From 56a77e48462355b42ae194ff01966c7e9355a65e Mon Sep 17 00:00:00 2001
From: tgiani <tgiani@nikhef.nl>
Date: Fri, 31 May 2024 16:45:11 +0200
Subject: [PATCH] starting ome

---
 crates/ekore/src/lib.rs                       |  1 +
 crates/ekore/src/operator_matrix_elements.rs  |  3 +++
 .../operator_matrix_elements/unpolarized.rs   |  3 +++
 .../unpolarized/spacelike.rs                  | 12 +++++++++
 .../unpolarized/spacelike/as1.rs              | 25 +++++++++++++++++++
 5 files changed, 44 insertions(+)
 create mode 100644 crates/ekore/src/operator_matrix_elements.rs
 create mode 100644 crates/ekore/src/operator_matrix_elements/unpolarized.rs
 create mode 100644 crates/ekore/src/operator_matrix_elements/unpolarized/spacelike.rs
 create mode 100644 crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as1.rs

diff --git a/crates/ekore/src/lib.rs b/crates/ekore/src/lib.rs
index af39644cc..f26ce2a4e 100644
--- a/crates/ekore/src/lib.rs
+++ b/crates/ekore/src/lib.rs
@@ -7,4 +7,5 @@ pub mod anomalous_dimensions;
 pub mod bib;
 mod constants;
 pub mod harmonics;
+pub mod operator_matrix_elements;
 pub mod util;
diff --git a/crates/ekore/src/operator_matrix_elements.rs b/crates/ekore/src/operator_matrix_elements.rs
new file mode 100644
index 000000000..cd27db57d
--- /dev/null
+++ b/crates/ekore/src/operator_matrix_elements.rs
@@ -0,0 +1,3 @@
+//! |OME|.
+
+pub mod unpolarized;
diff --git a/crates/ekore/src/operator_matrix_elements/unpolarized.rs b/crates/ekore/src/operator_matrix_elements/unpolarized.rs
new file mode 100644
index 000000000..a00885eec
--- /dev/null
+++ b/crates/ekore/src/operator_matrix_elements/unpolarized.rs
@@ -0,0 +1,3 @@
+//! The unpolarized |OME| for space-like and time-like kinematics.
+
+pub mod spacelike;
diff --git a/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike.rs b/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike.rs
new file mode 100644
index 000000000..86587fd77
--- /dev/null
+++ b/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike.rs
@@ -0,0 +1,12 @@
+//! The unpolarized, space-like |OME| at various couplings power.
+pub mod as1;
+
+// Compute the tower of the singlet |OME|.
+// pub fn A_singlet() -> Vec<Complex<f64>>{
+
+// }
+
+// Compute the tower of the non-singlet |OME|.
+// pub fn A_non_singlet() -> Vec<Complex<f64>>{
+
+// }
diff --git a/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as1.rs b/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as1.rs
new file mode 100644
index 000000000..58e39513c
--- /dev/null
+++ b/crates/ekore/src/operator_matrix_elements/unpolarized/spacelike/as1.rs
@@ -0,0 +1,25 @@
+//! NLO QCD
+
+use num::complex::Complex;
+
+use crate::constants::{CA, CF, TR};
+use crate::harmonics::cache::{Cache, K};
+
+/// Compute heavy-heavy |OME| :math:`A_{HH}^{(1)}`
+///
+/// Defined in Eq. () of .
+pub fn A_hh(c: &mut Cache, _nf: u8, L: f64) -> Complex<f64> {
+    let N = c.n;
+    let S1m = c.get(K::S1) - 1. / N;
+    let S2m = c.get(K::S2) - 1. / N.powu(2);
+    let ahh_l = (2. + N - 3. * N.powu(2)) / (N * (1. + N)) + 4. * S1m;
+    let ahh = 2.
+        * (2. + 5. * N + N.powu(2)
+            - 6. * N.powu(3)
+            - 2. * N.powu(4)
+            - 2. * N * (-1. - 2. * N + N.powu(3)) * S1m)
+        / (N * (1. + N)).powu(2)
+        + 4. * (S1m.powu(2) + S2m);
+
+    -CF * (ahh_l * L + ahh)
+}