Merge branch 'master' into lh-bench-23

.pre-commit-config.yaml

@@ -13,16 +13,16 @@ repos:
       - id: check-merge-conflict
       - id: debug-statements
   - repo: https://github.com/hadialqattan/pycln
-    rev: v2.2.1
+    rev: v2.2.2
     hooks:
       - id: pycln
         args: [--config=pyproject.toml]
   - repo: https://github.com/psf/black
-    rev: 23.7.0
+    rev: 23.9.1
     hooks:
       - id: black
   - repo: https://github.com/asottile/blacken-docs
-    rev: 1.15.0
+    rev: 1.16.0
     hooks:
       - id: blacken-docs
   - repo: https://github.com/pycqa/isort
@@ -43,6 +43,6 @@ repos:
         additional_dependencies:
           - toml
   - repo: https://github.com/pre-commit/pre-commit
-    rev: v3.3.3
+    rev: v3.4.0
     hooks:
       - id: validate_manifest

doc/source/refs.bib

@@ -999,3 +999,14 @@ @article{Falcioni:2023vqq
     month = "7",
     year = "2023"
 }
+
+@article{Gehrmann:2023cqm,
+    author = "Gehrmann, Thomas and von Manteuffel, Andreas and Sotnikov, Vasily and Yang, Tong-Zhi",
+    title = "{Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions}",
+    eprint = "2308.07958",
+    archivePrefix = "arXiv",
+    primaryClass = "hep-ph",
+    reportNumber = "MSUHEP-23-024, ZU-TH 43/23",
+    month = "8",
+    year = "2023"
+}

doc/source/theory/Mellin.rst

@@ -56,7 +56,7 @@ Plus Distributions
 ^^^^^^^^^^^^^^^^^^
 
 .. math ::
-    \mathcal M[1/(1-x)_+](N) = S_1(N)
+    \mathcal M[1/(1-x)_+](N) = - S_1(N - 1)
 
 with the harmonic sum :math:`S_1` (see :ref:`theory/mellin:harmonic sums`).
 

doc/source/theory/N3LO_ad.rst

@@ -90,7 +90,7 @@ In |EKO| they are implemented as follows:
         -   The large-N limit :cite:`Moch:2017uml`, which reads (Eq. 2.17):
 
             .. math ::
-                \gamma_{ns} \approx A^{(f)}_4 S_1(N) - B_4 + C_4 \frac{S_1(N)}{N} - (D_4 + \frac{1}{2} A^{(f)}_4) \frac{1}{N} + \mathcal{O}(\frac{\ln^k(N)}{N^2})
+                \gamma_{ns} \approx A^{(f)}_4 S_1(N) - B_4 + C_4 \frac{S_1(N)}{N} - D_4 \frac{1}{N}
 
             This limit is common for all :math:`\gamma_{ns,+}^{(3)},\gamma_{ns,-}^{(3)},\gamma_{ns,v}^{(3)}`.
             The coefficient :math:`A^{(f)}_4`, being related to the twist-2 spin-N operators,
@@ -193,8 +193,10 @@ the following terms:
             - |T|
             - |T|
 
-Only the parts proportional to :math:`n_f^3` are known analytically
+The parts proportional to :math:`n_f^3` are known analytically
 :cite:`Davies:2016jie` and have been included so far.
+For the :math:`n_f^2` only the :math:`\gamma_{qq,ps}` component
+have been computed in :cite:`Gehrmann:2023cqm` and it's used in our code.
 The other parts are approximated using some known limits:
 
     *   The small-x limit, given in the large :math:`N_c` approximation by

src/ekore/anomalous_dimensions/unpolarized/space_like/as4/gnsm.py

@@ -55,6 +55,8 @@ def gamma_ns_nf3(n, cache):
 def gamma_nsm_nf2(n, cache):
     r"""Return the parametrized valence-like non-singlet part proportional to :math:`nf^2`.
 
