Remarks on the pion-nucleon sigma-term

TL;DR

This paper discusses how fundamental principles and experimental data constrain the pion-nucleon sigma-term, highlighting discrepancies between phenomenological and lattice QCD results, and suggests lattice scattering lengths could clarify the issue.

Contribution

It emphasizes the importance of combining theoretical principles with experimental data to constrain the sigma-term and proposes lattice scattering lengths as a test for resolving current discrepancies.

Findings

Lattice calculations find lower sigma-term values than phenomenological estimates.

Analyticity, unitarity, and crossing symmetry constrain the sigma-term.

Measuring lattice scattering lengths could help resolve the discrepancy.

Abstract

The pion-nucleon $\sigma$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3\sigma$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.