Fast Evolution of Parton Distributions
Static Public Member Functions | List of all members
anomalous_dimensions Class Reference

#include <anomalous.h>

Static Public Member Functions

static complex_d anomalous_0_NS (const complex_d &N, int Nf)
 
static complex_d anomalous_0_qq (const complex_d &N, int Nf)
 
static complex_d anomalous_0_qg (const complex_d &N, int Nf)
 
static complex_d anomalous_0_gq (const complex_d &N, int Nf)
 
static complex_d anomalous_0_gg (const complex_d &N, int Nf)
 
static complex_d anomalous_1_NS (const complex_d &N, int eta, int Nf)
 
static complex_d anomalous_1_qq (const complex_d &N, int Nf)
 
static complex_d anomalous_1_qg (const complex_d &N, int Nf)
 
static complex_d anomalous_1_gq (const complex_d &N, int Nf)
 
static complex_d anomalous_1_gg (const complex_d &N, int Nf)
 

Detailed Description

Anomalous dimensions for the evolution of parton distributions.

The anomalous dimensions are expanded in $ a_s = \alpha_s / ( 4 \pi) $ as

\[ \gamma = \gamma_0 a_s + \gamma_1 a_s^2 + ... \]

and implemented in N-space.

The formulae for the one-loop and two-loop anomalous dimensions can be found for example in E.G. Floratos, C. Kounnas and R. Lacaze, Nucl. Phys. B192, (1981), 417.

Member Function Documentation

§ anomalous_0_gg()

complex_d anomalous_0_gg ( const complex_d &  N,
int  Nf 
)
static

The first coefficient $\gamma_0^{(gg)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

§ anomalous_0_gq()

complex_d anomalous_0_gq ( const complex_d &  N,
int  Nf 
)
static

The first coefficient $\gamma_0^{(gq)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

§ anomalous_0_NS()

complex_d anomalous_0_NS ( const complex_d &  N,
int  Nf 
)
static

The first coefficient $\gamma_0$ of the anomalous dimension of the quark non-singlet operator.

§ anomalous_0_qg()

complex_d anomalous_0_qg ( const complex_d &  N,
int  Nf 
)
static

The first coefficient $\gamma_0^{(qg)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

§ anomalous_0_qq()

complex_d anomalous_0_qq ( const complex_d &  N,
int  Nf 
)
static

The first coefficient $\gamma_0^{(qq)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

§ anomalous_1_gg()

complex_d anomalous_1_gg ( const complex_d &  N,
int  Nf 
)
static

The second coefficient $\gamma_1^{(gg)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

§ anomalous_1_gq()

complex_d anomalous_1_gq ( const complex_d &  N,
int  Nf 
)
static

The second coefficient $\gamma_1^{(gq)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

§ anomalous_1_NS()

complex_d anomalous_1_NS ( const complex_d &  N,
int  eta,
int  Nf 
)
static

The second coefficient $\gamma_1$ of the anomalous dimension of the quark non-singlet operator.

$ \eta = \pm 1$ selects the even or odd moments.

Valence non-singlet distributions like

\[ (u-\bar{u}), (d - \bar{d}), ... \]

have $\eta=-1$, while the singlet case and non-valence non-singlet combinations like

\[ (u+\bar{u}) - ( d + \bar{d} ), \]

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

have $\eta=1$.

§ anomalous_1_qg()

complex_d anomalous_1_qg ( const complex_d &  N,
int  Nf 
)
static

The second coefficient $\gamma_1^{(qg)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

§ anomalous_1_qq()

complex_d anomalous_1_qq ( const complex_d &  N,
int  Nf 
)
static

The second coefficient $\gamma_1^{(qq)}$ of the anomalous dimension appearing in the anomalous dimension matrix for the quark singlet / gluon.

The documentation for this class was generated from the following files:
Generated by   doxygen 1.8.12