Nucleon charges and $\sigma$-terms in lattice QCD

TL;DR

This paper uses lattice QCD with twisted mass fermions to calculate nucleon charges and $\sigma$-terms, providing results consistent with experimental data and including systematic error analysis.

Contribution

It presents new lattice QCD calculations of nucleon charges and $\sigma$-terms with multiple ensembles and systematic error evaluation, including disconnected contributions.

Findings

Nucleon isovector axial charge $g_A^{u-d}=1.250(24)$, matching experimental value.

Light quark $\sigma_{\pi N}=41.9(8.1)$ MeV.

Strange quark $\sigma_s=30(17)$ MeV.

Abstract

We determine the nucleon axial, scalar and tensor charges and the nucleon $\sigma$-terms using twisted mass fermions. We employ three ensembles with approximately equal physical volume of about 5.5~fm, three values of the lattice spacing, approximately 0.06~fm, 0.07~fm and 0.08~fm, and with the mass of the degenerate up and down, strange and charm quarks tuned to approximately their physical values. We compute both isovector and isoscalar charges and $\sigma$-terms and their flavor decomposition including the disconnected contributions. We use the Akaike Information Criterion to evaluate systematic errors due to excited states and the continuum extrapolation. For the nucleon isovector axial charge we find $g_A^{u-d}=1.250(24)$, in agreement with the experimental value. Moreover, we extract the nucleon $\sigma$-terms and find for the light quark content $\sigma_{\pi N}=41.9(8.1)$~MeV and for the strange $\sigma_{s}=30(17)$~MeV.