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more work on as2
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@tgiani
tgiani committed May 22, 2024
1 parent 929a1de commit c7a477f
Showing 1 changed file with 176 additions and 17 deletions.
193 changes: 176 additions & 17 deletions crates/ekore/src/anomalous_dimensions/unpolarized/spacelike/as2.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,7 @@ use crate::harmonics::cache::{Cache, K};
/// Compute the valence-like non-singlet anomalous dimension.
///
/// Implements Eq. (3.6) of [\[Moch:2004pa\]][crate::bib::Moch2004pa].
pub fn gamma_nsm(c: &mut Cache, _nf: u8) -> Complex<f64> {
pub fn gamma_nsm(c: &mut Cache, nf: u8) -> Complex<f64> {
let N = c.n;
let S1 = c.get(K::S1);
let S2 = c.get(K::S2);
Expand All @@ -23,14 +23,14 @@ pub fn gamma_nsm(c: &mut Cache, _nf: u8) -> Complex<f64> {
let gqq1m_cfcf = -32. * g3n + (24. - N * (-32. + 3. * N * (-8. + N * (3. + N) * (3. + N.powu(2)))))/(2. * N.powu(3) * (1. + N).powu(3)) + (12. - 8. / N + 8./(1. + N)) * S2 + S1 * (-24. / N.powu(2) - 8./(1. + N).powu(2) + 16. * S2 - 16. * Sp2m) + (8. * Sp2m)/(N + N.powu(2)) - 4. * Sp3m - 20. * ZETA3 + ZETA2 * (-32. * S1 + 32. * Sp1m + 32. * (1. / N + LN_2));
let gqq1m_cfnf = (-12. + N * (20. + N * (47. + 3. * N * (2. + N))))/(9. * N.powu(2) * (1. + N).powu(2)) - (40. * S1)/9. + (8. * S2)/3.;

CF * ( CA * gqq1m_cfca + CF * gqq1m_cfcf + 2.0 * TR * (_nf as f64) * gqq1m_cfnf )
CF * ( CA * gqq1m_cfca + CF * gqq1m_cfcf + 2.0 * TR * (nf as f64) * gqq1m_cfnf )
}


/// Compute the singlet-like non-singlet anomalous dimension.
///
/// Implements Eq. (3.5) of [\[Moch:2004pa\]][crate::bib::Moch2004pa].
pub fn gamma_nsp(c: &mut Cache, _nf: u8) -> Complex<f64> {
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);
Expand All @@ -43,35 +43,194 @@ pub fn gamma_nsp(c: &mut Cache, _nf: u8) -> Complex<f64> {
let gqq1p_cfcf = 32. * g3n - (8. + N * (32. + N * (40. + 3. * N * (3. + N) * (3. + N.powu(2))))) / (2. * N.powu(3) * (1. + N).powu(3)) + (12. - 8. / N + 8. / (1. + N)) * S2 + S1 * (40. / N.powu(2) - 8. / (1. + N).powu(2) + 16. * S2 - 16. * Sp2p) + (8. * Sp2p)/(N + N.powu(2)) - 4. * Sp3p - 20. * ZETA3 + ZETA2 * (-32. * S1 + 32. * Sp1p + 32. * (-(1./N) + LN_2));
let gqq1p_cfnf = (-12. + N * (20. + N * (47. + 3. * N * (2. + N))))/(9. * N.powu(2) * (1. + N).powu(2)) - (40. * S1) / 9. + (8. * S2) / 3.;

CF * ( CA * gqq1p_cfca + CF * gqq1p_cfcf + 2.0 * TR * (_nf as f64) * gqq1p_cfnf)
CF * ( CA * gqq1p_cfca + CF * gqq1p_cfcf + 2.0 * TR * (nf as f64) * gqq1p_cfnf)
}

