eko.scale_variations package
Define possible scale variations schemes.
A Mathematica snippet to check the formulas is available in the extras folder.
- class eko.scale_variations.Modes(value)[source]
Bases:
IntEnum
Enumerate scale variation modes.
- unvaried = 1
- exponentiated = 2
- expanded = 3
- eko.scale_variations.sv_mode(s: ScaleVariationsMethod) Modes [source]
Return the scale variation mode.
- Parameters:
s – string representation
- Returns:
int representation
- Return type:
i
- class eko.scale_variations.ScaleVariationModeMixin[source]
Bases:
object
Mixin to cast scale variation mode.
Submodules
eko.scale_variations.expanded module
Scale variation operator for the expanded scheme (ModSV=expanded
).
The expressions can be obtained using Eqs. (3.33) and (3.38) of [AK+19]. Be aware that corresponding the signs of the ingredients there are a number of differences. However, the ultimate sign can be obtained by comparing to the exponentiated scheme in the trunctated solution.
- eko.scale_variations.expanded.variation_as1(gamma, L)[source]
Compute the NLO anomalous dimension variation.
- Parameters:
gamma (numpy.ndarray) – anomalous dimensions
L (float) – logarithmic ratio of factorization and renormalization scale
- Returns:
variation at NLO
- Return type:
- eko.scale_variations.expanded.variation_as2(gamma, L, beta0, g0e2)[source]
Compute the NNLO anomalous dimension variation.
These kernels are meant to be used with alpha_s evaluated at the factorization scale. If one expresses everything in terms of alpha_s evaluated at the process scale, the sign of beta*gamma0 flips.
- Parameters:
gamma (numpy.ndarray) – anomalous dimensions
L (float) – logarithmic ratio of factorization and renormalization scale
beta0 (float) – \(\beta_0\)
g0e2 (complex or numpy.ndarray) – \(\left(\gamma^{(0)}\right)^2\)
- Returns:
variation at NNLO
- Return type:
- eko.scale_variations.expanded.variation_as3(gamma, L, beta0, beta1, g0e2, g0e3, g1g0, g0g1)[source]
Compute the N3LO anomalous dimension variation.
- Parameters:
gamma (numpy.ndarray) – anomalous dimensions
L (float) – logarithmic ratio of factorization and renormalization scale
beta0 (float) – \(\beta_0\)
beta0 – \(\beta_1\)
g0e2 (complex or numpy.ndarray) – \(\left(\gamma^{(0)}\right)^2\)
g0e3 (complex or numpy.ndarray) – \(\left(\gamma^{(0)}\right)^3\)
g1g0 (complex or numpy.ndarray) – \(\gamma^{(1)} \gamma^{(0)}\)
g0g1 (complex or numpy.ndarray) – \(\gamma^{(0)} \gamma^{(1)}\)
- Returns:
variation at N3LO
- Return type:
- eko.scale_variations.expanded.non_singlet_variation(gamma, a_s, order, nf, L)[source]
Non-singlet scale variation dispatcher.
- eko.scale_variations.expanded.singlet_variation(gamma, a_s, order, nf, L, dim)[source]
Singlet scale variation dispatcher.
- Parameters:
gamma (numpy.ndarray) – anomalous dimensions
a_s (float) – target coupling value
order (int) – perturbation order
nf (int) – number of active flavors
L (float) – logarithmic ratio of factorization and renormalization scale
- Returns:
scale variation kernel
- Return type:
- eko.scale_variations.expanded.non_singlet_variation_qed(gamma, a_s, a_em, alphaem_running, order, nf, L)[source]
Non-singlet scale variation dispatcher.
- eko.scale_variations.expanded.singlet_variation_qed(gamma, a_s, a_em, alphaem_running, order, nf, L)[source]
Singlet scale variation dispatcher.
- Parameters:
gamma (numpy.ndarray) – anomalous dimensions
a_s (float) – target coupling value
order (int) – perturbation order
nf (int) – number of active flavors
L (float) – logarithmic ratio of factorization and renormalization scale
- Returns:
scale variation kernel
- Return type:
- eko.scale_variations.expanded.valence_variation_qed(gamma, a_s, a_em, alphaem_running, order, nf, L)[source]
Singlet scale variation dispatcher.
- Parameters:
gamma (numpy.ndarray) – anomalous dimensions
a_s (float) – target coupling value
order (int) – perturbation order
nf (int) – number of active flavors
L (float) – logarithmic ratio of factorization and renormalization scale
- Returns:
scale variation kernel
- Return type:
eko.scale_variations.exponentiated module
Contains the scale variation for ModSV=exponentiated
.
- eko.scale_variations.exponentiated.gamma_variation(gamma, order, nf, L)[source]
Adjust the anomalous dimensions with the scale variations.
- Parameters:
- Returns:
adjusted anomalous dimensions
- Return type: