QCD Library
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Classes | |
class | MSbar_mass |
Implements the running and decoupling of a quark mass in the ![]() | |
struct | reference_coupling |
Value for strong coupling constant at a reference scale. More... | |
struct | reference_mass |
Value for ![]() | |
class | strong_coupling |
Implements the running and decoupling of the strong coupling constant. More... | |
struct | threshold |
Threshold for the decoupling of a quark flavour. More... | |
Enumerations | |
enum | scheme { , pole = 0, OS = pole, MSbar, MS = MSbar, scale_invariant, SI = scale_invariant } |
Mass schemes. More... | |
Functions | |
QCD_CONSTEXPR_AFTER_CXX14 double | beta (unsigned order, int nf, double alpha_s) |
The QCD beta function. More... | |
QCD_CONSTEXPR_AFTER_CXX14 double | beta (unsigned order, int nf) |
Perturbative coefficients of the QCD beta function. More... | |
QCD_CONSTEXPR_AFTER_CXX14 unsigned | beta_max_nf_pow (unsigned order) |
Highest power of number of flavours in appearing in the beta function. More... | |
QCD_CONSTEXPR_AFTER_CXX14 double | beta_nf_coeff (unsigned order, unsigned nfpow) |
Coefficient of some power of number of flavours in the beta function. More... | |
QCD_CONSTEXPR_AFTER_CXX14 double | gamma_m (unsigned order, int nf, double alpha_s) |
The QCD mass anomalous dimension. More... | |
QCD_CONSTEXPR_AFTER_CXX14 double | gamma_m (unsigned order, int nf) |
Perturbative coefficients of the QCD mass anomalous dimension. More... | |
QCD_CONSTEXPR_AFTER_CXX14 unsigned | gamma_m_max_nf_pow (unsigned order) |
Highest power of number of flavours in appearing in the mass anomalous dimension. More... | |
QCD_CONSTEXPR_AFTER_CXX14 double | gamma_m_nf_coeff (unsigned order, unsigned nfpow) |
Coefficient of some power of number of flavours in the mass anomalous dimension. More... | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_alpha_s (unsigned order, unsigned nf, double lm, double alpha_s) |
Decoupling constant for the strong coupling constant. More... | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_alpha_s_inv (unsigned order, unsigned nf, double lm, double alpha_s) |
Inverse decoupling constant for the strong coupling constant. More... | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_alpha_s (unsigned order, unsigned nf, double lm) |
Coefficients of the decoupling constant. More... | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_alpha_s_inv (unsigned order, unsigned nf, double lm) |
Coefficients of the inverse decoupling constant. More... | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_m (unsigned order, unsigned nf, double lm, double alpha_s) |
Decoupling constant for the mass in the ![]() | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_m_inv (unsigned order, unsigned nf, double lm, double alpha_s) |
Inverse decoupling constant for the mass in the ![]() | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_m (unsigned order, unsigned nf, double lm) |
Coefficients of the decoupling constant. More... | |
template<scheme s> | |
QCD_CONSTEXPR_AFTER_CXX14 double | zeta_m_inv (unsigned order, unsigned nf, double lm) |
Coefficients of the inverse decoupling constant. More... | |
Variables | |
constexpr double | alpha_s_mz = 0.1184 |
Default value for the strong coupling at the Z scale. | |
constexpr double | mz = 91.18 |
Default value for the Z boson mass. | |
constexpr unsigned | beta_max_order = 4 |
Highest implemented order of the beta function. | |
constexpr int | n_c = 3 |
Dimension of the fundamental representation. | |
constexpr int | d_r = 3 |
Dimension of the fundamental representation. | |
constexpr double | c_A = 3. |
Quadratic Casimir in the adjoint representation. | |
constexpr double | c_F = 4./3. |
Quadratic Casimir in the fundamental representation. | |
constexpr double | T_f = 1./2. |
Trace normalisation. | |
constexpr double | d_abcd_AA = 135. |
Product of two symmetrised traces in the adjoint representation. More... | |
constexpr double | d_abcd_AF = 15./2. |
Product of two symmetrised traces in the adjoint and fundamental representation. More... | |
constexpr double | d_abcd_FF = 5./12. |
Product of two symmetrised traces in the fundamental representation. More... | |
constexpr double | N_A = 8. |
Dimension of the adjoint representation. | |
constexpr double | mc_OS = 1.5 |
charm quark mass | |
constexpr double | mb_OS = 4.7 |
bottom quark mass | |
constexpr double | mt_OS = 175. |
top quark mass | |
enum scheme |
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The QCD beta function.
