The pion-nucleon sigma term from lattice QCD

TL;DR

This paper analyzes the pion-nucleon sigma term using lattice QCD with multiple ensembles, highlighting the importance of excited-state contamination and proposing a new analysis method that aligns better with phenomenological data.

Contribution

It introduces a chiral perturbation theory-motivated analysis to better account for excited states in lattice QCD calculations of the sigma term.

Findings

Standard analysis yields σπN = 41.9(4.9) MeV, consistent with previous lattice results.

New analysis including Nπ and Nππ states gives σπN = 59.6(7.4) MeV, aligning with phenomenology.

Physical pion mass data was key to revealing the difference between methods.

Abstract

We present an analysis of the pion-nucleon $\sigma$-term, $\sigma_{\pi N}$, using six ensembles with 2+1+1-flavor highly improved staggered quark action generated by the MILC collaboration. The most serious systematic effect in lattice calculations of nucleon correlation functions is the contribution of excited states. We estimate these using chiral perturbation theory ($\chi$PT), and show that the leading contribution to the isoscalar scalar charge comes from N$\pi$ and N$\pi\pi$ states. Therefore, we carry out two analyses of lattice data to remove excited-state contamination, the standard one and a new one including N$\pi$ and N$\pi\pi$ states. We find that the standard analysis gives $\sigma_{\pi N} = 41.9(4.9)$ MeV, consistent with previous lattice calculations, while our preferred $\chi$PT-motivated analysis gives $\sigma_{\pi N} = 59.6(7.4)$ MeV, which is consistent with phenomenological values obtained using $\pi$N scattering data. Our data on one physical pion mass ensemble was crucial for exposing this difference, therefore, calculations on additional physical mass ensembles are needed to confirm our result and resolve the tension between lattice QCD and phenomenology.