From ba704fff2998ef78986febbf6c908563f16e9d9e Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Mon, 21 Oct 2024 10:02:00 +0200 Subject: [PATCH] adding some more tests --- doc/source/theory/pQCD.rst | 11 ++++++++-- .../polarized/space_like/test_ad_as1.py | 9 ++++++++- .../polarized/space_like/test_ad_as2.py | 20 +++++++++++++++++-- .../polarized/space_like/test_ad_as3.py | 14 +++++++++++++ 4 files changed, 49 insertions(+), 5 deletions(-) diff --git a/doc/source/theory/pQCD.rst b/doc/source/theory/pQCD.rst index 2223b327c..27c5cb543 100644 --- a/doc/source/theory/pQCD.rst +++ b/doc/source/theory/pQCD.rst @@ -86,8 +86,9 @@ 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 +103,12 @@ 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 --------------------------- diff --git a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as1.py b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as1.py index 4b7b24d38..ad0a3363d 100755 --- a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as1.py +++ b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as1.py @@ -2,7 +2,7 @@ import numpy as np import ekore.anomalous_dimensions.polarized.space_like.as1 as as1 -from eko import constants +from eko import beta, constants from ekore import harmonics NF = 5 @@ -30,3 +30,10 @@ def test_gluon_momentum(): def test_qg_helicity_conservation(): N = complex(1.0, 0.0) np.testing.assert_almost_equal(as1.gamma_qg(N, NF), 0) + + +def test_axial_anomaly(): + # violation of the axial current conservation happens only through loops + N = complex(1.0, 0.0) + cache = harmonics.cache.reset() + np.testing.assert_allclose(as1.gamma_gg(N, cache, NF), -beta.beta_qcd_as2(NF)) diff --git a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as2.py b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as2.py index b77fd7a83..06ed35541 100755 --- a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as2.py +++ b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as2.py @@ -1,7 +1,9 @@ # Test NLO Polarized splitting functions import numpy as np +import ekore.anomalous_dimensions.polarized.space_like.as1 as as1 import ekore.anomalous_dimensions.polarized.space_like.as2 as as2 +from eko import beta from eko.constants import CA, CF, TR from ekore import harmonics @@ -32,7 +34,10 @@ def test_qg_momentum(): cache = harmonics.cache.reset() np.testing.assert_allclose( -as2.gamma_qg(N, nf, cache), - 4 * nf * (0.574074 * CF - 2 * CA * (-7 / 18 + 1 / 6 * (5 - np.pi**2 / 3))) * TR, + 4 + * nf + * (0.574074 * CF - 2 * CA * (-7 / 18 + 1 / 6 * (5 - np.pi**2 / 3))) + * TR, ) @@ -55,5 +60,16 @@ def test_gg_momentum(): cache = harmonics.cache.reset() np.testing.assert_almost_equal( -as2.gamma_gg(N, nf, cache), - 4 * (-1.7537256813471833 * CA**2 + ((29 * CA) / 27 - (28 * CF) / 27) * nf * TR), + 4 + * (-1.7537256813471833 * CA**2 + ((29 * CA) / 27 - (28 * CF) / 27) * nf * TR), + ) + + +def test_axial_anomaly(): + # violation of the axial current conservation happens only through loops + N = complex(1.0, 0.0) + cache = harmonics.cache.reset() + np.testing.assert_allclose( + as2.gamma_gg(N, nf, cache), -beta.beta_qcd_as3(nf), rtol=9e-7 ) + np.testing.assert_allclose(as2.gamma_ps(N, nf), -2 * nf * as1.gamma_gq(N)) diff --git a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py index 82bd48675..fc75fedbe 100755 --- a/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py +++ b/tests/ekore/anomalous_dimensions/polarized/space_like/test_ad_as3.py @@ -1,8 +1,10 @@ # Test NNLO Polarized splitting functions import numpy as np +import ekore.anomalous_dimensions.polarized.space_like.as2 as as2 import ekore.anomalous_dimensions.polarized.space_like.as3 as as3 import ekore.anomalous_dimensions.unpolarized.space_like.as3 as as3_unpol +from eko import beta from eko.constants import zeta2, zeta3 from ekore import harmonics @@ -54,3 +56,15 @@ def test_ns(): np.testing.assert_allclose( as3_unpol.gamma_nsp(N, nf, cache), as3.gamma_nsm(N, nf, cache) ) + + +def test_axial_anomaly(): + # violation of the axial current conservation happens only through loops + N = complex(1.0, 0.0) + cache = harmonics.cache.reset() + np.testing.assert_allclose( + as3.gamma_gg(N, nf, cache), -beta.beta_qcd_as4(nf), rtol=2e-5 + ) + np.testing.assert_allclose( + as3.gamma_ps(N, nf, cache), -2 * nf * as2.gamma_gq(N, nf, cache), rtol=3e-6 + )