order | Perturbative order of the beta function |
nf | Number of active flavours |
alpha_s | Value of the strong coupling constant |
The beta function is defined via the renormalisation group equation , where
is the strong coupling constant at the scale
.
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Perturbative coefficients of the QCD beta function.
order | Perturbative order of the coefficient |
nf | Number of active flavours |
The coefficients of the beta function are given by . For example, beta(0, 5) returns the value of
for 5 active flavours.
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Highest power of number of flavours in appearing in the beta function.
order | Perturbative order of the beta function |
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Coefficient of some power of number of flavours in the beta function.
order | Perturbative order |
nfpow | Power of number of active flavour |
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The QCD mass anomalous dimension.
order | Perturbative order of the mass anomalous dimension |
nf | Number of active flavours |
alpha_s | Value of the strong coupling constant |
The mass anomalous dimension is defined via the renormalisation group equation , where
is the running mass at the scale
.
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inline |
Perturbative coefficients of the QCD mass anomalous dimension.
order | Perturbative order of the coefficient |
nf | Number of active flavours |
The coefficients of the mass anomalous dimension are given by . For example, gamma_m(1, 5) returns the value of
for 5 active flavours.
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Highest power of number of flavours in appearing in the mass anomalous dimension.
order | Perturbative order of the mass anomalous dimension |
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Coefficient of some power of number of flavours in the mass anomalous dimension.
order | Perturbative order |
nfpow | Power of number of active flavour |
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Decoupling constant for the strong coupling constant.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
alpha_s | strong coupling constant at the decoupling scale |
The decoupling constant is defined by
, where
is the coupling constant in the theory with $n_f$ active flavours.
All input parameters are defined in the theory with nf active flavours.
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Inverse decoupling constant for the strong coupling constant.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
alpha_s | strong coupling constant with nf active flavours at the decoupling scale |
The inverse decoupling constant is defined by
, where
is the coupling constant in the theory with $n_f$ active flavours.
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Coefficients of the decoupling constant.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
The coefficients are defined via
.
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inline |
Coefficients of the inverse decoupling constant.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
The coefficients are defined via
.
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Decoupling constant for the mass in the scheme.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
alpha_s | strong coupling constant at the decoupling scale |
The decoupling constant is defined by
, where
is the mass in the theory with $n_f$ active flavours.
All input parameters are defined in the theory with nf active flavours.
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inline |
Inverse decoupling constant for the mass in the scheme.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
alpha_s | strong coupling constant with nf active flavours at the decoupling scale |
The inverse decoupling constant is defined by
, where
is the mass in the theory with $n_f$ active flavours.
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inline |
Coefficients of the decoupling constant.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
The coefficients are defined via
.
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inline |
Coefficients of the inverse decoupling constant.
s | Decoupling scheme |
order | Perturbative order |
nf | Number of active flavours before decoupling |
lm | ![]() ![]() ![]() |
The coefficients are defined via
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constexpr double d_abcd_AA = 135. |
Product of two symmetrised traces in the adjoint representation.
d_abcd_AA = (d^abcd_A)^2, where d^abcd_A is the trace over the symmetrised product of four generators in the adjoint representation
constexpr double d_abcd_AF = 15./2. |
Product of two symmetrised traces in the adjoint and fundamental representation.
d_abcd_AF = (d^abcd_A) (d^abcd_F), where d^abcd_A/d^abcd_F is the trace over the symmetrised product of four generators in the adjoint/fundamental representation
constexpr double d_abcd_FF = 5./12. |
Product of two symmetrised traces in the fundamental representation.
d_abcd_FF = (d^abcd_F)^2, where d^abcd_F is the trace over the symmetrised product of four generators in the fundamental representation