.

Static Public Member Functions
static double	getMinimalShowerSize ()
	Get minimal shower size.

Protected Attributes
const double	a0
const double	a1
const double	b
const double	Emin

Detailed Description

Function object for longitudinal profile of EM-shower.

    \f[P(z)  \propto  z^{a-1} \times e^{-z/b}\f]

where:

The parametrisation is taken from reference: C. Kopper, "Performance Studies for the KM3NeT Neutrino Telescope.", PhD thesis, University of Erlangen.

Definition at line 31 of file JGeanz.hh.

Constructor & Destructor Documentation

JGeanz()

JPHYSICS::JGeanz::JGeanz ( const double __a0, const double __a1, const double __b )

inline

constructor

Parameters

__a0	power term (constant)
__a1	power term (E dependence)
__b	expontial slope

Definition at line 39 of file JGeanz.hh.

                             :
      a0(__a0),
      a1(__a1),
      b (__b),
      Emin(exp(-a0/a1))
    {}

Member Function Documentation

getProbability()

double JPHYSICS::JGeanz::getProbability ( const double E, const double z ) const

inline

Probability Density Function.

Parameters

E	EM-shower energy [GeV]
z	z position of light emission point relative to vertex location (z >= 0) [m]

Returns

dP/dz

Definition at line 56 of file JGeanz.hh.

    {
      if (E > Emin) {
 
        const double a = a0 + a1 * log(E);
        const double y = pow(z,a-1.0) * exp(-z/b) / (pow(b,a) * std::tgamma(a));
        
        return y;
      } 
          
      if (z <= getMinimalShowerSize()) 
        return 1.0 / getMinimalShowerSize();
      else
        return 0.0;
    }

operator()()

double JPHYSICS::JGeanz::operator() ( const double E, const double z ) const

inline

Probability Density Function.

Parameters

E	EM-shower energy [GeV]
z	z position of light emission point relative to vertex location (z >= 0) [m]

Returns

dP/dz

Definition at line 81 of file JGeanz.hh.

    {
      return getProbability(E, z);
    }

getIntegral()

double JPHYSICS::JGeanz::getIntegral ( const double E, const double z ) const

inline

Integral of PDF (starting from 0).

Parameters

E	EM-shower energy [GeV]
z	z position [m] (>= 0)

Returns

dP

Definition at line 95 of file JGeanz.hh.

    {
      if (E > Emin) {
 
        const double a = a0 + a1 * log(E);
        const double x = z / b;
        const double y = JMATH::Gamma(a,x);
        
        return y;
      }
      
      if (z <= getMinimalShowerSize())
        return z / getMinimalShowerSize();
      else
        return 1.0;
    }

getLength()

double JPHYSICS::JGeanz::getLength ( const double E, const double P, const double eps = 1.0e-3 ) const

inline

Get shower length for a given integrated probability.

Parameters

E	EM-shower energy [GeV]
P	integrated probability [0,1]
eps	relative precision

Returns

shower length [m]

Definition at line 122 of file JGeanz.hh.

    {
      double zmin  =   0.0;     // [m]
      double zmax  =  30.0;     // [m]
 
      if (E > Emin) {
 
        const double Q = P * (1.0 - eps);
        
        for (int i = 100; i != 0; --i) {
          
          const double z = 0.5 * (zmin + zmax);
          const double p = getIntegral(E, z);
          
          if (fabs(p-Q) < p*eps) {
            return z;
          }
          
          if (p > P)
            zmax = z;
          else
            zmin = z;
        }
        
        return 0.5 * (zmin + zmax);
 
      } else
 
        return 0.0;
    }

getMaximum()

double JPHYSICS::JGeanz::getMaximum ( const double E ) const

inline

Get depth of shower maximum.

Parameters

E	EM-shower energy[GeV]

Returns

depth of maximum [m]

Definition at line 162 of file JGeanz.hh.

    {
      const double a = a0 + a1 * log(E); 
 
      return (a-1)*b;
    }

getMinimalShowerSize()

static double JPHYSICS::JGeanz::getMinimalShowerSize ( )

inlinestatic

Get minimal shower size.

Returns

size [m]

Definition at line 175 of file JGeanz.hh.

    {
      return 1e-6;
    }

Member Data Documentation

a0

const double JPHYSICS::JGeanz::a0

protected

Definition at line 181 of file JGeanz.hh.

a1

const double JPHYSICS::JGeanz::a1

protected

Definition at line 182 of file JGeanz.hh.

b

const double JPHYSICS::JGeanz::b

protected

Definition at line 183 of file JGeanz.hh.

Emin

const double JPHYSICS::JGeanz::Emin

protected

Definition at line 184 of file JGeanz.hh.

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

• JGeanz.hh