REVIEW
Flavor decomposition of the nucleon axial and tensor charges from lattice QCD
High Energy Physics - Lattice · Submitted 7 Nov 2026 · 59 references
Pith's verdict: A thorough lattice calculation of nucleon axial and tensor charges with four physical-point ensembles and a continuum limit; the singlet renormalization assumption is standard but unvalidated, yet the paper is solid enough to send to referee.
T0 · AI review
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Referee report
The paper
The paper claims
Lattice QCD computes axial and tensor charges of the nucleon from physical-mass ensembles at four lattice spacings, obtaining the isovector axial charge consistent with experiment and providing a flavor decomposition.
The reading
What carries the argument
The central object is the nucleon matrix element of axial-vector and tensor currents at zero momentum transfer, extracted from two- and three-point correlation functions computed with twisted-mass clover-improved fermions on Nf=2+1+1 ensembles. Excited-state contamination is controlled via multi-state fits and the use of the temporal axial current with nonzero momentum transfer. Renormalization is performed nonperturbatively in the RI'-MOM scheme and converted to MS at 2 GeV, with separate nonsinglet and singlet factors.
Extended reading notes
Core claim
The paper establishes the nucleon axial and tensor charges at the physical point via a continuum extrapolation using ensembles at four lattice spacings, all with quark masses tuned to their physical values. It obtains $g_A^{{u-d}}$ = 1.263(34)(26), in agreement with the experimental neutron decay constant, and reports for the first time a full flavor decomposition of both axial and tensor charges from this setup. The isoscalar axial charge is $g_A^{{u+d}}$ = 0.458(16)(1), the isovector tensor charge $g_T^{{u-d}}$ = 0.951(21)(5), and the isoscalar tensor charge $g_T^{{u+d}}$ = 0.556(16)(5). The individual quark contributions are also given, with the strange and charm charges consistent with zero within uncertainties.
Load-bearing premise
The singlet renormalization constants are computed on Nf=4 ensembles with mass-degenerate quarks and then applied to the Nf=2+1+1 physical-point ensembles, assuming that the renormalization is insensitive to the sea-quark content and the heavier quark masses.
Editorial extensions
If this is right
- The isovector axial charge provides a direct lattice QCD input to precision tests of CKM unitarity and to the interpretation of neutrinoless double-beta decay.
- The isovector tensor charge constrains beyond-the-Standard-Model scalar and tensor interactions in neutron and nuclear beta decays.
- The flavor-diagonal axial charges, combined with deep-inelastic scattering data, improve the determination of the quark spin contributions to the nucleon spin.
- The tensor flavor decomposition serves as a benchmark for phenomenological analyses of transversity parton distribution functions.
- The results can be used to reduce uncertainties in dark matter direct detection cross sections that depend on nucleon tensor matrix elements.
Reading between the lines
- Because all ensembles are at physical pion mass, the continuum extrapolation avoids chiral extrapolation; if the lattice-spacing dependence is mild, the final errors may be dominated by statistics and systematic variations in the excited-state handling rather than by chiral uncertainties.
- A cross-check using a larger volume or additional lattice spacings would test the residual finite-volume and discretization systematics; the current volume is about 5.5 fm, which is likely sufficient for the nucleon ground state but could be verified.
- The singlet renormalization constants, computed on Nf=4 ensembles and applied to Nf=2+1+1 ensembles, assume sea-quark independence; a dedicated validation on the target ensembles would strengthen the error budget for the isoscalar charges.
- The flavor-separated strange and charm charges are consistent with zero; future higher-statistics calculations could reveal small non-zero values that would probe the role of heavy quarks in nucleon spin.
Original abstract
We determine the nucleon axial and tensor charges using four ensembles of twisted-mass clover-improved fermions with approximately equal physical volumes of about 5.5~fm and four lattice spacings, $ a=0.05$~fm, 0.06~fm, 0.07~fm, and 0.08~fm. The mass of the degenerate up and down, strange and charm quarks are tuned to approximately their physical values. We compute both connected and disconnected contributions to determine the isovector and isoscalar charges and their flavour decomposition. For the nucleon isovector axial charge we find $g_A^{u-d}=1.263(34)(26)$, in agreement with the experimental value. For the isoscalar axial charge we find $g_A^{u+d}=0.458(16)(1)$, while for the corresponding tensor charges we find $g_T^{u-d}=0.951(21)(5)$ and $g_T^{u+d}=0.556(16)(5)$.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We determine the nucleon axial and tensor charges using four ensembles of twisted-mass clover-improved fermions with approximately equal physical volumes of about 5.5~fm and four lattice spacings, $ a=0.05$~fm, 0.06~fm, 0.07~fm, and 0.08~fm. The mass of the degenerate up and down, strange and charm quarks are tuned to approximately their physical values. We compute both connected and disconnected contributions to determine the isovector and isoscalar charges and their flavour decomposition. For the nucleon isovector axial charge we find $g_A^{u-d}=1.263(34)(26)$, in agreement with the experimental value. For the isoscalar axial charge we find $g_A^{u+d}=0.458(16)(1)$, while for the corresponding tensor charges we find $g_T^{u-d}=0.951(21)(5)$ and $g_T^{u+d}=0.556(16)(5)$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We determine the nucleon axial and tensor charges using four ensembles of twisted-mass clover-improved fermions with approximately equal physical volumes of about 5.5~fm and four lattice spacings, $ a=0.05$~fm, 0.06~fm, 0.07~fm, and 0.08~fm. | method 0.96 | 0.95 | 0.03 | asserted 1.00 |
| s1 | The mass of the degenerate up and down, strange and charm quarks are tuned to approximately their physical values. | method 1.00 | 0.79 | 0.02 | asserted 0.98 |
| s2 | We compute both connected and disconnected contributions to determine the isovector and isoscalar charges and their flavour decomposition. | method 0.80 | 0.97 | 0.04 | asserted 0.99 |
| s3 | For the nucleon isovector axial charge we find $g_A^{u-d}=1.263(34)(26)$, in agreement with the experimental value. | result 1.00 | 0.97 | 0.26 | asserted 1.00 |
| s4 | For the isoscalar axial charge we find $g_A^{u+d}=0.458(16)(1)$, while for the corresponding tensor charges we find $g_T^{u-d}=0.951(21)(5)$ and $g_T^{u+d}=0.556(16)(5)$. | result 1.00 | 0.98 | 0.47 | asserted 1.00 |
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Figures
Showing 18 of the paper's 22 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2611.10816 by the authors.
References
Discussion
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