"""The |FHMRUVV| |N3LO| Altarelli-Parisi splitting kernels approximations.
Authors follow Pegasus convention and so there is an additional global
minus sign with respect to our conventions.
"""
import numba as nb
import numpy as np
from .ggg import gamma_gg
from .ggq import gamma_gq
from .gnsm import gamma_nsm
from .gnsp import gamma_nsp
from .gnsv import gamma_nsv
from .gps import gamma_ps
from .gqg import gamma_qg
[docs]
@nb.njit(cache=True)
def gamma_singlet(N, nf, cache, variation):
r"""Compute the |N3LO| singlet anomalous dimension matrix.
.. math::
\gamma_S^{(3)} = \left(\begin{array}{cc}
\gamma_{qq}^{(3)} & \gamma_{qg}^{(3)}\\
\gamma_{gq}^{(3)} & \gamma_{gg}^{(3)}
\end{array}\right)
Parameters
----------
N : complex
Mellin moment
nf : int
Number of active flavors
cache: numpy.ndarray
Harmonic sum cache
variation : tuple
|N3LO| anomalous dimension variation ``(gg, gq, qg, qq)``
Returns
-------
numpy.ndarray
|N3LO| singlet anomalous dimension matrix
:math:`\gamma_{S}^{(3)}(N)`
"""
gamma_qq = gamma_nsp(N, nf, cache, variation[3]) + gamma_ps(
N, nf, cache, variation[3]
)
gamma_S_0 = np.array(
[
[gamma_qq, gamma_qg(N, nf, cache, variation[2])],
[
gamma_gq(N, nf, cache, variation[1]),
gamma_gg(N, nf, cache, variation[0]),
],
],
np.complex128,
)
return gamma_S_0
[docs]
@nb.njit(cache=True)
def gamma_singlet_qed(N, nf, cache, variation):
r"""Compute the leading-order singlet anomalous dimension matrix for the
unified evolution basis.
.. math::
\\gamma_S^{(3,0)} = \\left(\begin{array}{cccc}
\\gamma_{gg}^{(3,0)} & 0 & \\gamma_{gq}^{(3,0)} & 0\\
0 & 0 & 0 & 0 \\
\\gamma_{qg}^{(3,0)} & 0 & \\gamma_{qq}^{(3,0)} & 0 \\
0 & 0 & 0 & \\gamma_{qq}^{(3,0)} \\
\\end{array}\right)
Parameters
----------
N : complex
Mellin moment
nf : int
Number of active flavors
cache: numpy.ndarray
Harmonic sum cache
variation : tuple
|N3LO| anomalous dimension variation ``(gg, gq, qg, qq)``
Returns
-------
numpy.ndarray
Leading-order singlet anomalous dimension matrix :math:`\\gamma_{S}^{(3,0)}(N)`
"""
gamma_np_p = gamma_nsp(N, nf, cache, variation[3])
gamma_qq = gamma_np_p + gamma_ps(N, nf, cache, variation[3])
gamma_S = np.array(
[
[
gamma_gg(N, nf, cache, variation[0]),
0.0 + 0.0j,
gamma_gq(N, nf, cache, variation[1]),
0.0 + 0.0j,
],
[0.0 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j],
[gamma_qg(N, nf, cache, variation[2]), 0.0 + 0.0j, gamma_qq, 0.0 + 0.0j],
[0.0 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j, gamma_np_p],
],
np.complex128,
)
return gamma_S
[docs]
@nb.njit(cache=True)
def gamma_valence_qed(N, nf, cache, variation):
r"""Compute the leading-order valence anomalous dimension matrix for the
unified evolution basis.
.. math::
\\gamma_V^{(3,0)} = \\left(\begin{array}{cc}
\\gamma_{nsV}^{(3,0)} & 0\\
0 & \\gamma_{ns-}^{(3,0)}
\\end{array}\right)
Parameters
----------
N : complex
Mellin moment
nf : int
Number of active flavors
cache: numpy.ndarray
Harmonic sum cache
variation : tuple
|N3LO| anomalous dimension variation ``(nsm, nsv)``
Returns
-------
numpy.ndarray
Leading-order singlet anomalous dimension matrix :math:`\\gamma_{V}^{(3,0)}(N)`
"""
gamma_V = np.array(
[
[gamma_nsv(N, nf, cache, variation[-1]), 0.0],
[0.0, gamma_nsm(N, nf, cache, variation[-2])],
],
np.complex128,
)
return gamma_V