add n3lo ns ad

crates/ekore/src/anomalous_dimensions/unpolarized/spacelike/as3.rs

@@ -1,6 +1,6 @@
 //! |NNLO| |QCD|.
 
-use ::num::complex::Complex;
+use num::complex::Complex;
 use num::traits::Pow;
 
 use crate::cmplx;

crates/ekore/src/anomalous_dimensions/unpolarized/spacelike/as4.rs

@@ -0,0 +1,22 @@
+//! |N3LO| |QCD|.
+
+// pub mod ggg;
+// pub mod ggq;
+// pub mod gqg;
+// pub mod gps;
+
+pub mod gnsm;
+pub mod gnsp;
+pub mod gnsv;
+
+// /// Compute the singlet anomalous dimension matrix.
+// pub fn gamma_singlet(c: &mut Cache, nf: u8, variation: [u8; 4]) -> [[Complex<f64>; 2]; 2] {
+//     let gamma_qq = gamma_nsp(c, nf, variation[3]) + gamma_ps(c, nf, variation[3]);
+//     [
+//         [gamma_qq, gamma_qg(c, nf, variation[2])],
+//         [gamma_gq(c, nf, variation[1]), gamma_gg(c, nf, variation[0])],
+//     ]
+// }
+
+#[cfg(test)]
+mod tests {}

