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Add N3LO ren SV #145

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Dec 14, 2023
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32 changes: 24 additions & 8 deletions src/pineko/scale_variations.py
Original file line number Diff line number Diff line change
Expand Up @@ -51,16 +51,32 @@ def ren_sv_coeffs(m, max_as, logpart, which_part, nf):
float
renormalization scale variation contribution
"""
bcoeff = beta.beta_qcd((max_as - logpart - which_part + 2, 0), nf)
as_normalization = AS_NORM ** (max_as - which_part)
# nothing to do?
if max_as == 0:
return 0.0
if max_as == 2:
if which_part > 0:
m += 1
elif logpart > 1:
m = 0.5 * m * (m + 1)
return m * as_normalization * bcoeff
# eko uses as = alpha_s/(4pi), but pineappl just alpha_s
as_normalization = AS_NORM ** (max_as - which_part)
# the coefficients can be found in the NNLO MHOU paper
# (which also contains a generating MMa script)
beta0 = beta.beta_qcd_as2(nf)
beta1 = beta.beta_qcd_as3(nf)
beta2 = beta.beta_qcd_as4(nf)
ren_coeffs = {
# NLO
(1, 1, 0): m * beta0,
# NNLO
(2, 1, 1): (m + 1) * beta0,
(2, 1, 0): (m + 0) * beta1,
(2, 2, 0): m * (m + 1) / 2.0 * beta0**2,
# N3LO
(3, 1, 2): (m + 2) * beta0,
(3, 1, 1): (m + 1) * beta1,
(3, 1, 0): (m + 0) * beta2,
(3, 2, 1): (m + 1) * (m + 2) / 2.0 * beta0**2,
(3, 2, 0): m * (2 * m + 3) / 2.0 * beta0 * beta1,
(3, 3, 0): m * (m + 1) * (m + 2) / 6 * beta0**3,
}
return as_normalization * ren_coeffs[(max_as, logpart, which_part)]


def requirements(m: int, max_as: int, al: int) -> Dict[OrderTuple, List[OrderTuple]]:
Expand Down
36 changes: 36 additions & 0 deletions tests/test_scale_variations.py
Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,42 @@ def test_ren_sv_coeffs():
scale_variations.ren_sv_coeffs(m=0, max_as=2, logpart=2, which_part=0, nf=5),
0.0,
)
# check all coeff are set
for m in (0, 1, 10):
for max_as in range(1, 3 + 1):
for logpart in range(1, max_as + 1):
for which_part in range(0, max_as - logpart + 1):
for nf in (4, 5):
c = scale_variations.ren_sv_coeffs(
m=m,
max_as=max_as,
logpart=logpart,
which_part=which_part,
nf=nf,
)
assert np.isfinite(c)
if which_part > 0 and not m == 0:
assert c > 0.0
else:
assert c >= 0.0
# due to the exponential structure we can predict some things:
for nf in (4, 5):
# the highest log is always proportional beta0^k
for k in range(1, 3 + 1):
c = scale_variations.ren_sv_coeffs(
m=1, max_as=k, logpart=k, which_part=0, nf=nf
)
bare_c = c * (4.0 * np.pi / beta_qcd((2, 0), nf)) ** k
int_c = bare_c * np.math.factorial(k)
np.testing.assert_allclose(int_c, int(int_c))
# and even the second highest for the highest coeff
for k in range(2, 3 + 1):
c = scale_variations.ren_sv_coeffs(
m=1, max_as=k, logpart=k - 1, which_part=1, nf=nf
)
bare_c = c * (4.0 * np.pi / beta_qcd((2, 0), nf)) ** (k - 1)
int_c = bare_c * np.math.factorial(k)
np.testing.assert_allclose(int_c, int(int_c))


def test_requirements():
Expand Down
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