"""Collection of QED singlet EKOs."""
import numba as nb
import numpy as np
from ekore import anomalous_dimensions as ad
from .. import beta
[docs]
@nb.njit(cache=True)
def eko_iterate(gamma_singlet, as_list, a_half, nf, order, ev_op_iterations, dim):
"""Singlet QEDxQCD iterated (exact) EKO.
Parameters
----------
gamma_singlet : numpy.ndarray
singlet anomalous dimensions matrices
a1 : float
target strong coupling value
a0 : float
initial strong coupling value
aem_list : float
electromagnetic coupling values
nf : int
number of active flavors
order : tuple(int,int)
QCDxQED perturbative orders
ev_op_iterations : int
number of evolution steps
Returns
-------
e_s^{order} : numpy.ndarray
singlet QEDxQCD iterated (exact) EKO
"""
e = np.identity(dim, np.complex_)
betaQCD = np.zeros((order[0] + 1, order[1] + 1))
for i in range(1, order[0] + 1):
betaQCD[i, 0] = beta.beta_qcd((i + 1, 0), nf)
betaQCD[1, 1] = beta.beta_qcd((2, 1), nf)
for step in range(1, ev_op_iterations + 1):
ah = as_list[step]
al = as_list[step - 1]
as_half = a_half[step - 1, 0]
aem = a_half[step - 1, 1]
delta_a = ah - al
gamma = np.zeros((dim, dim), np.complex_)
betatot = 0
for i in range(0, order[0] + 1):
for j in range(0, order[1] + 1):
betatot += betaQCD[i, j] * as_half ** (i + 1) * aem**j
gamma += gamma_singlet[i, j] * as_half**i * aem**j
ln = gamma / betatot * delta_a
ek = np.ascontiguousarray(ad.exp_matrix(ln)[0])
e = ek @ e
return e
[docs]
@nb.njit(cache=True)
def dispatcher(
order,
method,
gamma_singlet,
as_list,
a_half,
nf,
ev_op_iterations,
ev_op_max_order,
):
"""Determine used kernel and call it.
Parameters
----------
order : tuple(int,int)
perturbative order
method : str
method
gamma_singlet : numpy.ndarray
singlet anomalous dimensions matrices
a1 : float
target coupling value
a0 : float
initial coupling value
aem_list : numpy.ndarray
electromagnetic coupling values
nf : int
number of active flavors
ev_op_iterations : int
number of evolution steps
ev_op_max_order : tuple(int,int)
perturbative expansion order of U
Returns
-------
e_s : numpy.ndarray
singlet EKO
"""
if method in ["iterate-exact", "iterate-expanded"]:
return eko_iterate(
gamma_singlet, as_list, a_half, nf, order, ev_op_iterations, 4
)
raise NotImplementedError('Only "iterate-exact" is implemented with QED')