Main Page | Namespace List | Class Hierarchy | Class List | File List | Namespace Members | Class Members

alpha_strong Class Reference

#include <coupling.h>

List of all members.

Public Types

enum  { exact, truncate_in_one_over_L }

Static Public Member Functions

double beta_0 (int Nf)
double beta_1 (int Nf)
int get_active_flavours (double Q)
double get_lambda_QCD (double Q)
double get_lambda_QCD (int Nf)
double get_value (double Q, int Nf)

Static Public Attributes

double lambda_3 = 0.374
double lambda_4 = 0.327
double lambda_5 = 0.226
double charm_threshold = 1.3
double bottom_threshold = 4.7
int method = alpha_strong::truncate_in_one_over_L

Static Private Member Functions

double get_F (double Q, double a_s, int Nf)
double get_dF (double Q, double a_s, int Nf)
double root_safeI (double a, double b, double Q, int Nf)

Detailed Description

The strong coupling constant.

The class works with the quantity

\[ a_s = \frac{\alpha_s}{4\pi} \]

.

If alpha_strong::method == alpha_strong::exact, the value of $a_s$ is obtained by solving numerically the equation

\[ \frac{1}{a_s} \mbox{} - \frac{\beta_1}{\beta_0} \ln \left( \beta_1 + \frac{\beta_0}{a_s} \right) \mbox{} - \beta_0 L = 0 \]

where $ L = \ln \frac{Q^2}{\Lambda^2_{QCD}}$.

If alpha_strong::method == alpha_strong::truncate_in_one_over_L, the value of $a_s$ is given by the formula

\[ a_s = \frac{1}{\beta_0 L} \left( 1 - \frac{\beta_1}{\beta_0^2} \frac{\ln L}{L} \right). \]

Member Function Documentation

double beta_0 (  int  Nf  )  [static]
 

The first coefficient $\beta_0$ of the beta function

\[ \mu^2 \frac{d}{d\mu^2} a_s = - \varepsilon a_s \mbox{} - \beta_0 a_s^2 - \beta_1 a_s^3 - \beta_2 a_s^4 - ... \]

with $ a_s = \alpha_s / ( 4 \pi) $ and

\[ \beta_0 = \frac{11}{3} C_A - \frac{4}{3} T_R N_f \]

double beta_1 (  int  Nf  )  [static]
 

The second coefficient $\beta_1$ of the beta function

\[ \mu^2 \frac{d}{d\mu^2} a_s = - \varepsilon a_s \mbox{} - \beta_0 a_s^2 - \beta_1 a_s^3 - \beta_2 a_s^4 - ... \]

with $ a_s = \alpha_s / ( 4 \pi) $ and

\[ \beta_1 = \frac{34}{3} C_A^2 - 4 \left( \frac{5}{3} C_A + C_F \right) T_R N_f \]

int get_active_flavours (  double  Q  )  [static]
 

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

double get_dF (  double  Q,
double  a_s,
int  Nf
)  [static, private]
 

Evaluates

\[ \frac{d}{da_s} F(Q,a_s) = - \frac{\beta_0}{a_s^2} \frac{1}{(\beta_0+\beta_1 a_s)}. \]

double get_F (  double  Q,
double  a_s,
int  Nf
)  [static, private]
 

Evaluates

\[ F(Q,a_s) = \frac{1}{a_s} \mbox{} - \frac{\beta_1}{\beta_0} \ln \left( \beta_1 + \frac{\beta_0}{a_s} \right) \mbox{} - \beta_0 L \]

with $ L = \ln \frac{Q^2}{\Lambda^2_{QCD}}$.

double get_lambda_QCD (  int  Nf  )  [static]
 

Returns the appropriate $\Lambda_{QCD}$ corresponding to $N_f$ active flavours.

double get_lambda_QCD (  double  Q  )  [static]
 

Returns the appropriate $\Lambda_{QCD}$ corresponding to the scale $Q$.

double get_value (  double  Q,
int  Nf
)  [static]
 

Returns the value of $ a_s = \frac{\alpha_s}{4\pi}$ at the scale $Q$ with $N_f$ active flavours.

The parameter $N_f$ ensures that the correct formula is used close to flavour thresholds.

double root_safeI (  double  a,
double  b,
double  Q,
int  Nf
)  [static, private]
 

Numerical solution of the equation

\[ \frac{1}{a_s} \mbox{} - \frac{\beta_1}{\beta_0} \ln \left( \beta_1 + \frac{\beta_0}{a_s} \right) \mbox{} - \beta_0 L = 0 \]

for $a_s$.

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 doxygen 1.3.7