/// Compute the pure-singlet quark-quark anomalous dimension.
///
/// Implements Eq. (3.6) of [\[Vogt:2004mw\]][crate::bib::Vogt:2004mw].
pub fn gamma_ps(c: &mut Cache, nf: u8) -> Complex<f64> {
let N = c.n;
let gqqps1_nfcf = ( -4. * (2. + N * (5. + N)) * (4. + N * (4. + N * (7. + 5. * N))))/((-1. + N) * N.powu(3) * (1. + N).powu(3) * (2. + N).powu(2));
2.0 * TR * (nf as f64) * CF * gqqps1_nfcf
}

/// Compute the quark-gluon singlet anomalous dimension.
///
/// Implements Eq. (3.7) of [\[Vogt:2004mw\]][crate::bib::Vogt:2004mw].
pub fn gamma_qg(c: &mut Cache, nf: u8) -> Complex<f64> {
let N = c.n;
let S1 = c.get(K::S1);
let S2 = c.get(K::S2);
let Sp2p = c.get(K::S2h);

let gqg1_nfca = ( -4. * (16. + N * (64. + N * (104. + N * (128. + N * (85. + N * (36. + N * (25. + N * (15. + N * (6. + N ))))))))))/((-1. + N) * N.powu(3) * (1. + N).powu(3) * (2. + N).powu(3)) - (16. * (3. + 2. * N) * S1) / (2. + 3. * N + N.powu(2)).powu(2) + (4. * (2. + N + N.powu(2)) * S1.powu(2))/(N*(2. + 3. * N + N.powu(2))) - (4. * (2. + N + N.powu(2)) * S2)/(N * (2. + 3. * N + N.powu(2))) + (4. * (2. + N + N.powu(2)) * Sp2p)/(N * (2. + 3. * N + N.powu(2)));
let gqg1_nfcf = (-2. * (4. + N * (8. + N * (1. + N) * (25. + N * (26. + 5. * N * (2. + N))))))/(N.powu(3) * (1. + N).powu(3) * (2. + N)) + (8. * S1) / N.powu(2) - (4. * (2. + N + N.powu(2)) * S1.powu(2))/(N * (2. + 3. * N + N.powu(2))) + (4. * (2. + N + N.powu(2)) * S2)/(N * (2. + 3. * N + N.powu(2)));
2.0 * TR * (nf as f64) * (CA * gqg1_nfca + CF * gqg1_nfcf)
}

/// Compute the gluon-quark singlet anomalous dimension.
///
/// Implements Eq. (3.8) of [\[Vogt:2004mw\]][crate::bib::Vogt:2004mw].
pub fn gamma_gq(c: &mut Cache, nf: u8) -> Complex<f64> {
let N = c.n;
let S1 = c.get(K::S1);
let S2 = c.get(K::S2);
let Sp2p = c.get(K::S2h);

let ggq1_cfcf = (-8. + 2. * N * (-12. + N * (-1. + N * (28. + N * (43. + 6. * N * (5. + 2. * N))))))/((-1. + N) * N.powu(3)*(1. + N).powu( 3)) - (4. * (10. + N * (17. + N * (8. + 5. * N)))*S1) / ((-1. + N) * N * (1. + N).powu(2)) + (4. * (2. + N + N.powu(2)) * S1.powu(2))/(N * (-1. + N.powu(2))) + (4. * (2. + N + N.powu(2)) * S2)/(N*(-1. + N.powu(2)));
let ggq1_cfca = (-4. * (144. + N * (432. + N * (-152. + N * (-1304. + N * (-1031. + N * (695. + N * (1678. + N * (1400. + N * (621. + 109. * N))))))))))/(9. * N.powu(3) * (1. + N).powu(3) * (-2. + N + N.powu(2)).powu(2)) + (4. * (-12. + N*(-22. + 41. * N + 17. * N.powu(3)))*S1)/(3. * (-1. + N).powu(2) * N.powu(2)*(1. + N)) + ((8. + 4. * N + 4. * N.powu(2)) * S1.powu(2))/(N - N.powu(3)) + ((8. + 4. * N + 4. * N.powu(2))*S2)/(N - N.powu(3)) + (4. * (2. + N + N.powu(2)) * Sp2p)/(N * (-1. + N.powu(2)));
let ggq1_cfnf = (8. * (16. + N * (27. + N * (13. + 8. * N))))/(9. * (-1. + N) * N * (1. + N).powu(2)) - (8. * (2. + N + N.powu(2)) * S1)/(3. * N * (-1. + N.powu(2)));
CF * ( CA * ggq1_cfca + CF * ggq1_cfcf + 2.0 * TR * (nf as f64) * ggq1_cfnf)
}