+    From :cite:`Moch:2017uml` ancillary files.
+
     Parameters
     ----------
     n : complex
@@ -71,26 +73,28 @@ def gamma_nsm_nf2(n, cache):
     """
     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 (
-        -193.89011158240442
-        - 18.962962962962962 / n**5
-        + 99.1604938271605 / n**4
-        - 226.44075306899038 / n**3
-        + 395.60497732877303 / n**2
-        + 278.2205375565073 / n
-        - 192.0247446101425 / (1.0 + n) ** 3
-        + 93.91039406948033 / (1.0 + n) ** 2
-        - 85.81679567653221 / (3.0 + n)
-        + 195.5772257829161 * S1
-        - (488.477491593376 * S1) / n**2
-        + (26.68861454046639 * S1) / n
-        + 361.0392247000297 * Lm11m1
-        + 232.1144024429168 * Lm12m1
-        + 35.38568209541474 * Lm13m1
+        -193.84583328013258
+        - 23.7037032 / n**5
+        + 117.5967 / n**4
+        - 256.5896 / n**3
+        + 437.881 / n**2
+        + 720.385709813466 / n
+        - 48.720000000000006 / (1 + n) ** 4
+        + 189.51000000000002 / (1 + n) ** 3
+        + 391.02500000000003 / (1 + n) ** 2
+        + 367.4750000000001 / (1 + n)
+        + 404.47249999999997 / (2 + n)
+        - 2063.325 / ((1 + n) ** 2 * (2 + n))
+        - (1375.55 * n) / ((1 + n) ** 2 * (2 + n))
+        + 687.775 / ((1 + n) * (2 + n))
+        - 81.71999999999998 / (3 + n)
+        + 114.9225 / (4 + n)
+        + 195.5772 * S1
+        - (817.725 * S1) / n**2
+        + (714.46361 * S1) / n
+        - (687.775 * S1) / (1 + n)
+        - (817.725 * S2) / n
     )
 
 
@@ -119,22 +123,22 @@ def gamma_nsm_nf1(n, cache):
     Lm12m1 = lm12m1(n, S1, S2)
     Lm13m1 = lm13m1(n, S1, S2, S3)
     return (
-        5550.182834015097
+        5550.079294018526
         - 126.41975308641975 / n**6
         + 752.1975308641976 / n**5
         - 2253.1105700880144 / n**4
         + 5247.1769880520205 / n**3
         - 8769.153217295072 / n**2
-        - 5834.355552528428 / n
-        - 1969.0104529610248 / (1.0 + n) ** 3
-        - 2742.0697059315535 / (1.0 + n) ** 2
-        + 2512.6444931763654 / (3.0 + n)
+        - 3248.3974879855336 / n
+        - 2898.2943249560426 / (1.0 + n) ** 3
+        - 689.0970388084964 / (1.0 + n) ** 2
+        - 19.315781886816087 / (3.0 + n)
         - 5171.916129085788 * S1
-        + (13862.898314841788 * S1) / n**2
+        + (12317.648319304566 * S1) / n**2
         - (2741.830025124657 * S1) / n
-        - 2121.855469704418 * Lm11m1
-        - 3590.759053757736 * Lm12m1
-        - 413.4348940200741 * Lm13m1
+        + 2591.510450390595 * Lm11m1
+        - 1731.0652413316732 * Lm12m1
+        - 170.02391773352406 * Lm13m1
     )
 
 
@@ -163,23 +167,23 @@ def gamma_nsm_nf0(n, cache):
     Lm12m1 = lm12m1(n, S1, S2)
     Lm13m1 = lm13m1(n, S1, S2, S3)
     return (
-        -23372.01191013195
+        -23371.597456219817
         - 252.8395061728395 / n**7
         + 1580.2469135802469 / n**6
         - 5806.800104704373 / n**5
         + 14899.91711929902 / n**4
         - 28546.38768506619 / n**3
         + 50759.65541232588 / n**2
-        + 21477.757730073346 / n
-        + 194339.87834020052 / (1.0 + n) ** 3
-        - 88491.39062175922 / (1.0 + n) ** 2
-        - 16673.930496518376 / (3.0 + n)
+        + 11126.581215589995 / n
+        + 198059.65286720797 / (1.0 + n) ** 3
+        - 96709.11158512249 / (1.0 + n) ** 2
+        - 6538.89846648667 / (3.0 + n)
         + 20702.353028966703 * S1
-        - (103246.60425090564 * S1) / n**2
+        - (97061.21566841986 * S1) / n**2
         + (16950.937339235086 * S1) / n
-        - 178815.0878250944 * Lm11m1
-        - 49111.66189344577 * Lm12m1
-        - 11804.70644702107 * Lm13m1
+        - 197681.93739849582 * Lm11m1
+        - 56555.718627160735 * Lm12m1
+        - 12779.041608676462 * Lm13m1
     )
 