crates/ekore/src/anomalous_dimensions/unpolarized/spacelike/as4/gnsm.rs

@@ -0,0 +1,242 @@
+/// Compute the non-singlet-like non-singlet anomalous dimension.
+use num::complex::Complex;
+use num::traits::Pow;
+
+use crate::cmplx;
+use crate::constants::{CF, ZETA3};
+use crate::harmonics::cache::{Cache, K};
+use crate::harmonics::log_functions::{lm11, lm11m1, lm12m1, lm13m1};
+
+// The routine is taken from [\[`Moch:2017uml\]][crate::bib:Moch:2017uml].
+
+// The nf^{0,1} leading large-nc contributions and the nf^2 part are
+// high-accuracy (0.1% or better) parametrizations of the exact
+// results. The nf^3 expression is exact up to numerical truncations.
+
+// The remaining nf^{0,1} terms are approximations based on the first
+// eight odd moments together with small-x and large-x constraints.
+// The two sets spanning the error estimate are called via  IMOD = 1
+// and  IMOD = 2.  Any other value of IMOD invokes their average.
+pub fn gamma_nsm(c: &mut Cache, nf: u8, variation: 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 S4 = c.get(K::S4);
+
+    // Leading large-n_c, nf^0 and nf^1, parametrized
+    #[rustfmt::skip]
+    let P3NSA0 = 360.0 / n.powu(7)
+        - 1920.0 / n.powu(6)
+        + 7147.812 / n.powu(5)
+        - 17179.356 / n.powu(4)
+        + 34241.9 / n.powu(3)
+        - 51671.329999999994 / n.powu(2)
+        + 19069.8 * lm11(n, S1)
+        - (491664.8019540468 / n)
+        - 4533.0 / (1. + n).powu(3)
+        - 11825.0 / (1. + n).powu(2)
+        + 129203.0 / (1. + n)
+        - 254965.0 / (2. + n)
+        + 83377.5 / (3. + n)
+        - 45750.0 / (4. + n)
+        + (49150.0 * (6.803662258392675 + n) * S1) / (n.powu(2) * (1.0 + n))
+        + (334400.0 * S2) / n;
+    #[rustfmt::skip]
+    let P3NSA1 = 160.0 / n.powu(6)
+        - 864.0 / n.powu(5)
+        + 2583.1848 / n.powu(4)
+        - 5834.624 / n.powu(3)
+        + 9239.374 / n.powu(2)
+        - 3079.76 * lm11(n, S1)
+        - (114047.0 / n)
+        - 465.0 / (1. + n).powu(4)
+        - 1230.0 / (1. + n).powu(3)
+        + 7522.5 / (1. + n).powu(2)
+        + 55669.3 / (1. + n)
+        - 43057.8 / (2. + n)
+        + 13803.8 / (3. + n)
+        - 7896.0 / (4. + n)
+        - (120.0 * (-525.063 + n) * S1) / (n.powu(2) * (1.0 + n))
+        + (63007.5 * S2) / n;
+
+    // Nonleading large-n_c, nf^0 and nf^1: two approximations
+    #[rustfmt::skip]
+    let P3NMA01 = 0.4964335 * (720. / n.powu(7) - 720.0 / n.powu(6))
+        - 13.5288 / n.powu(4)
+        + 1618.07 / n.powu(2)
+        - 2118.8669999999997 * lm11(n, S1)
+        + 31897.8 * lm11m1(n, S1)
+        + 4653.76 * lm12m1(n, S1, S2)
+        + 3902.3590000000004 / n
+        + 5992.88 / (1. + n)
+        + 19335.7 / (2. + n)
+        - 31321.4 / (3. + n);
+    #[rustfmt::skip]
+    let P3NMA02 = 0.4964335 * (720. / n.powu(7) - 2160.0 / n.powu(6))
+        - 189.6138 / n.powu(4)
+        + 3065.92 / n.powu(3)
+        - 2118.8669999999997 * lm11(n, S1)
+        - 3997.39 * lm11m1(n, S1)
+        + 511.567 * lm13m1(n, S1, S2, S3)
+        - (2099.268 / n)
+        + 4043.59 / (1. + n)
+        - 19430.190000000002 / (2. + n)
+        + 15386.6 / (3. + n);
+
+    #[rustfmt::skip]
+    let P3NMA11 = 64.7083 / n.powu(5)
+        - 254.024 / n.powu(3)
+        + 337.931 * lm11(n, S1)
+        + 1856.63 * lm11m1(n, S1)
+        + 440.17 * lm12m1(n, S1, S2)
+        + 419.53485 / n
+        + 114.457 / (1. + n)
+        + 2341.816 / (2. + n)
+        - 2570.73 / (3. + n);
+
+    #[rustfmt::skip]
+    let P3NMA12 = -17.0616 / n.powu(6)
+        - 19.53254 / n.powu(3)
+        + 337.931 * lm11(n, S1)
+        - 1360.04 * lm11m1(n, S1)
+        + 38.7337 * lm13m1(n, S1, S2, S3)
+        - (367.64646999999997 / n)
+        + 335.995 / (1. + n)
+        - 1269.915 / (2. + n)
+        + 1605.91 / (3. + n);
+
+    // nf^2 (parametrized) and nf^3 (exact)
+    #[rustfmt::skip]
+    let P3NSMA2 = -(
+        -193.84583328013258
+        - 23.7037032 / n.powu(5)
+        + 117.5967 / n.powu(4)
+        - 256.5896 / n.powu(3)
+        + 437.881 / n.powu(2)
+        + 720.385709813466 / n
