The pion-nucleon sigma term from Lattice QCD

TL;DR

This paper reviews recent lattice QCD and chiral perturbation theory findings on the pion-nucleon sigma term, highlighting the impact of excited-state contamination and the small effect of the $$ resonance inclusion.

Contribution

It provides new insights into the excited-state contamination issue and extends chiral perturbation theory analysis by explicitly including the $$ resonance.

Findings

Excited-state contamination may explain discrepancies in $$ sigma term.

Including the $$ resonance has a small effect on $$ calculations.

Results support the robustness of previous $$ sigma term estimates.

Abstract

We summarize recent evidence, both from lattice QCD and chiral perturbation theory, that suggests that larger-than-expected excited-state contamination could be the reason for the tension between phenomenological determinations and previous direct lattice-QCD calculations of the pion--nucleon sigma term $\sigma_{\pi N}$. In addition, we extend the $\chi$PT analysis by calculating the corrections due to including the $\Delta(1232)$ resonance as an explicit degree of freedom. This correction is found to be small, thereby corroborating the excited-state effects found in the $\Delta$-less calculation and the result for $\sigma_{\pi N}$.