partondistribution Class Reference

#include <partondistribution.h>

Inheritance diagram for partondistribution:


Public Member Functions
	partondistribution (void)
	partondistribution (int n, double Q0, double A[], double alpha[], double beta[], int eta=1)
	partondistribution (int n, double Q0, const std::valarray< double > &A, const std::valarray< double > &alpha, const std::valarray< double > &beta, int eta=1)
double	get_Q0 (void) const
int	get_eta (void) const
complex_d	get_Mellin_transform (complex_d z) const
double	get_F (double x, double z) const
double	get_dF (double x, double z) const
double	get_ddF (double x, double z) const
double	get_dddF (double x, double z) const
double	get_c0 (double x) const
virtual bool	with_qed (void) const
virtual double	get_electric_charge (void) const
Protected Attributes
int	n
double	Q0
std::valarray< double >	A
std::valarray< double >	alpha
std::valarray< double >	beta
int	eta
Private Member Functions
double	root_safeI (double a, double b, double x) const
Friends
partondistribution	operator+ (const partondistribution &f1, const partondistribution &f2)

Detailed Description

The class partondistribution represents the parameterization of a parton distribution in the form

$x f(x,Q_0^2) = \sum\limits_{i=0}^{n-1} A_i x^{\alpha_i} (1-x)^{\beta_i}$

In addition this class has a data member $\eta = \pm 1$ , which selects odd or even moments for the evolution. The default value for $\eta$ in the constructor is $+1$ , which is good for the singlet distributions and non-singlet non-valence distributions like

$(u+\bar{u}) - ( d + \bar{d} ),$

$(u+\bar{u}) + ( d + \bar{d} ) - 2 ( s + \bar{s} ), ...$

Valence non-singlet distributions like

$(u-\bar{u}), (d - \bar{d}), ...$

need $\eta=-1$ , which has to passed explicitly to the constructor.

Constructor & Destructor Documentation

partondistribution ( void )

Default constructor

partondistribution ( int nr,

double Q0r,

double Ar[],

double alphar[],

double betar[],

int etar = 1

)

Standard constructor

partondistribution ( int nr,

double Q0r,

const std::valarray< double > & Ar,

const std::valarray< double > & alphar,

const std::valarray< double > & betar,

int etar = 1

)

Standard constructor from valarray

Member Function Documentation

double get_c0 ( double x ) const

Returns for fixed $x$ the position of the minimum in the $z$ -plane of the function
$F(x,z) = x^{-z} \sum\limits_{i=0}^{n-1} A_i B(z+\alpha_i-1,1+\beta_i).$
on the real axis right to the rightmost pole.

double get_dddF ( double x,

double z

) const

Evaluates
$\frac{d^3}{dz^3} F(x,z) = \sum\limits_{i=0}^{n-1} \left( G_i''' + 3 G_i'' G_i' + G_i'^3 \right) F_i$
where
$G_i''' = \Psi''(z+\alpha_i-1) - \Psi''(z+\alpha_i+\beta_i)$

double get_ddF ( double x,

double z

) const

Evaluates
$\frac{d^2}{dz^2} F(x,z) = \sum\limits_{i=0}^{n-1} \left( G_i'' + G_i'^2 \right) F_i$
where
$G_i'' = \Psi'(z+\alpha_i-1) - \Psi'(z+\alpha_i+\beta_i)$

double get_dF ( double x,

double z

) const

Evaluates
$\frac{d}{dz} F(x,z) = \sum\limits_{i=0}^{n-1} G_i' F_i$
where
$F_i = x^{-z} A_i B(z+\alpha_i-1,1+\beta_i),$

$G_i = \ln \left( x^{-z} B(z+\alpha_i-1,1+\beta_i) \right)$

$G_i' = -\ln x + \Psi(z+\alpha_i-1) - \Psi(z+\alpha_i+\beta_i)$

virtual double get_electric_charge ( void ) const [inline, virtual]

Return zero for a partondistribution. The method is overridden by the derived class partondistribution_with_qed.
Reimplemented in partondistribution_with_qed.

int get_eta ( void ) const

Returns $\eta$ .

double get_F ( double x,

double z

) const

Evaluates the function
$F(x,z) = x^{-z} \sum\limits_{i=0}^{n-1} A_i B(z+\alpha_i-1,1+\beta_i).$
for the given pair $(x,z)$ .

complex_d get_Mellin_transform ( complex_d z ) const

Evaluates the Mellin transform of the parton distribution
$f^z(Q_0^2) = \sum\limits_{i=0}^{n-1} A_i B(z+\alpha_i-1,1+\beta_i)$
at the point $z$ .

double get_Q0 ( void ) const

Returns $Q_0$ .

double root_safeI ( double a,

double b,

double x

) const [private]

Solves numerically the equation
$\frac{d}{dz} F(x,z) = 0$
for $z$ .

virtual bool with_qed ( void ) const [inline, virtual]

Return false for a partondistribution. The method is overridden by the derived class partondistribution_with_qed.
Reimplemented in partondistribution_with_qed.

Friends And Related Function Documentation

partondistribution operator+ ( const partondistribution & f1,

const partondistribution & f2

) [friend]

Addition of two parton distributions
The sum of two parton distributions is given by
$\sum\limits_{i=0}^{n-1} A_i x^{\alpha_i} (1-x)^{\beta_i} + \sum\limits_{i=0}^{n'-1} A_i' x^{\alpha_i'} (1-x)^{\beta_i'}$

The values of $Q_0$ and $\eta$ of the two summands have to agree, otherwise the function throws an exception.

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

Generated on Wed May 11 20:46:25 2005 for Fast Evolution of Parton Distributions by

1.3.7

partondistribution Class Reference

Public Member Functions

Protected Attributes

Private Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation