r"""The unpolarized, space-like anomalous dimension :math:`\gamma_{ns,+}^{(3)}`."""
import numba as nb
from .....harmonics import cache as c
from .....harmonics.log_functions import lm11m1, lm12m1, lm13m1
from .gnsm import gamma_ns_nf3
[docs]
@nb.njit(cache=True)
def gamma_nsp_nf2(n, cache):
r"""Return the parametrized singlet-like non-singlet part proportional to :math:`nf^2`.
From :cite:`Moch:2017uml` ancillary files.
Parameters
----------
n : complex
Mellin moment
cache: numpy.ndarray
Harmonic sum cache
Returns
-------
complex
|N3LO| singlet-like non-singlet anomalous dimension :math:`\gamma_{ns,+}^{(3)}|_{nf^2}`
"""
S1 = c.get(c.S1, cache, n)
S2 = c.get(c.S2, cache, n)
return (
-193.85906555742952
- 18.962964 / n**5
+ 99.1605 / n**4
- 225.141 / n**3
+ 393.0056000000001 / n**2
- 403.50217685814835 / n
- 34.425000000000004 / (1 + n) ** 4
+ 108.42 / (1 + n) ** 3
- 93.8225 / (1 + n) ** 2
+ 534.725 / (1 + n)
+ 246.50250000000003 / (2 + n)
- 25.455 / ((1 + n) ** 2 * (2 + n))
- (16.97 * n) / ((1 + n) ** 2 * (2 + n))
+ 8.485 / ((1 + n) * (2 + n))
- 110.015 / (3 + n)
+ 78.9875 / (4 + n)
+ 195.5772 * S1
- (101.0775 * S1) / n**2
+ (35.17361 * S1) / n
- (8.485 * S1) / (1 + n)
- (101.0775 * S2) / n
)
[docs]
@nb.njit(cache=True)
def gamma_nsp_nf1(n, cache):
r"""Return the parametrized singlet-like non-singlet part proportional to :math:`nf^1`.
Parameters
----------
n : complex
Mellin moment
cache: numpy.ndarray
Harmonic sum cache
Returns
-------
complex
|N3LO| singlet-like non-singlet anomalous dimension :math:`\gamma_{ns,+}^{(3)}|_{nf^1}`
"""
S1 = c.get(c.S1, cache, n)
S2 = c.get(c.S2, cache, n)
S3 = c.get(c.S3, cache, n)
Lm11m1 = lm11m1(n, S1)
Lm12m1 = lm12m1(n, S1, S2)
Lm13m1 = lm13m1(n, S1, S2, S3)
return (
5550.218627756056
- 126.41975308641975 / n**6
+ 752.1975308641976 / n**5
- 2253.1105700880144 / n**4
+ 5247.1769880520205 / n**3
- 8769.153217295072 / n**2
- 3248.3974879855336 / n
+ 1045.759889779711 / (1.0 + n) ** 3
- 1517.7637756534405 / (1.0 + n) ** 2
- 71.40345295295322 / (2.0 + n)
- 5171.916129085788 * S1
+ (11292.198190230158 * S1) / n**2
- (2741.830025124657 * S1) / n
- 380.3748812945835 * Lm11m1
- 2478.792283615627 * Lm12m1
- 308.36695798751623 * Lm13m1
)
[docs]
@nb.njit(cache=True)
def gamma_nsp_nf0(n, cache):
r"""Return the parametrized singlet-like non-singlet part proportional to :math:`nf^0`.
Parameters
----------
n : complex
Mellin moment
cache: numpy.ndarray
Harmonic sum cache
Returns
-------
complex
|N3LO| singlet-like non-singlet anomalous dimension :math:`\gamma_{ns,+}^{(3)}|_{nf^0}`
"""
S1 = c.get(c.S1, cache, n)
S2 = c.get(c.S2, cache, n)
S3 = c.get(c.S3, cache, n)
Lm11m1 = lm11m1(n, S1)
Lm12m1 = lm12m1(n, S1, S2)
Lm13m1 = lm13m1(n, S1, S2, S3)
return (
-23391.048834675064
- 252.8395061728395 / n**7
+ 1580.2469135802469 / n**6
- 5806.800104704373 / n**5
+ 14899.91711929902 / n**4
- 28546.38768506619 / n**3
+ 50759.65541232588 / n**2
+ 11126.581215589995 / n
+ 45365.96043751846 / (1.0 + n) ** 3
- 11976.515209798297 / (1.0 + n) ** 2
- 858.6772726856868 / (2.0 + n)
+ 20702.353028966703 * S1
- (67084.61612292472 * S1) / n**2
+ (16950.937339235086 * S1) / n
- 45610.240259669365 * Lm11m1
- 5030.833428351564 * Lm12m1
- 1337.0046605808507 * Lm13m1
)
[docs]
@nb.njit(cache=True)
def gamma_nsp(n, nf, cache):
r"""Compute the |N3LO| singlet-like non-singlet anomalous dimension.
Parameters
----------
n : complex
Mellin moment
nf : int
Number of active flavors
cache: numpy.ndarray
Harmonic sum cache
Returns
-------
complex
|N3LO| singlet-like non-singlet anomalous dimension
:math:`\gamma_{ns,+}^{(3)}(N)`
"""
return (
gamma_nsp_nf0(n, cache)
+ nf * gamma_nsp_nf1(n, cache)
+ nf**2 * gamma_nsp_nf2(n, cache)
+ nf**3 * gamma_ns_nf3(n, cache)
)