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@@ -1,5 +1,7 @@ | ||
"""The unpolarized, time-like |NLO| Altarelli-Parisi splitting kernels.""" | ||
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import math | ||
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import numba as nb | ||
import numpy as np | ||
from numpy import power as npp | ||
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@@ -46,6 +48,8 @@ def gamma_nsp(N, nf, cache): | |
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S1 = c.get(c.S1, cache, N) | ||
S2 = c.get(c.S2, cache, N) | ||
S2ph = c.get(c.S2ph, cache, N) | ||
S3ph = c.get(c.S3ph, cache, N) | ||
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N3 = N + 3 | ||
N4 = N + 4 | ||
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@@ -62,22 +66,25 @@ def gamma_nsp(N, nf, cache): | |
ZETA2 = zeta2 | ||
ZETA3 = zeta3 | ||
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SPMOM = ( | ||
1.0000 * (ZETA2 - S1 / N) / N | ||
- 0.9992 * (ZETA2 - S11 / N1) / N1 | ||
+ 0.9851 * (ZETA2 - S12 / N2) / N2 | ||
- 0.9005 * (ZETA2 - S13 / N3) / N3 | ||
+ 0.6621 * (ZETA2 - S14 / N4) / N4 | ||
- 0.3174 * (ZETA2 - S15 / N5) / N5 | ||
+ 0.0699 * (ZETA2 - S16 / N6) / N6 | ||
) | ||
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# SPMOM = ( | ||
# 1.0000 * (ZETA2 - S1 / N) / N | ||
# - 0.9992 * (ZETA2 - S11 / N1) / N1 | ||
# + 0.9851 * (ZETA2 - S12 / N2) / N2 | ||
# - 0.9005 * (ZETA2 - S13 / N3) / N3 | ||
# + 0.6621 * (ZETA2 - S14 / N4) / N4 | ||
# - 0.3174 * (ZETA2 - S15 / N5) / N5 | ||
# + 0.0699 * (ZETA2 - S16 / N6) / N6 | ||
# ) | ||
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g3 = c.get(c.g3, cache, N) | ||
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SLC = -5 / 8 * ZETA3 | ||
SLV = -ZETA2 / 2 * (polygamma(N1 / 2, 0) - polygamma(N / 2, 0)) + S1 / NS + SPMOM | ||
SLV = -ZETA2 / 2 * (polygamma(N1 / 2, 0) - polygamma(N / 2, 0)) + S1 / NS + g3 | ||
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SSCHLP = SLC + SLV | ||
SSTR2P = ZETA2 - polygamma(N2 / 2, 1) | ||
SSTR3P = 0.5 * polygamma(N2 / 2, 2) + ZETA3 | ||
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SSTR2P = S2ph #ZETA2 - polygamma(N2 / 2, 1) | ||
SSTR3P = S3ph #0.5 * polygamma(N2 / 2, 2) + ZETA3 | ||
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PNPA = ( | ||
16 * S1 * (2 * N + 1) / (NS * N1S) | ||
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@@ -150,6 +157,8 @@ def gamma_nsm(N, nf, cache): | |
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S1 = c.get(c.S1, cache, N) | ||
S2 = c.get(c.S2, cache, N) | ||
S2ph = c.get(c.S2ph, cache, N) | ||
S3ph = c.get(c.S3ph, cache, N) | ||
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N3 = N + 3 | ||
N4 = N + 4 | ||
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@@ -166,21 +175,23 @@ def gamma_nsm(N, nf, cache): | |
ZETA2 = zeta2 | ||
ZETA3 = zeta3 | ||
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SPMOM = ( | ||
1.0000 * (ZETA2 - S1 / N) / N | ||
- 0.9992 * (ZETA2 - S11 / N1) / N1 | ||
+ 0.9851 * (ZETA2 - S12 / N2) / N2 | ||
- 0.9005 * (ZETA2 - S13 / N3) / N3 | ||
+ 0.6621 * (ZETA2 - S14 / N4) / N4 | ||
- 0.3174 * (ZETA2 - S15 / N5) / N5 | ||
+ 0.0699 * (ZETA2 - S16 / N6) / N6 | ||
) | ||
g3 = c.get(c.g3, cache, N) | ||
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# SPMOM = ( | ||
# 1.0000 * (ZETA2 - S1 / N) / N | ||
# - 0.9992 * (ZETA2 - S11 / N1) / N1 | ||
# + 0.9851 * (ZETA2 - S12 / N2) / N2 | ||
# - 0.9005 * (ZETA2 - S13 / N3) / N3 | ||
# + 0.6621 * (ZETA2 - S14 / N4) / N4 | ||
# - 0.3174 * (ZETA2 - S15 / N5) / N5 | ||
# + 0.0699 * (ZETA2 - S16 / N6) / N6 | ||
# ) | ||
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SLC = -5 / 8 * ZETA3 | ||
SLV = -ZETA2 / 2 * (polygamma(N1 / 2, 0) - polygamma(N / 2, 0)) + S1 / NS + SPMOM | ||
SLV = -ZETA2 / 2 * (polygamma(N1 / 2, 0) - polygamma(N / 2, 0)) + S1 / NS + g3 | ||
SSCHLM = SLC - SLV | ||
SSTR2M = ZETA2 - polygamma(N1 / 2, 1) | ||
SSTR3M = 0.5 * polygamma(N1 / 2, 2) + ZETA3 | ||
SSTR2M = S2ph #ZETA2 - polygamma(N1 / 2, 1) | ||
SSTR3M = S3ph #0.5 * polygamma(N1 / 2, 2) + ZETA3 | ||
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giacomomagni
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PNMA = ( | ||
16 * S1 * (2 * N + 1) / (NS * N1S) | ||
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giacomomagniMay 2, 2023
Collaborator