"""Note, the factor `fl11` is not contributing to charged currents according to `xcdiff3p.f`.
To generate `c2nm3a,c2nm3c` we follow `xcdiff3p.f` or the reference paper :cite:`Davies:2016ruz`.
"""
import numba as nb
import numpy as np
from .common import d3, d27, d81, d243
from .xcdiff3p import c2q3dfp, c2q3dfpc
[docs]
@nb.njit("f8(f8,f8[:])", cache=True)
def c2np3a_fl2(y, args):
"""The math:`fl_{2}`: regular piece of the non singlet coefficient."""
nf = args[0]
dl = np.log(y)
dl1 = np.log(1.0 - y)
res = (
-4926.0
+ 7725.0 * y
+ 57256.0 * y**2
+ 12898.0 * y**3
- 32.0 * d27 * dl**5
- 8796.0 * d243 * dl**4
- 309.1 * dl**3
- 899.6 * dl**2
- 775.8 * dl
+ 4.719 * y * dl**5
- 512.0 * d27 * dl1**5
+ 6336.0 * d27 * dl1**4
- 3368.0 * dl1**3
- 2978.0 * dl1**2
+ 18832.0 * dl1
- 56000.0 * (1.0 - y) * dl1**2
- dl * dl1 * (6158.0 + 1836.0 * dl)
+ nf
* (
831.6
- 6752.0 * y
- 2778.0 * y**2
+ 728.0 * d243 * dl**4
+ 12224.0 * d243 * dl**3
+ 187.3 * dl**2
+ 275.6 * dl
+ 4.102 * y * dl**4
- 1920.0 * d243 * dl1**4
+ 153.5 * dl1**3
- 828.7 * dl1**2
- 501.1 * dl1
+ 171.0 * (1.0 - y) * dl1**4
+ dl * dl1 * (4365.0 + 716.2 * dl - 5983.0 * dl1)
)
+ nf**2
* (
129.2 * y
+ 102.5 * y**2
- 368.0 * d243 * dl**3
- 1984.0 * d243 * dl**2
- 8.042 * dl
- 192.0 * d243 * dl1**3
+ 18.21 * dl1**2
- 19.09 * dl1
+ dl * dl1 * (-96.07 - 12.46 * dl + 85.88 * dl1)
)
)
return res
[docs]
@nb.njit("f8(f8,f8[:])", cache=True)
def c2ns3b_fl2(y, args):
nf = args[0]
dl1 = np.log(1.0 - y)
dm = 1.0 / (1.0 - y)
res = (
+1536.0 * d81 * dl1**5
- 16320.0 * d81 * dl1**4
+ 5.01099e2 * dl1**3
+ 1.17154e3 * dl1**2
- 7.32845e3 * dl1
+ 4.44276e3
+ nf
* (
640.0 * d81 * dl1**4
- 6592.0 * d81 * dl1**3
+ 220.573 * dl1**2
+ 294.906 * dl1
- 729.359
)
+ nf**2 * (64.0 * d81 * dl1**3 - 464.0 * d81 * dl1**2 + 7.67505 * dl1 + 1.00830)
)
res = dm * res
return res
[docs]
@nb.njit("f8(f8,f8[:])", cache=True)
def c2np3c_fl2(y, args):
"""The math:`fl_{2}`: local piece of the non singlet coefficient."""
nf = args[0]
dl1 = np.log(1.0 - y)
res = (
+256.0 * d81 * dl1**6
- 3264.0 * d81 * dl1**5
+ 1.252745e2 * dl1**4
+ 3.905133e2 * dl1**3
- 3.664225e3 * dl1**2
+ 4.44276e3 * dl1
- 9195.48
+ 25.10
+ nf
* (
128.0 * d81 * dl1**5
- 1648.0 * d81 * dl1**4
+ 220.573 * d3 * dl1**3
+ 147.453 * dl1**2
- 729.359 * dl1
+ 2575.074
- 0.387
)
+ nf**2
* (
16.0 * d81 * dl1**4
- 464.0 * d81 * d3 * dl1**3
+ 7.67505 * 1 / 5.0 * dl1**2
+ 1.0083 * dl1
- 103.2521
+ 0.0155
)
)
return res
[docs]
@nb.njit("f8(f8,f8[:])", cache=True)
def c2nm3a_fl2(y, args):
return c2np3a_fl2(y, args) - c2q3dfp(y, args)
[docs]
@nb.njit("f8(f8,f8[:])", cache=True)
def c2nm3c_fl2(y, args):
return c2np3c_fl2(y, args) - c2q3dfpc(y, args)