 

src/ekore/anomalous_dimensions/unpolarized/space_like/as4/gnsp.py

@@ -10,6 +10,8 @@
 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
@@ -25,26 +27,28 @@ def gamma_nsp_nf2(n, cache):
     """
     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 (
-        -193.862483821757
-        - 18.962962962962962 / n**5
-        + 99.1604938271605 / n**4
-        - 226.44075306899038 / n**3
-        + 395.60497732877303 / n**2
-        + 278.2205375565073 / n
-        + 59.46630017646719 / (1.0 + n) ** 3
-        - 152.70402416764668 / (1.0 + n) ** 2
-        - 94.57207315818547 / (2.0 + n)
-        + 195.5772257829161 * S1
-        - (517.9354004395117 * S1) / n**2
-        + (26.68861454046639 * S1) / n
-        + 1.5006487633206929 * Lm11m1
-        + 113.48340560825889 * Lm12m1
-        + 13.865450025251006 * Lm13m1
+        -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
     )
 
 
@@ -72,22 +76,22 @@ def gamma_nsp_nf1(n, cache):
     Lm12m1 = lm12m1(n, S1, S2)
     Lm13m1 = lm13m1(n, S1, S2, S3)
     return (
-        5550.285178175209
+        5550.218627756056
         - 126.41975308641975 / n**6
         + 752.1975308641976 / n**5
         - 2253.1105700880144 / n**4
         + 5247.1769880520205 / n**3
         - 8769.153217295072 / n**2
-        - 5834.355552528428 / n
-        + 537.8609133198307 / (1.0 + n) ** 3
-        - 718.3874592628895 / (1.0 + n) ** 2
-        + 2487.96294221855 / (2.0 + n)
+        - 3248.3974879855336 / n
+        + 1045.759889779711 / (1.0 + n) ** 3
+        - 1517.7637756534405 / (1.0 + n) ** 2
+        - 71.40345295295322 / (2.0 + n)
         - 5171.916129085788 * S1
-        + (12894.65275887218 * S1) / n**2
+        + (11292.198190230158 * S1) / n**2
         - (2741.830025124657 * S1) / n
-        - 849.8232086542307 * Lm11m1
-        - 3106.3285877376907 * Lm12m1
-        - 399.22204467960154 * Lm13m1
+        - 380.3748812945835 * Lm11m1
+        - 2478.792283615627 * Lm12m1
+        - 308.36695798751623 * Lm13m1
     )
 
 
@@ -115,23 +119,23 @@ def gamma_nsp_nf0(n, cache):
     Lm12m1 = lm12m1(n, S1, S2)
     Lm13m1 = lm13m1(n, S1, S2, S3)
     return (
-        -23391.315223909038
+        -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
-        + 21477.757730073346 / n
-        + 47399.00434062458 / (1.0 + n) ** 3
-        - 15176.296853013831 / (1.0 + n) ** 2
-        - 11103.411980157494 / (2.0 + n)
+        + 11126.581215589995 / n
+        + 45365.96043751846 / (1.0 + n) ** 3
+        - 11976.515209798297 / (1.0 + n) ** 2
+        - 858.6772726856868 / (2.0 + n)
         + 20702.353028966703 * S1
-        - (73498.98594171858 * S1) / n**2
+        - (67084.61612292472 * S1) / n**2
         + (16950.937339235086 * S1) / n
-        - 43731.12143482942 * Lm11m1
-        - 2518.9090401926924 * Lm12m1
-        - 973.3270027901576 * Lm13m1
+        - 45610.240259669365 * Lm11m1
+        - 5030.833428351564 * Lm12m1
+        - 1337.0046605808507 * Lm13m1
     )