Merge branch 'master' into aem1

.pre-commit-config.yaml

@@ -14,12 +14,12 @@ repos:
       - id: check-merge-conflict
       - id: debug-statements
   - repo: https://github.com/hadialqattan/pycln
-    rev: v2.4.0
+    rev: v2.5.0
     hooks:
       - id: pycln
         args: [--config=pyproject.toml]
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.6.9
+    rev: v0.9.0
     hooks:
       # Run the linter.
       - id: ruff
@@ -30,13 +30,13 @@ repos:
       # Run the formatter.
       - id: ruff-format
   - repo: https://github.com/PyCQA/docformatter
-    rev: "master"
+    rev: eb1df34 # TODO: wait for https://github.com/PyCQA/docformatter/issues/293
     hooks:
       - id: docformatter
         additional_dependencies: [tomli]
         args: [--in-place, --config, ./pyproject.toml]
   - repo: https://github.com/pre-commit/mirrors-mypy
-    rev: v1.11.2
+    rev: v1.14.1
     hooks:
       - id: mypy
         additional_dependencies: [types-PyYAML]

benchmarks/eko/benchmark_inverse_matching.py

@@ -90,14 +90,10 @@ def benchmark_inverse_matching():
     with pytest.raises(AssertionError):
         np.testing.assert_allclose(op1_nf3.operator, op2_nf3.operator)
 
-    pdf1 = apply.apply_pdf(eko_output1, toy.mkPDF("ToyLH", 0))
-    pdf2 = apply.apply_pdf(eko_output2, toy.mkPDF("ToyLH", 0))
+    pdf1, _ = apply.apply_pdf(eko_output1, toy.mkPDF("ToyLH", 0))
+    pdf2, _ = apply.apply_pdf(eko_output2, toy.mkPDF("ToyLH", 0))
 
     # test that different PTO matching is applied correctly
-    np.testing.assert_allclose(
-        pdf1[(MC**2, 4)]["pdfs"][C_PID], pdf2[(MC**2, 4)]["pdfs"][C_PID]
-    )
+    np.testing.assert_allclose(pdf1[(MC**2, 4)][C_PID], pdf2[(MC**2, 4)][C_PID])
     with pytest.raises(AssertionError):
-        np.testing.assert_allclose(
-            pdf1[(MC**2, 3)]["pdfs"][C_PID], pdf2[(MC**2, 3)]["pdfs"][C_PID]
-        )
+        np.testing.assert_allclose(pdf1[(MC**2, 3)][C_PID], pdf2[(MC**2, 3)][C_PID])

crates/ekore/src/anomalous_dimensions/polarized/spacelike/as1.rs

@@ -82,4 +82,14 @@ mod tests {
         let me = gamma_qg(&mut c, NF);
         assert_approx_eq_cmplx!(f64, me, Complex::zero(), epsilon = 1e-12);
     }
+
+    // TODO: activate this test once the beta function will be available
+    // #[test]
+    // fn axial_anomaly() {
+    //     const N: Complex<f64> = cmplx!(1., 0.);
+    //     let mut c = Cache::new(N);
+    //     let me = gamma_gg(&mut c, NF);
+    //     let beta = -1.0 * beta_qcd_as2(NF);
+    //     assert_approx_eq_cmplx!(f64, me, beta);
+    // }
 }

crates/ekore/src/anomalous_dimensions/polarized/spacelike/as2.rs

@@ -128,6 +128,7 @@ pub fn gamma_singlet(c: &mut Cache, nf: u8) -> [[Complex<f64>; 2]; 2] {
 
 #[cfg(test)]
 mod tests {
+    use super::super::as1::gamma_gq as as1_gamma_gq;
     use super::*;
     use crate::harmonics::cache::Cache;
     use crate::{assert_approx_eq_cmplx, cmplx};
@@ -192,4 +193,17 @@ mod tests {
             epsilon = 1e-13
         );
     }
+
+    #[test]
+    fn axial_anomaly() {
+        const N: Complex<f64> = cmplx!(1., 0.);
+        let mut c = Cache::new(N);
+        let me_ps = gamma_ps(&mut c, NF);
+        let as1_gq = -2.0 * (NF as f64) * as1_gamma_gq(&mut c, NF);
+        assert_approx_eq_cmplx!(f64, me_ps, as1_gq);
+        // TODO: activate this test once the beta function will be available
+        // let me_gg = gamma_gg(&mut c, NF);
+        // let beta = -1.0 * beta_qcd_as2(NF);
+        // assert_approx_eq_cmplx!(f64, me_gg, beta, rel=9e-7);
+    }
 }

doc/source/refs.bib

@@ -1049,6 +1049,17 @@ @article{Moch:2023tdj
     year = "2024"
 }
 
+@article{Falcioni:2024qpd,
+    author = "Falcioni, G. and Herzog, F. and Moch, S. and Pelloni, A. and Vogt, A.",
+    title = "{Four-loop splitting functions in QCD -- The gluon-gluon case --}",
+    eprint = "2410.08089",
+    archivePrefix = "arXiv",
+    primaryClass = "hep-ph",
+    reportNumber = "ZU-TH 47/24, DESY-24-144, LTH 1384",
+    month = "10",
+    year = "2024"
+}
+
 @article{Ablinger:2024xtt,
     author = {Ablinger, J. and Behring, A. and Bl\"umlein, J. and De Freitas, A. and von Manteuffel, A. and Schneider, C. and Sch\"onwald, K.},
     title = "{The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$}",

doc/source/theory/N3LO_ad.rst

@@ -7,6 +7,28 @@ Moreover, the analytical structure of these function is already known to be comp
 since in Mellin space they include harmonics sum up to weight 7, for which an
 analytical expression is not available.
 