/// Compute the gluon-gluon singlet anomalous dimension.
///
/// Implements Eq. (3.9) of [\[Vogt:2004mw\]][crate::bib::Vogt:2004mw].
pub fn gamma_gg(c: &mut Cache, nf: u8) -> Complex<f64> {
let N = c.n;
let S1 = c.get(K::S1);
let Sp1p = c.get(K::S1h);
let Sp2p = c.get(K::S2h);
let Sp3p = c.get(K::S3h);
let g3n = c.get(K::G3);
let ggg1_caca = 16. * g3n - (2. * (576. + N * (1488. + N * (560. + N * (-1248. + N * (-1384. + N * (1663. + N * (4514. + N * (4744. + N * (3030. + N * (1225. + 48. * N * (7. + N))))))))))))/(9. * (-1. + N).powu(2) * N.powu(3) * (1. + N).powu(3) * (2. + N).powu(3)) + S1 * (29.77777777777778 + 16./(-1. + N).powu(2) + 16./(1. + N).powu(2) - 16./(2. + N).powu(2) - 8.*Sp2p) + (16. * (1. + N + N.powu(2)) * Sp2p)/(N * (1. + N)*(-2. + N + N.powu(2))) - 2. * Sp3p - 10. * ZETA3 + ZETA2 * (-16. * S1 + 16. * Sp1p + 16. * (-(1./N) + LN_2));
let ggg1_canf = (8. * (6. + N * (1. + N) * (28. + N * (1. + N) * (13. + 3. * N * (1. + N)))))/(9. * N.powu(2) * (1. + N).powu(2) * (-2. + N + N.powu(2))) - (40. * S1)/9.;
let ggg1_cfnf = (2. * (-8. + N * (-8. + N * (-10. + N * (-22. + N * (-3. + N * (6. + N * (8. + N * (4. + N)))))))))/(N.powu(3) * (1. + N).powu(3)*(-2. + N + N.powu(2)));

CA * CA * ggg1_caca + 2.0 * TR * (nf as f64) * (CA * ggg1_canf + CF * ggg1_cfnf)

}

/// Compute the singlet anomalous dimension matrix.
pub fn gamma_singlet(c: &mut Cache, nf: u8) -> [[Complex<f64>; 2]; 2] {
let gamma_qq = gamma_nsp(c, nf) + gamma_ps(c, nf);
[
[gamma_qq, gamma_qg(c, nf)],
[gamma_gq(c, nf), gamma_gg(c, nf)],
]
}

pub fn test_const() -> f64 {
CA
}

#[cfg(test)]
mod tests {
use crate::cmplx;
use crate::constants::{CA, CF, TR, ZETA2, ZETA3};
use crate::{anomalous_dimensions::unpolarized::spacelike::as2::*, harmonics::cache::Cache};
use float_cmp::assert_approx_eq;
use num::complex::Complex;
use std::f64::consts::{PI, LN_2};
use std::f64::consts::PI;
use num::traits::Pow;

const NF: u8 = 5;

#[test]
fn try_test() {
fn gamma_1() {
// number conservation
let mut c = Cache::new(cmplx![1., 0.]);
let me = gamma_nsm(&mut c, NF);
assert_approx_eq!(f64, me.re, 0.0, epsilon=2e-6);
assert_approx_eq!(f64, gamma_nsm(&mut c, NF).re, 0.0, epsilon=2e-6);

let mut c = Cache::new(cmplx![2., 0.]);
let me = gamma_nsp(&mut c, NF);
let check = (-112.0 * CF + 376.0 * CA - 64.0 * (NF as f64)) * CF / 27.0;
assert_approx_eq!(f64, me.re, check, epsilon=2e-6);

