r"""The polarized, space-like Altarelli-Parisi splitting kernels.
Normalization is given by
.. math::
\mathbf{P}(x) = \sum\limits_{j=0} a_s^{j+1} \mathbf P^{(j)}(x)
with :math:`a_s = \frac{\alpha_S(\mu^2)}{4\pi}`.
"""
import numba as nb
import numpy as np
from ....harmonics import cache as c
from . import as1, as2, as3
[docs]
@nb.njit(cache=True)
def gamma_ns(order, mode, n, nf):
r"""Compute the tower of the non-singlet anomalous dimensions.
Parameters
----------
order : tuple(int,int)
perturbative orders
mode : 10201 | 10101 | 10200
sector identifier
n : complex
Mellin variable
nf : int
Number of active flavors
Returns
-------
numpy.ndarray
non-singlet anomalous dimensions
"""
cache = c.reset()
gamma_ns = np.zeros(order[0], np.complex128)
gamma_ns[0] = as1.gamma_ns(n, cache)
# NLO and beyond
if order[0] >= 2:
if mode == 10101:
gamma_ns_1 = as2.gamma_nsp(n, nf, cache)
# To fill the full valence vector in NNLO we need to add gamma_ns^1 explicitly here
elif mode in [10201, 10200]:
gamma_ns_1 = as2.gamma_nsm(n, nf, cache)
else:
raise NotImplementedError("Non-singlet sector is not implemented")
gamma_ns[1] = gamma_ns_1
if order[0] >= 3:
gamma_ns_2 = 0.0
if mode == 10101:
gamma_ns_2 = as3.gamma_nsp(n, nf, cache)
elif mode == 10201:
gamma_ns_2 = as3.gamma_nsm(n, nf, cache)
elif mode == 10200:
gamma_ns_2 = as3.gamma_nsv(n, nf, cache)
gamma_ns[2] = gamma_ns_2
if order[0] >= 4:
raise NotImplementedError("Polarized beyond NNLO is not yet implemented")
return gamma_ns
[docs]
@nb.njit(cache=True)
def gamma_singlet(order, n, nf):
r"""Compute the tower of the singlet anomalous dimensions matrices.
Parameters
----------
order : tuple(int,int)
perturbative orders
n : complex
Mellin variable
nf : int
Number of active flavors
Returns
-------
numpy.ndarray
singlet anomalous dimensions matrices
"""
cache = c.reset()
gamma_s = np.zeros((order[0], 2, 2), np.complex128)
gamma_s[0] = as1.gamma_singlet(n, cache, nf)
if order[0] >= 2:
gamma_s[1] = as2.gamma_singlet(n, nf, cache)
if order[0] >= 3:
gamma_s[2] = as3.gamma_singlet(n, nf, cache)
if order[0] >= 4:
raise NotImplementedError("Polarized beyond NNLO is not yet implemented")
return gamma_s