From 678efa9e4490da2b56a977dbea5896fd7eca1801 Mon Sep 17 00:00:00 2001
From: tgiani <tgiani@nikhef.nl>
Date: Thu, 5 Sep 2024 15:44:23 +0200
Subject: [PATCH] working on as2

---
 .../unpolarized/spacelike/as2.rs              | 99 +++++++++++++++++++
 1 file changed, 99 insertions(+)

diff --git a/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as2.rs b/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as2.rs
index 7fee55609..ae46e50ff 100644
--- a/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as2.rs
+++ b/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as2.rs
@@ -79,3 +79,102 @@ pub fn A_hq_ps(c: &mut Cache, _nf: u8, L: f64) -> Complex<f64> {
 
     CF * TR * (a_hq_l2 * L.pow(2) + a_hq_l1 * L + a_hq_l0)
 }
+
+/// |NNLO| heavy-gluon |OME|
+/// It is given in Eq.() of
+pub fn A_hg(c: &mut Cache, _nf: u8, L: f64) -> Complex<f64> {
+    let N = c.n();
+    let S1 = c.get(K::S1);
+    let S2 = c.get(K::S2);
+    let Sm2e = c.get(K::Sm2e);
+    let S3 = c.get(K::S3);
+    let Sm21e = c.get(K::Sm21e);
+    let Sm3e = c.get(K::Sm3e);
+    let S1m = S1 - 1. / N;
+    let S2m = S2 - 1. / N.powu(2);
+
+    #[rustfmt::skip]
+    let a_hg_l0 =
+        -(
+            3084.
+            + 192. / N.powu(4)
+            + 1056. / N.powu(3)
+            + 2496. / N.powu(2)
+            + 2928. / N
+            + 2970. * N
+            + 1782. * N.powu(2)
+            + 6. * N.powu(3)
+            - 1194. * N.powu(4)
+            - 1152. * N.powu(5)
+            - 516. * N.powu(6)
+            - 120. * N.powu(7)
+            - 12. * N.powu(8)
+        )
+        / ((N - 1.) * ((1. + N) * (2. + N)).powu(4))
+        + (
+            764.
+            - 16. / N.powu(4)
+            - 80. / N.powu(3)
+            - 100. / N.powu(2)
+            + 3. * 72. / N
+            + 208. * N.powu(3)
+            + 3. * (288. * N + 176. * N.powu(2) + 16. * N.powu(4))
+        )
+        / (3. * (1. + N).powu(4) * (2. + N))
+        + 12. * Sm3e * (2. + N + N.powu(2)) / (N * (1. + N) * (2. + N))
+        - 24. * Sm2e * (4. + N - N.powu(2)) / ((1. + N) * (2. + N)).powu(2)
+        - S1
+        * (48. / N + 432. + 564. * N + 324. * N.powu(2) + 138. * N.powu(3) + 48. * N.powu(4) + 6. * N.powu(5))
+        / ((1. + N) * (2. + N)).powu(3)
+        + S1
+        * (-160. - 32. / N.powu(2) - 80. / N + 8. * N * (N - 1.))
+        / (3. * (1. + N).powu(2) * (2. + N))
+        - 6. * S1.powu(2) * (11. + 8. * N + N.powu(2) + 2. / N) / ((1. + N) * (2. + N)).powu(2)
+        + 8. * S1.powu(2) * (2. / (3. * N) + 1.) / (N * (2. + N))
+        - 2.
+        * S2
+        * (63. + 48. / N.powu(2) + 54. / N + 39. * N + 63. * N.powu(2) + 21. * N.powu(3))
+        / ((N - 1.) * (1. + N).powu(2) * (2. + N).powu(2))
+        + 8. * S2 * (17. - 2. / N.powu(2) - 5. / N + N * (17. + N)) / (3. * (1. + N).powu(2) * (2. + N))
+        + (1. + 2. / N + N)
+        / ((1. + N) * (2. + N))
+        * (24. * Sm2e * S1 + 10. * S1.powu(3) / 9. + 46. * S1 * S2 / 3. + 176. * S3 / 9. - 24. * Sm21e);
+
+    #[rustfmt::skip]
+    let mut a_hg_l1 =
+        2.
+        * (
+            640. + 2192. * N
+            + 2072. * N.powu(2)
+            + 868. * N.powu(3)
+            + 518. * N.powu(4)
+            + 736. * N.powu(5)
+            + 806. * N.powu(6)
+            + 542. * N.powu(7)
+            + 228. * N.powu(8)
+            + 38. * N.powu(9)
+        )
+        / (3. * (N * (N + 1.) * (N + 2.)).powu(3) * (N - 1.));
+
+    a_hg_l1 -= 2.
+        * (N * (N.powu(2) - 1.)
+            * (N + 2.)
+            * (4. * (36. + N * (88. + N * (33. + N * (8. + 9. * N)))) * S1m
+                + N * (N + 1.)
+                    * (N + 2.)
+                    * (2. + N + N.powu(2))
+                    * (10. * S1m.powu(2) + 18. * (2. * Sm2e + ZETA2) + 26. * S2m)))
+        / (3. * (N * (N + 1.) * (N + 2.)).powu(3) * (N - 1.));
+
+    a_hg_l1 += 12. * ZETA2 * (-2. + N + N.powu(3)) / (N * (N.powu(2) - 1.) * (N + 2.));
+
+    #[rustfmt::skip]
+    let a_hg_l2 = (
+        4.
+        * (2. + N + N.powu(2))
+        * (2. * (-11. + N + N.powu(2)) * (1. + N + N.powu(2)) / (N - 1.))
+        / (3. * (N * (N + 1.) * (N + 2.)).powu(2))
+    ) + 20. * (2. + N + N.powu(2)) * S1 / (3. * N * (N + 1.) * (N + 2.));
+
+    a_hg_l2 * L.pow(2) + a_hg_l1 * L + a_hg_l0
+}