Rustify QED

crates/ekore/src/anomalous_dimensions/unpolarized/spacelike/as1aem1.rs

@@ -1,7 +1,8 @@
 //! The $O(a_s^1a_{em}^1)$ Altarelli-Parisi splitting kernels.
+use crate::cmplx;
 use num::complex::Complex;
 
-use crate::constants::{CA, CF};
+use crate::constants::{ed2, eu2, uplike_flavors, CA, CF, NC, TR, ZETA2, ZETA3};
 use crate::harmonics::cache::{Cache, K};
 
 /// Compute the $O(a_s^1a_{em}^1)$ photon-quark anomalous dimension.
@@ -44,6 +45,7 @@ pub fn gamma_qph(c: &mut Cache, nf: u8) -> Complex<f64> {
     let S1 = c.get(K::S1);
     let S2 = c.get(K::S2);
 
+    #[rustfmt::skip]
     let tmp_const = -2.0
         * (4.0
             + 8.0 * N
@@ -60,3 +62,81 @@ pub fn gamma_qph(c: &mut Cache, nf: u8) -> Complex<f64> {
 
     2.0 * (nf as f64) * CA * CF * (tmp_const + tmp_S1 * S1 + tmp_S12 * S1.powu(2) + tmp_S2 * S2)
 }
+
+/// Compute the $O(a_s^1a_{em}^1)$ gluon-photon anomalous dimension.
+///
+/// Implements Eq. (27) of
+pub fn gamma_gph(c: &mut Cache, _nf: u8) -> Complex<f64> {
+    let N = c.n();
+    CF * CA
+        * (8.0 * (-4.0 + N * (-4.0 + N * (-5.0 + N * (-10.0 + N + 2.0 * N.powu(2) * (2.0 + N))))))
+        / (N.powu(3) * (1.0 + N).powu(3) * (-2.0 + N + N.powu(2)))
+}
+
+/// Compute the $O(a_s^1a_{em}^1)$ photon-gluon anomalous dimension.
+///
+/// Implements Eq. (30) of
+pub fn gamma_phg(c: &mut Cache, nf: u8) -> Complex<f64> {
+    TR / CF / CA * (NC as f64) * gamma_gph(c, nf)
+}
+
+/// Compute the $O(a_s^1a_{em}^1)$ quark-gluon singlet anomalous dimension.
+///
+/// Implements Eq. (29) of
+pub fn gamma_qg(c: &mut Cache, nf: u8) -> Complex<f64> {
+    TR / CF / CA * (NC as f64) * gamma_qph(c, nf)
+}
+
+/// Compute the $O(a_s^1a_{em}^1)$ gluon-quark singlet anomalous dimension.
+///
+/// Implements Eq. (35) of
+pub fn gamma_gq(c: &mut Cache, nf: u8) -> Complex<f64> {
+    gamma_phq(c, nf)
+}
+
+/// Compute the $O(a_s^1a_{em}^1)$ photon-photon singlet anomalous dimension.
+///
+/// Implements Eq. (28) of
+pub fn gamma_phph(_c: &mut Cache, nf: u8) -> Complex<f64> {
+    let nu = uplike_flavors(nf);
+    let nd = nf - nu;
+    cmplx!(4.0 * CF * CA * ((nu as f64) * eu2 + (nd as f64) * ed2), 0.)
+}
+
+/// Compute the $O(a_s^1a_{em}^1)$ gluon-gluon singlet anomalous dimension.
+///
+/// Implements Eq. (31) of
+pub fn gamma_gg(_c: &mut Cache, _nf: u8) -> Complex<f64> {
+    cmplx!(4.0 * TR * (NC as f64), 0.)
+}
+
+/// Compute the $O(a_s^1a_{em}^1)$ singlet-like non singlet anomalous dimension.
+///
+/// Implements Eqs. (33-34) of
+pub fn gamma_nsp(c: &mut Cache, _nf: u8) -> Complex<f64> {
+    let N = c.n();
+    let S1 = c.get(K::S1);
+    let S2 = c.get(K::S2);
+    let S3 = c.get(K::S3);
+    let S1h = c.get(K::S1h);
+    let S2h = c.get(K::S2h);
+    let S3h = c.get(K::S3h);
+    let S1p1h = c.get(K::S1ph);
+    let S2p1h = c.get(K::S2ph);
+    let S3p1h = c.get(K::S3ph);
+    let g3N = c.get(K::G3);
+    let g3Np2 = c.get(K::G3p2);
+
+    #[rustfmt::skip]
+    let result = 32.0 * ZETA2 * S1h - 32.0 * ZETA2 * S1p1h
+        + 8.0 / (N + N.powu(2)) * S2h
+        - 4.0 * S3h + (24.0 + 16.0 / (N + N.powu(2))) * S2
+        - 32.0 * S3 - 8.0 / (N + N.powu(2)) * S2p1h
+        + S1 * (16.0 * (3.0 / N.powu(2) - 3.0 / (1.0 + N).powu(2) + 2.0 * ZETA2) - 16.0 * S2h
+            - 32.0 * S2 + 16.0 * S2p1h )
+        + (-8.0 + N * (-32.0 + N * ( -8.0 - 3.0 * N * (3.0 + N) * (3.0 + N.powu(2)) - 48.0 * (1.0 + N).powu(2) * ZETA2)))
+        / (N.powu(3) * (1.0 + N).powu(3))
+        + 32.0 * (g3N + g3Np2) + 4.0 * S3p1h - 16.0 * ZETA3;
+
+    CF * result
+}

crates/ekore/src/harmonics/cache.rs

@@ -46,6 +46,12 @@ pub enum K {
     Sm21e,
     /// $S_{-2,1}(N)$ odd moments
     Sm21o,
+    /// recursive harmonics
+    S1ph,
+    S2ph,
+    S3ph,
+    S1p2,
+    G3p2,
 }
 
 /// Hold all cached values.
@@ -90,6 +96,7 @@ impl Cache {
             K::S2mh => w2::S2((self.n - 1.) / 2.),
             K::S3mh => w3::S3((self.n - 1.) / 2.),
             K::G3 => g_functions::g3(self.n, self.get(K::S1)),
+            K::G3p2 => g_functions::g3(self.n + 2., self.get(K::S1p2)),
             K::Sm1e => w1::Sm1e(self.get(K::S1), self.get(K::S1h)),
             K::Sm1o => w1::Sm1o(self.get(K::S1), self.get(K::S1mh)),
             K::Sm2e => w2::Sm2e(self.get(K::S2), self.get(K::S2h)),
@@ -98,6 +105,10 @@ impl Cache {
             K::Sm3o => w3::Sm3o(self.get(K::S3), self.get(K::S3mh)),
             K::Sm21e => w3::Sm21e(self.n, self.get(K::S1), self.get(K::Sm1e)),
             K::Sm21o => w3::Sm21o(self.n, self.get(K::S1), self.get(K::Sm1o)),
+            K::S1ph => recursive_harmonic_sum(self.get(K::S1mh), (self.n - 1.) / 2., 1, 1),
+            K::S2ph => recursive_harmonic_sum(self.get(K::S2mh), (self.n - 1.) / 2., 1, 2),
+            K::S3ph => recursive_harmonic_sum(self.get(K::S3mh), (self.n - 1.) / 2., 1, 3),
+            K::S1p2 => recursive_harmonic_sum(self.get(K::S1), self.n, 2, 1),
         };
         // insert
         self.m.insert(k, val);