Pion-nucleon sigma term revisited in covariant baryon chiral perturbation theory

TL;DR

This paper refines the value of the pion-nucleon sigma term using advanced chiral perturbation theory and recent lattice QCD data, confirming previous estimates and showing robustness against certain model variations.

Contribution

It provides a precise determination of the sigma term from lattice QCD data within covariant baryon chiral perturbation theory, including higher-order corrections and the effect of the virtual Delta resonance.

Findings

Sigma term value: 50.2(1.2)(2.0) MeV

Good fit to lattice data at NNLO and N3LO

Virtual Delta(1232) inclusion does not alter results significantly

Abstract

We study the latest $N_f=2+1+1$ and $N_f=2$ ETMC lattice QCD simulations of the nucleon masses and extract the pion-nucleon sigma term utilizing the Feynman-Hellmann theorem in SU(2) baryon chiral perturbation theory with the extended-on-mass-shell scheme. We find that the lattice QCD data can be described quite well already at the next-to-next-to-leading order. The overall picture remains essentially the same at the next-to-next-to-next-to-leading order. Our final result is $\sigma_{\pi N}=50.2(1.2)(2.0)$ MeV, or equivalently, $f_{u/d}^N=0.0535(13)(21)$, where the first uncertainty is statistical and second is theoretical originated from chiral truncations, which is in agreement with that determined previously from the $N_f=2+1$ and $N_f=2$ lattice QCD data and that determined by the Cheng-Dashen theorem. In addition, we show that the inclusion of the virtual $\Delta(1232)$ does not change qualitatively our results.