rust: Init ad/u/s/aem2

crates/ekore/refs.bib

@@ -143,3 +143,16 @@ @article{deFlorian2015ujt
     pages = "282",
     year = "2016"
 }
+@article{deFlorian2016gvk,
+    author = "de Florian, Daniel and Sborlini, Germ\'an F. R. and Rodrigo, Germ\'an",
+    title = "{Two-loop QED corrections to the Altarelli-Parisi splitting functions}",
+    eprint = "1606.02887",
+    archivePrefix = "arXiv",
+    primaryClass = "hep-ph",
+    reportNumber = "ICAS-09-16, IFIC-15-88",
+    doi = "10.1007/JHEP10(2016)056",
+    journal = "JHEP",
+    volume = "10",
+    pages = "056",
+    year = "2016"
+}

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

@@ -7,6 +7,7 @@ use crate::harmonics::cache::Cache;
 use num::complex::Complex;
 use num::Zero;
 pub mod aem1;
+pub mod aem2;
 pub mod as1;
 pub mod as1aem1;
 pub mod as2;

crates/ekore/src/anomalous_dimensions/unpolarized/spacelike/aem2.rs

@@ -0,0 +1,158 @@
+//! |NLO| |QED|.
+use num::complex::Complex;
+use num::Zero;
+
+use crate::constants::{ChargeCombinations, CA, CF, ED2, EU2, NC};
+use crate::harmonics::cache::{Cache, K};
+
+use crate::anomalous_dimensions::unpolarized::spacelike::as1aem1;
+
+/// Compute the photon-photon anomalous dimension.
+///
+/// Implements Eq. (68) of [\[deFlorian:2016gvk\]][crate::bib::deFlorian2016gvk].
+pub fn gamma_phph(c: &mut Cache, nf: u8) -> Complex<f64> {
+    let cc = ChargeCombinations { nf };
+    (NC as f64)
+        * ((cc.nu() as f64) * EU2.powi(2) + (cc.nd() as f64) * ED2.powi(2))
+        * (as1aem1::gamma_gph(c, nf) / CF / CA + 4.)
+}
+
+/// Compute the up-photon anomalous dimension.
+///
+/// Implements Eq. (55) of [\[deFlorian:2016gvk\]][crate::bib::deFlorian2016gvk] for q=u.
+pub fn gamma_uph(c: &mut Cache, nf: u8) -> Complex<f64> {
+    EU2 * as1aem1::gamma_qph(c, nf) / CF
+}
+
+/// Compute the down-photon anomalous dimension.
+///
+/// Implements Eq. (55) of [\[deFlorian:2016gvk\]][crate::bib::deFlorian2016gvk] for q=d.
+pub fn gamma_dph(c: &mut Cache, nf: u8) -> Complex<f64> {
+    ED2 * as1aem1::gamma_qph(c, nf) / CF
+}
+
+/// Compute the photon-quark anomalous dimension.
+///
+/// Implements singlet part of Eq. (56) of [\[deFlorian:2016gvk\]][crate::bib::deFlorian2016gvk].
+fn gamma_phq(c: &mut Cache, nf: u8) -> Complex<f64> {
+    let N = c.n();
+    let S1 = c.get(K::S1);
+    let gamma = (-16.0 * (-16.0 - 27.0 * N - 13.0 * N.powu(2) - 8.0 * N.powu(3)))
+        / (9.0 * (-1.0 + N) * N * (1.0 + N).powu(2))
+        - 16.0 * (2.0 + 3.0 * N + 2.0 * N.powu(2) + N.powu(3))
+            / (3.0 * (-1.0 + N) * N * (1.0 + N).powu(2))
+            * S1;
+    let cc = ChargeCombinations { nf };
+    let eSigma2 = (NC as f64) * cc.e2avg() * (nf as f64);
+    eSigma2 * gamma
+}
+
+/// Compute the photon-up anomalous dimension.
+///
+/// Implements Eq. (56) of [\[deFlorian:2016gvk\]][crate::bib::deFlorian2016gvk].
+pub fn gamma_phu(c: &mut Cache, nf: u8) -> Complex<f64> {
+    EU2 * as1aem1::gamma_phq(c, nf) / CF + gamma_phq(c, nf)
+}
+
+/// Compute the photon-down anomalous dimension.
+///
+/// Implements Eq. (56) of [\[deFlorian:2016gvk\]][crate::bib::deFlorian2016gvk].
+pub fn gamma_phd(c: &mut Cache, nf: u8) -> Complex<f64> {
+    ED2 * as1aem1::gamma_phq(c, nf) / CF + gamma_phq(c, nf)
+}
+
+// /// Compute the non-singlet anomalous dimension.
+// ///
+// /// Implements Eq. (2.5) of [\[deFlorian:2016gvk\]][crate::bib::deFlorian2016gvk].
+// pub fn gamma_ns(c: &mut Cache, nf: u8) -> Complex<f64> {
+//     as1::gamma_ns(c, nf) / CF
+// }
+
+// /// Compute the singlet anomalous dimension matrix.
