Pion-Nucleon Sigma Term from Lattice QCD

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 ('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 alpha N-pi = 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 were 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.

Automated summary

In this study, analysis of the pion-nucleon sigma-term using lattice data was conducted to remove excited-state contamination, with results consistent with phenomenological values. Further calculations on additional physical mass ensembles are needed to confirm the results and resolve the tension between lattice QCD and phenomenology.