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Merge pull request #380 from NNPDF/new_n3lo_pgq
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Add new P_gq parametrisation
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@felixhekhorn
felixhekhorn authored Jul 15, 2024
2 parents 7b36c21 + 85c7cbc commit 38cc28c
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11 changes: 11 additions & 0 deletions doc/source/refs.bib
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Expand Up @@ -1062,3 +1062,14 @@ @article{Ablinger:2024xtt
year = "2024",
journal = ""
}

@article{Falcioni:2024xyt,
author = "Falcioni, G. and Herzog, F. and Moch, S. and Pelloni, A. and Vogt, A.",
title = "{Four-loop splitting functions in QCD -- The quark-to-gluon case}",
eprint = "2404.09701",
archivePrefix = "arXiv",
primaryClass = "hep-ph",
reportNumber = "ZU-TH 20/24, DESY-24-053, LTH 1367",
month = "4",
year = "2024"
}
5 changes: 3 additions & 2 deletions doc/source/theory/N3LO_ad.rst
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Expand Up @@ -264,7 +264,8 @@ The other parts are approximated using some known limits:
& \gamma_{qg}(2) + \gamma_{gg}(2) = 0 \\
& \gamma_{qq}(2) + \gamma_{gq}(2) = 0 \\
For :math:`\gamma_{qq,ps}, \gamma_{qg}` other 5 additional moments are available :cite:`Falcioni:2023luc,Falcioni:2023vqq`.
For :math:`\gamma_{qq,ps}, \gamma_{qg},\gamma_{gq}` other 5 additional moments are available from
:cite:`Falcioni:2023luc,Falcioni:2023vqq,Falcioni:2024xyt` respectively.
making the parametrization of this splitting function much more accurate.

The difference between the known moments and the known limits is parametrized
Expand Down Expand Up @@ -337,7 +338,7 @@ final reduced sets of candidates.
* - :math:`f_4(N)`
- :math:`\frac{1}{N^4},\ \frac{1}{N^3},\ \frac{1}{N^2},\ \frac{1}{(N+1)},\ \frac{1}{(N+2)},\ \mathcal{M}[\ln^2(1-x)],\ \mathcal{M}[\ln(1-x)]`

Following :cite:`Moch:2023tdj` we have assumed no violation of the scaling with :math:`\gamma_{gg}`
Following :cite:`Moch:2023tdj,Falcioni:2024xyt` we have assumed no violation of the scaling with :math:`\gamma_{gg}`
also for the |NLL| small-x term, to help the convergence. We expect that any possible deviation can be parametrized as a shift in the |NNLL| terms
which are free to vary independently.

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2 changes: 1 addition & 1 deletion extras/n3lo_bench/plot_msht.py
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Expand Up @@ -15,7 +15,7 @@

n3lo_vars_dict = {
"gg": 19,
"gq": 21,
"gq": 15,
"qg": 15,
"qq": 6,
}
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131 changes: 93 additions & 38 deletions src/ekore/anomalous_dimensions/unpolarized/space_like/as4/fhmruvv/ggq.py
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Expand Up @@ -2,15 +2,28 @@

import numba as nb

from eko.constants import zeta2

from ......harmonics import cache as c
from ......harmonics.log_functions import lm12, lm13, lm14, lm15
from ......harmonics.log_functions import (
lm11,
lm12,
lm12m1,
lm13,
lm14,
lm14m1,
lm15,
lm15m1,
)


@nb.njit(cache=True)
def gamma_gq(n, nf, cache, variation):
r"""Compute the |N3LO| gluon-quark singlet anomalous dimension.
The routine is taken from :cite:`Moch:2023tdj`.
The routine is taken from :cite:`Falcioni:2024xyt`.
Lower moments were published also in :cite:`Moch:2023tdj`.
Parameters
----------
Expand Down Expand Up @@ -40,76 +53,118 @@ def gamma_gq(n, nf, cache, variation):
# Known large-x coefficients
x1L5cff = 1.3443073 * 10 - 5.4869684 * 0.1 * nf
x1L4cff = 3.7539831 * 10**2 - 3.4494742 * 10 * nf + 8.7791495 * 0.1 * nf2
y1L5cff = 2.2222222 * 10 - 5.4869684 * 0.1 * nf
y1L4cff = 6.6242163 * 10**2 - 4.7992684 * 10 * nf + 8.7791495 * 0.1 * nf2

# Small-x, Casimir scaled from P_gg (approx. for bfkl1)
bfkl0 = -8.3086173 * 10**3 / 2.25
bfkl1 = (-1.0691199 * 10**5 - nf * 9.9638304 * 10**2) / 2.25

# Small-x double-logs with x^0
x0L6cff = 5.2235940 * 10 - 7.3744856 * nf
x0L5cff = -2.9221399 * 10**2 + 1.8436214 * nf
x0L4cff = 7.3106077 * 10**3 - 3.7887135 * 10**2 * nf - 3.2438957 * 10 * nf2

# The resulting part of the function
P3GQ01 = (
+bfkl0 * (-(6 / (-1 + n) ** 4))
+ bfkl1 * 2 / (-1 + n) ** 3
+ x0L6cff * 720 / n**7
+ x0L5cff * -120 / n**6
+ x0L4cff * 24 / n**5
+ x1L4cff * lm14(n, S1, S2, S3, S4)
+ x1L5cff * lm15(n, S1, S2, S3, S4, S5)
+ y1L4cff * lm14m1(n, S1, S2, S3, S4)
+ y1L5cff * lm15m1(n, S1, S2, S3, S4, S5)
)