}


}
let gS1 = gamma_singlet(&mut c, NF);
// gluon momentum conservation
assert_approx_eq!(f64, (gS1[0][1] + gS1[1][1]).re, 0.0, epsilon=4e-5);
// quark momentum conservation
assert_approx_eq!(f64, (gS1[0][0] + gS1[1][0]).re, 0.0, epsilon=2e-6);

assert_eq!(gS1.len(), 2);
assert_eq!((gS1[0]).len(), 2);
assert_eq!((gS1[1]).len(), 2);

// reference values are obtained from MMa
// non-singlet sector
let mut c = Cache::new(cmplx![2., 0.]);
assert_approx_eq!(
f64,
gamma_nsp(&mut c, NF).re,
(-112.0 * CF + 376.0 * CA - 64.0 * (NF as f64)) * CF / 27.0,
epsilon=2e-6
);

// singlet sector
assert_approx_eq!(
f64,
gamma_ps(&mut c, NF).re,
-40.0 * CF * (NF as f64) / 27.0
);
// qg
assert_approx_eq!(
f64,
gS1[0][1].re,
(-74.0 * CF - 35.0 * CA) * (NF as f64) / 27.0
);
// gq
assert_approx_eq!(
f64,
gS1[1][0].re,
(112.0 * CF - 376.0 * CA + 104.0 * (NF as f64)) * CF / 27.0,
epsilon=1e-13
);

// add additional point at (analytical) continuation point
let check = (
(34.0 / 27.0 * (-47.0 + 6. * PI.pow(2)) - 16.0 * ZETA3) * CF
+ (373.0 / 9.0 - 34.0 * PI.pow(2) / 9.0 + 8.0 * ZETA3) * CA
- 64.0 * (NF as f64) / 27.0
)* CF;
assert_approx_eq!(
f64,
gamma_nsm(&mut c, NF).re,
check,
epsilon=2e-6);

let mut c = Cache::new(cmplx![3.,0.]);
let check = (
(-34487.0 / 432.0 + 86.0 * PI.pow(2) / 9.0 - 16.0 * ZETA3) * CF
+ (459.0 / 8.0 - 43.0 * PI.pow(2) / 9.0 + 8.0 * ZETA3) * CA
- 415.0 * (NF as f64) / 108.0
)* CF;
assert_approx_eq!(
f64,
gamma_nsp(&mut c, NF).re,
check,
epsilon=2e-6
);

assert_approx_eq!(
f64,
gamma_ps(&mut c, NF).re,
-1391.0 * CF * (NF as f64) / 5400.0
);

let gS1 = gamma_singlet(&mut c, NF);
// gq
assert_approx_eq!(
f64,
gS1[1][0].re,
(973.0 / 432.0 * CF
+ (2801.0 / 5400.0 - 7.0 * PI.pow(2) / 9.0) * CA
+ 61.0 / 54.0 * (NF as f64)) * CF
);
//gg
assert_approx_eq!(
f64,
gS1[1][1].re,
(-79909.0 / 3375.0 + 194.0 * PI.pow(2) / 45.0 - 8.0 * ZETA3)
* CA.pow(2)
- 967.0 / 270.0 * CA * (NF as f64)
+ 541.0 / 216.0 * CF * (NF as f64),
epsilon=1e-4 // lower numerical precision than python code?
);

let mut c = Cache::new(cmplx![4.,0.]);
let gS1 = gamma_singlet(&mut c, NF);
assert_approx_eq!(
f64,
gS1[0][1].re,
(-56317.0 / 18000.0 * CF + 16387.0 / 9000.0 * CA) * (NF as f64),
epsilon=1e-14
)
}
}

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