+// pub fn gamma_singlet(c: &mut Cache, nf: u8) -> [[Complex<f64>; 4]; 4] {
+//     let cc = ChargeCombinations { nf };
+
+//     let gamma_ph_q = gamma_phq(c, nf);
+//     let gamma_q_ph = gamma_qph(c, nf);
+//     let gamma_nonsinglet = gamma_ns(c, nf);
+
+//     [
+//         [
+//             Complex::<f64>::zero(),
+//             Complex::<f64>::zero(),
+//             Complex::<f64>::zero(),
+//             Complex::<f64>::zero(),
+//         ],
+//         [
+//             Complex::<f64>::zero(),
+//             gamma_phph(c, nf),
+//             cc.e2avg() * gamma_ph_q,
+//             cc.vue2m() * gamma_ph_q,
+//         ],
+//         [
+//             Complex::<f64>::zero(),
+//             cc.e2avg() * gamma_q_ph,
+//             cc.e2avg() * gamma_nonsinglet,
+//             cc.vue2m() * gamma_nonsinglet,
+//         ],
+//         [
+//             Complex::<f64>::zero(),
+//             cc.vde2m() * gamma_q_ph,
+//             cc.vde2m() * gamma_nonsinglet,
+//             cc.e2delta() * gamma_nonsinglet,
+//         ],
+//     ]
+// }
+
+// /// Compute the valence anomalous dimension matrix.
+// pub fn gamma_valence(c: &mut Cache, nf: u8) -> [[Complex<f64>; 2]; 2] {
+//     let cc = ChargeCombinations { nf };
+
+//     [
+//         [cc.e2avg() * gamma_ns(c, nf), cc.vue2m() * gamma_ns(c, nf)],
+//         [cc.vde2m() * gamma_ns(c, nf), cc.e2delta() * gamma_ns(c, nf)],
+//     ]
+// }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{assert_approx_eq_cmplx, cmplx};
+    use num::complex::Complex;
+    use num::Zero;
+    const NF: u8 = 5;
+
+    // #[test]
+    // fn number_conservation() {
+    //     const N: Complex<f64> = cmplx!(1., 0.);
+    //     let mut c = Cache::new(N);
+    //     let me = gamma_ns(&mut c, NF);
+    //     assert_approx_eq_cmplx!(f64, me, Complex::zero(), epsilon = 1e-12);
+    // }
+
+    // #[test]
+    // fn quark_momentum_conservation() {
+    //     const N: Complex<f64> = cmplx!(2., 0.);
+    //     let mut c = Cache::new(N);
+    //     let me = gamma_ns(&mut c, NF) + gamma_phq(&mut c, NF);
+    //     assert_approx_eq_cmplx!(f64, me, Complex::zero(), epsilon = 1e-12);
+    // }
+
+    #[test]
+    fn photon_momentum_conservation() {
+        const N: Complex<f64> = cmplx!(2., 0.);
+        let mut c = Cache::new(N);
+
+        for nf in 2..7 {
+            let cc = ChargeCombinations { nf };
+            assert_approx_eq_cmplx!(
+                f64,
+                EU2 * gamma_uph(&mut c, cc.nu())
+                    + ED2 * gamma_dph(&mut c, cc.nd())
+                    + gamma_phph(&mut c, nf),
+                Complex::zero(),
+                epsilon = 1e-12
+            );
+        }
+    }
+}

crates/ekore/src/bib.rs

@@ -1,4 +1,4 @@
-//! List of References (autogenerated on 2025-01-13T14:59:31.519662).
+//! List of References (autogenerated on 2025-01-13T15:14:10.528903).
 
 #[allow(non_snake_case)]
 /// The Three loop splitting functions in QCD: The Nonsinglet case
@@ -143,3 +143,15 @@ pub fn Carrazza2015dea() {}
 ///
 /// DOI: [10.1140/epjc/s10052-016-4131-8](https:dx.doi.org/10.1140/epjc/s10052-016-4131-8)
 pub fn deFlorian2015ujt() {}
+
+#[allow(non_snake_case)]
+/// Two-loop QED corrections to the Altarelli-Parisi splitting functions
+///
+/// de Florian, Daniel and Sborlini, Germán F. R. and Rodrigo, Germán
+///
+/// Published in: JHEP 10 (2016), 056
+///
+/// e-Print: [1606.02887](https://arxiv.org/abs/1606.02887)
+///
+/// DOI: [10.1007/JHEP10(2016)056](https:dx.doi.org/10.1007/JHEP10(2016)056)
+pub fn deFlorian2016gvk() {}