+        - 48.720000000000006 / (1. + n).powu(4)
+        + 189.51000000000002 / (1. + n).powu(3)
+        + 391.02500000000003 / (1. + n).powu(2)
+        + 367.4750000000001 / (1. + n)
+        + 404.47249999999997 / (2. + n)
+        - 2063.325 / ((1. + n).powu(2) * (2. + n))
+        - (1375.55 * n) / ((1. + n).powu(2) * (2. + n))
+        + 687.775 / ((1. + n) * (2. + n))
+        - 81.71999999999998 / (3. + n)
+        + 114.9225 / (4. + n)
+        + 195.5772 * S1
+        - (817.725 * S1) / n.powu(2)
+        + (714.46361 * S1) / n
+        - (687.775 * S1) / (1. + n)
+        - (817.725 * S2) / n
+    );
+    let eta = 1. / n * 1. / (n + 1.);
+    #[rustfmt::skip]
+    let P3NSA3 = -CF * (
+        -32. / 27. * ZETA3 * eta
+        - 16. / 9. * ZETA3
+        - 16. / 27. * eta.powu(4)
+        - 16. / 81. * eta.powu(3)
+        + 80. / 27. * eta.powu(2)
+        - 320. / 81. * eta
+        + 32. / 27. * 1. / (n + 1.).powu(4)
+        + 128. / 27. * 1. / (n + 1.).powu(2)
+        + 64. / 27. * S1 * ZETA3
+        - 32. / 81. * S1
+        - 32. / 81. * S2
+        - 160. / 81. * S3
+        + 32. / 27. * S4
+        + 131. / 81.
+    );
+
+    let mut result = cmplx!(0., 0.);
+
+    // Assembly regular piece.
+    let NF = nf as f64;
+    let P3NSMAI = P3NSA0 + NF * P3NSA1 + NF.pow(3) * P3NSA3 + NF.pow(2) * P3NSMA2;
+    result += Complex::from(match variation {
+        1 => P3NSMAI + P3NMA01 + NF * P3NMA11,
+        2 => P3NSMAI + P3NMA02 + NF * P3NMA12,
+        _ => P3NSMAI + 0.5 * ((P3NMA01 + P3NMA02) + NF * (P3NMA11 + P3NMA12)),
+    });
+
+    // The singular piece.
+    let A4qI = 2.120902 * f64::pow(10., 4) - 5.179372 * f64::pow(10., 3) * NF
+        // + 1.955772 * f64::pow(10.,2) * NF.pow(2)
+        // + 3.272344 * NF.pow(3)
+    ;
+    let A4ap1 = -511.228 + 7.08645 * NF;
+    let A4ap2 = -502.481 + 7.82077 * NF;
+    let D1 = 1. / n - S1;
+    result += Complex::from(match variation {
+        1 => (A4qI + A4ap1) * D1,
+        2 => (A4qI + A4ap2) * D1,
+        _ => (A4qI + 0.5 * (A4ap1 + A4ap2)) * D1,
+    });
+
+    // ..The local piece.
+    let B4qI = 2.579609 * f64::pow(10., 4) + 0.08 - (5.818637 * f64::pow(10., 3) + 0.97) * NF
+        // + (1.938554 * f64::pow(10.,2) + 0.0037) * NF.pow(2)
+        // + 3.014982 * NF.pow(3)
+    ;
+    let B4ap1 = -2426.05 + 266.674 * NF - 0.05 * NF;
+    let B4ap2 = -2380.255 + 270.518 * NF - 0.05 * NF;
+    result += Complex::from(match variation {
+        1 => B4qI + B4ap1,
+        2 => B4qI + B4ap2,
+        _ => B4qI + 0.5 * (B4ap1 + B4ap2),
+    });
+
+    -result
+}
+
+#[cfg(test)]
+mod tests {
+
+    use super::*;
+    use crate::harmonics::cache::Cache;
+    use crate::{assert_approx_eq_cmplx, cmplx};
+    use num::complex::Complex;
+
+    #[test]
+    fn test_quark_number_conservation() {
+        let NF = 4;
+        let mut c = Cache::new(cmplx!(1., 0.));
+        // TODO: why these numbers are different from python, 
+        // while the higher moments matches ?
+        let refs: [f64; 3] = [
+            -0.002068452870616966,
+            -0.006379286212450097,
+            0.002242380471443539,
+        ];
+        for var in [0, 1, 2] {
+            let test_value = gamma_nsm(&mut c, NF, var);
+            assert_approx_eq_cmplx!(f64, test_value, cmplx!(refs[var as usize], 0.));
+        }
+    }
+
+    #[test]
+    fn test_non_singlet_reference_moments() {
+        let NF = 4;
+        let nsm_nf4_refs: [f64; 7] = [
+            4322.890485339998,
+            5491.581109692005,
+            6221.256799360004,
+            6774.606221595994,
+            7229.056043916002,
+            7618.358743427995,
+            7960.658678124,
+        ];
+        for N in [3.0, 5.0, 7.0, 9.0, 11.0, 13.0, 15.0] {
+            let mut c = Cache::new(cmplx!(N, 0.));
+            let test_value = gamma_nsm(&mut c, NF, 0);
+            assert_approx_eq_cmplx!(
+                f64,
+                test_value,
+                cmplx!(nsm_nf4_refs[((N - 2.) / 2.) as usize], 0.),
+                rel = 8e-5
+            );
+        }
+    }
+}