QCDConstants Struct Reference

Collection of QCD-specific constants and coefficients. More...

#include <QCDHelper.h>

Static Public Attributes
static constexpr int	Nc = 3
	Number of colors.
static constexpr double	C_F = (Nc * Nc - 1.) / (2. * Nc)
	Fundamental Casimir C_F = (N_c^2 - 1) / (2 N_c).
static constexpr double	C_A = Nc
	Adjoint Casimir C_A = N_c.
static constexpr std::array< std::array< double, 3 >, 6 >	beta
	β-function coefficients β_0, β_1, β_2 for nf = 1..6.
static constexpr std::array< std::array< double, 3 >, 6 >	gamma
	γ-function coefficients γ_0, γ_1, γ_2 for nf = 1..6.

Detailed Description

Collection of QCD-specific constants and coefficients.

Contains:

• Color factors for SU(3): N_c, C_F, C_A,
• β-function coefficients (up to three loops) for nf = 1..6,
• γ-function (anomalous dimension) coefficients for the quark mass running (up to three loops).

These constants are exposed through QCDHelper::constants and used in the explicit α_s and mass-running formulae.

Definition at line 41 of file QCDHelper.h.

Member Data Documentation

beta

constexpr std::array<std::array<double, 3>, 6> QCDConstants::beta

staticconstexpr

Initial value:

{{{31. / 3, 134. / 3, 2309.8}, 
                                                                 {29. / 3, 115. / 3, 1786.7}, 
                                                                 {9      , 32      , 1287.6}, 
                                                                 {25. / 3, 77. / 3 , 812.7 }, 
                                                                 {23. / 3, 58. / 3 , 361.81}, 
                                                                 {7      , 13      , -65   }}}

β-function coefficients β_0, β_1, β_2 for nf = 1..6.

Indexed as beta[nf-1][i] with i = 0,1,2.

Definition at line 54 of file QCDHelper.h.

C_A

constexpr double QCDConstants::C_A = Nc

staticconstexpr

Adjoint Casimir C_A = N_c.

Definition at line 47 of file QCDHelper.h.

C_F

constexpr double QCDConstants::C_F = (Nc * Nc - 1.) / (2. * Nc)

staticconstexpr

Fundamental Casimir C_F = (N_c^2 - 1) / (2 N_c).

Definition at line 45 of file QCDHelper.h.

gamma

constexpr std::array<std::array<double, 3>, 6> QCDConstants::gamma

staticconstexpr

Initial value:

{{{2, 8.1388, 34.408},
                                                                  {2, 7.8611, 29.678}, 
                                                                  {2, 7.5833, 24.840}, 
                                                                  {2, 7.3055, 19.894}, 
                                                                  {2, 7.0277, 14.839}, 
                                                                  {2, 6.75  , 9.6773}}}

γ-function coefficients γ_0, γ_1, γ_2 for nf = 1..6.

Indexed as gamma[nf-1][i] with i = 0,1,2.

Definition at line 66 of file QCDHelper.h.

Nc

constexpr int QCDConstants::Nc = 3

staticconstexpr

Number of colors.

Definition at line 43 of file QCDHelper.h.

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

• /home/runner/work/Hyperiso/Hyperiso/Hyperiso/Hyperiso/core/src/Core/infrastructure/QCDHelper.h