# The selected approximations for nf = 3, 4, 5
if nf == 3:
P3gqApp1 = (
P3GQ01
+ 3.4 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 161562.0 * 1 / ((-1 + n) * n)
+ 36469.0 * 1 / n
+ 72317.0 * (-(1 / n**2))
- 3977.3 * lm12(n, S1, S2)
+ 484.4 * lm13(n, S1, S2, S3)
+ 6.0 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 744384.0 * 1 / ((-1 + n) * n)
+ 2453640.0 * 1 / n
- 1540404.0 * (2 / (1 + n) + 1 / (2 + n))
+ 1933026.0 * -1 / n**2
+ 1142069.0 * 2 / n**3
+ 162196.0 * -6 / n**4
- 2172.1 * lm13(n, S1, S2, S3)
- 93264.1 * lm12(n, S1, S2)
- 786973.0 * lm11(n, S1)
+ 875383.0 * lm12m1(n, S1, S2)
)
P3gqApp2 = (
P3GQ01
+ 5.4 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 546482.0 * 1 / ((-1 + n) * n)
- 39464.0 * 1 / n
- 401000.0 * (-(1 / n**2))
+ 13270.0 * lm12(n, S1, S2)
+ 3289.0 * lm13(n, S1, S2, S3)
+ 3.0 * bfkl1 * (-(1 / (-1 + n) ** 2))
+ 142414.0 * 1 / ((-1 + n) * n)
- 326525.0 * 1 / n
+ 2159787.0 * ((3 + n) / (2 + 3 * n + n**2))
- 289064.0 * -1 / n**2
- 176358.0 * 2 / n**3
+ 156541.0 * -6 / n**4
+ 9016.5 * lm13(n, S1, S2, S3)
+ 136063.0 * lm12(n, S1, S2)
+ 829482.0 * lm11(n, S1)
- 2359050.0 * (S1 - n * (zeta2 - S2)) / n**2
)
elif nf == 4:
P3gqApp1 = (
P3GQ01
+ 3.4 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 158805.0 * 1 / ((-1 + n) * n)
+ 35098.0 * 1 / n
+ 87258.0 * (-(1 / n**2))
- 4834.1 * lm12(n, S1, S2)
+ 176.6 * lm13(n, S1, S2, S3)
+ 6.0 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 743535.0 * 1 / ((-1 + n) * n)
+ 2125286.0 * 1 / n
- 1332472.0 * (2 / (1 + n) + 1 / (2 + n))
+ 1631173.0 * -1 / n**2
+ 1015255.0 * 2 / n**3
+ 142612.0 * -6 / n**4
- 1910.4 * lm13(n, S1, S2, S3)
- 80851.0 * lm12(n, S1, S2)
- 680219.0 * lm11(n, S1)
+ 752733.0 * lm12m1(n, S1, S2)
)
P3gqApp2 = (
P3GQ01
+ 5.4 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 547215.0 * 1 / ((-1 + n) * n)
- 41523.0 * 1 / n
- 390350.0 * (-(1 / n**2))
+ 12571.0 * lm12(n, S1, S2)
+ 3007.0 * lm13(n, S1, S2, S3)
+ 3.0 * bfkl1 * (-(1 / (-1 + n) ** 2))
+ 160568.0 * 1 / ((-1 + n) * n)
- 361207.0 * 1 / n
+ 2048948.0 * ((3 + n) / (2 + 3 * n + n**2))
- 245963.0 * -1 / n**2
- 171312.0 * 2 / n**3
+ 163099.0 * -6 / n**4
+ 8132.2 * lm13(n, S1, S2, S3)
+ 124425.0 * lm12(n, S1, S2)
+ 762435.0 * lm11(n, S1)
- 2193335.0 * (S1 - n * (zeta2 - S2)) / n**2
)
elif nf == 5:
P3gqApp1 = (
P3GQ01
+ 3.4 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 154336.0 * 1 / ((-1 + n) * n)
+ 33889.0 * 1 / n
+ 103440.0 * (-(1 / n**2))
- 5745.8 * lm12(n, S1, S2)
- 128.6 * lm13(n, S1, S2, S3)
+ 6.0 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 785864.0 * 1 / ((-1 + n) * n)
+ 285034.0 * 1 / n
- 131648.0 * (2 / (1 + n) + 1 / (2 + n))
- 162840.0 * -1 / n**2
+ 321220.0 * 2 / n**3
+ 12688.0 * -6 / n**4
+ 1423.4 * lm13(n, S1, S2, S3)
+ 1278.9 * lm12(n, S1, S2)
- 30919.9 * lm11(n, S1)
+ 47588.0 * lm12m1(n, S1, S2)
)
P3gqApp2 = (
P3GQ01
+ 5.4 * bfkl1 * (-(1 / (-1 + n) ** 2))
- 546236.0 * 1 / ((-1 + n) * n)
- 43421.0 * 1 / n
- 378460.0 * (-(1 / n**2))
+ 11816.0 * lm12(n, S1, S2)
+ 2727.3 * lm13(n, S1, S2, S3)
+ 3.0 * bfkl1 * (-(1 / (-1 + n) ** 2))
+ 177094.0 * 1 / ((-1 + n) * n)
- 470694.0 * 1 / n
+ 1348823.0 * ((3 + n) / (2 + 3 * n + n**2))
- 52985.0 * -1 / n**2
- 87354.0 * 2 / n**3
+ 176885.0 * -6 / n**4
+ 4748.8 * lm13(n, S1, S2, S3)
+ 65811.9 * lm12(n, S1, S2)
+ 396390.0 * lm11(n, S1)
- 1190212.0 * (S1 - n * (zeta2 - S2)) / n**2
)
else:
raise NotImplementedError("nf=6 is not available at N3LO")
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