From e96738befac3cd2d8c5f54dca3264cf2ec37bd2d Mon Sep 17 00:00:00 2001
From: giacomomagni <giac.magni@gmail.com>
Date: Mon, 1 May 2023 20:29:21 +0200
Subject: [PATCH] expand as3 NS sea on even moments

---
 .../polarized/space_like/as3.py                  |  7 +++----
 .../polarized/space_like/test_ad_as3.py          | 16 ++++++++++------
 2 files changed, 13 insertions(+), 10 deletions(-)

diff --git a/src/ekore/anomalous_dimensions/polarized/space_like/as3.py b/src/ekore/anomalous_dimensions/polarized/space_like/as3.py
index 92ec3b34d..a180c6782 100644
--- a/src/ekore/anomalous_dimensions/polarized/space_like/as3.py
+++ b/src/ekore/anomalous_dimensions/polarized/space_like/as3.py
@@ -349,12 +349,11 @@ def gamma_nss(N, nf, cache):
         :math:`\\gamma_{ns,s}^{(2)}(N)`
 
     """
-    # TODO: CHECK is this true or false ??
     S1 = c.get(c.S1, cache, N)
     S3 = c.get(c.S3, cache, N)
-    Sm2 = c.get(c.Sm2, cache, N, is_singlet=False)
-    Sm3 = c.get(c.Sm3, cache, N, is_singlet=False)
-    Sm21 = c.get(c.Sm21, cache, N, is_singlet=False)
+    Sm2 = c.get(c.Sm2, cache, N, is_singlet=True)
+    Sm3 = c.get(c.Sm3, cache, N, is_singlet=True)
+    Sm21 = c.get(c.Sm21, cache, N, is_singlet=True)
     nss_nf1 = (
         40
         / 9
diff --git a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py
index bd4f1fac8..82bd48675 100755
--- a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py
+++ b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py
@@ -3,6 +3,7 @@
 
 import ekore.anomalous_dimensions.polarized.space_like.as3 as as3
 import ekore.anomalous_dimensions.unpolarized.space_like.as3 as as3_unpol
+from eko.constants import zeta2, zeta3
 from ekore import harmonics
 
 nf = 5
@@ -25,16 +26,19 @@ def test_qg_helicity_conservation():
 
 def test_ns_sea():
     ref_moments = [
-        -220 / 3,
-        -103175 / 34992,
-        -4653353 / 5467500,
-        -7063530941 / 17425497600,
-        -218695344199 / 911421315000,
+        (20 / 9)
+        * (
+            23 - 12 * zeta2 - 16 * zeta3
+        ),  # reference value from eq 27 of :cite:`Moch:2015usa`
+        -0.0004286694101508916 * (-12139.872394862155 - 21888 * -0.6738675265146354),
+        0.5486968449931413 * (3.844116190831125 + 6.624 * -0.712742410330442),
+        1.1187158441230356 + 1.927437641723356 * -0.7278824381560618,
+        0.6893728427287487 + 1.1939643347050755 * -0.7354233751216146,
     ]
     for i, mom in enumerate(ref_moments):
         N = 1 + 2 * i
         cache = harmonics.cache.reset()
-        np.testing.assert_allclose(-as3.gamma_nss(N, nf, cache), mom * nf, rtol=7e-7)
+        np.testing.assert_allclose(-as3.gamma_nss(N, nf, cache), mom * nf, rtol=5e-7)
 
 
 def test_ns():