Fast Evolution of Parton Distributions: alpha_finestruc Class Reference

Fast Evolution of Parton Distributions

#include <coupling_qed.h>

Static Public Member Functions
static double	beta_0 (int Nf_down, int Nf_up, int Nl)

static int	get_active_flavours (double Q)

static int	get_active_leptons (double Q)

static double	get_value (double Q, int Nf_down, int Nf_up, int Nl)

Static Public Attributes
static double	value_at_charm = 0.0005949448010

static double	value_at_tau = 0.0005965224393

static double	value_at_bottom = 0.0006024255586

static double	charm_threshold = 1.3

static double	tau_threshold = 1.777

static double	bottom_threshold = 4.7

Detailed Description

The electromagnetic constant.

The class works with the quantity

$a = \frac{\alpha}{4\pi}.$

The value of $a$ is given by

$a(Q^2) = a(Q_0^2) \frac{1}{ 1 + a(Q_0^2) \beta_0 L } .$

where $L = \ln \frac{Q^2}{Q_0^2}$ .

Member Function Documentation

§ beta_0()

double beta_0	(	int	Nf_down,
		int	Nf_up,
		int	Nl
	)

static

The first coefficient $\beta_0$ of the QED beta function

$\mu^2 \frac{d}{d\mu^2} a_{fs} = - \varepsilon a_{fs} \mbox{} - \beta_0 a_{fs}^2 - \beta_1 a_{fs}^3 - \beta_2 a_{fs}^4 - ...$

with $a_{fs} = \alpha_{fs} / ( 4 \pi)$ and

$\beta_0 = - \frac{4}{3} \sum\limits_{i=e,\mu,\tau,u,d,s,c,b} N_c(i) Q_i^2$

§ get_active_flavours()

int get_active_flavours ( double Q )

static

Returns the number of active flavours at the scale $Q$ .

§ get_active_leptons()

int get_active_leptons ( double Q )

static

Returns the number of active leptons at the scale $Q$ .

§ get_value()

double get_value	(	double	Q,
		int	Nf_down,
		int	Nf_up,
		int	Nl
	)

static

Returns the value of $a_{fs} = \frac{\alpha_{fs}}{4\pi}$ at the scale $Q$ with $N_f=N_{f,down}+N_{f,up}$ active flavours and $N_l$ active leptons.

The top quark is neglected. For a detailed discussion see S. Eidelman and F. Jegerlehner, hep-ph/9502298

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