+We provide two different types of approximations, depending on the key ``use_fhmruvv``.
+The theory card parameter ``n3lo_ad_variation=(gg, gq, qg, qq, nsp, nsm, nsv)``,
+which is set to ``(0,0,0,0,0,0,0)`` as default, can be varied to obtain parametrization uncertainties.
+
+In particular:
+
+* ``use_fhmruvv = True`` (default option) adopts the parametrizations as provided
+  in :cite:`Moch:2017uml,Falcioni:2023luc,Falcioni:2023vqq,Falcioni:2024xyt,Falcioni:2024qpd`.
+  For each of the 7 splitting functions, the approximation error can be obtained by varying
+  the entries of ``n3lo_ad_variation`` in the range: ``0``,
+  cental value (default), ``1`` down variation, ``2`` up variation.
+
+* ``use_fhmruvv = False`` adopts an in-house parametrization, constructed as described below.
+  In this case only variations of the singlet sector are available. Currently one
+  can vary ``n3lo_ad_variation`` in the range: ``0-19`` for ``gg``, ``0-15`` for ``gg``,
+  ``0-15`` for ``qg``, ``0-6`` for ``qq``.
+  Note these approximations will be no longer updated and are now deprecated.
+
+
+In house approximation
+----------------------
+
 Here, we describe the various assumptions and limits used in order to reconstruct a parametrization
 that can approximate their contribution.
 In particular we take advantage of some known physical constrains,
@@ -21,7 +43,7 @@ In any case |N3LO| |DGLAP| evolution at small-x, especially for singlet-like PDF
 until the splitting function resummation is available up to |NNLL|.
 
 Non-singlet sector
-------------------
+^^^^^^^^^^^^^^^^^^
 
 In the non-singlet sector we construct a parametrization for
 :math:`\gamma_{ns,-}^{(3)},\gamma_{ns,-}^{(3)},\gamma_{ns,s}^{(3)}` where:
@@ -147,7 +169,7 @@ In |EKO| they are implemented as follows:
             It is checked that this contribution is much more smaller than the values of :math:`B_4`.
 
 Singlet sector
---------------
+^^^^^^^^^^^^^^
 
 In the singlet sector we construct a parametrization for
 :math:`\gamma_{gg}^{(3)},\gamma_{gq}^{(3)},\gamma_{qg}^{(3)},\gamma_{qq}^{(3)}` where:
@@ -272,7 +294,6 @@ The difference between the known moments and the known limits is parametrized
 in Mellin space using different basis, in order to estimate the uncertainties of
 our determination.
 
-
 Uncertainties estimation
 ^^^^^^^^^^^^^^^^^^^^^^^^
 

doc/source/theory/pQCD.rst

@@ -51,7 +51,6 @@ can be specified at ``scale_ref`` along with ``nf_ref`` and, the computed result
 depend on the number of flavors at the target scale, see :meth:`eko.couplings.Couplings.a_s`
 An example how the evolution path is determined is given :doc:`here</code/Utilities/>`.
 
-
 QCD Splitting Functions
 -----------------------
 
@@ -86,8 +85,9 @@ At |NLO|, the singlet entry of the quark-quark anomalous dimension can be decomp
     \gamma^{(1)}_{qq} =\gamma^{(1)}_{ps} + \gamma^{(1)}_{ns,+}
 
 The non-singlet sector in the polarized case swaps the plus and minus non-singlet relative to the unpolarized case.
-This is because the polarized non-singlet splitting functions are defined as the difference between the probability of the polarized parton splitting into daughter partons of the same flavour
-and daughters splitting into a different flavours and opposite helicity. The first moments of the anomalous dimensions are:
+This is because the polarized non-singlet splitting functions are defined as the difference between the probability of the polarized parton splitting
+into daughter partons of the same flavour and same helicity and daughters of a different flavours and opposite helicity.
+The first moments of the anomalous dimensions are:
 
 .. math ::
     \gamma^{(1)}_{ns,+} (N=1) &= 0 \\
@@ -102,6 +102,12 @@ At |NNLO| the non-singlet is further decomposed into the helicity difference qua
 where :math:`\gamma^{(2)}_{ns,-}` is the minus flavour asymmetry non-singlet and :math:`\gamma^{(2)}_{ns,s}` the sea-like polarized non-singlet.
 The singlet entry :math:`\gamma^{(2)}_{qq}` is defined as above in the |NLO| case.
 
+Finally the violation of the axial current conservation :math:`\bar{\psi} \gamma_\mu \gamma_5 \bar{\psi}` only through
+loop corrections impose the following relations to the singlet splittings at all orders :cite:`Moch:2014sna` :
+
+.. math ::
+     \gamma^{(n)}_{gg} & = - \beta_n \\
+     \gamma^{(n)}_{ps} & = - 2 n_f \gamma^{(n-1)}_{gq}
 
 Unified Splitting Functions
 ---------------------------