Consistent determination of the pion-nucleon sigma term

Determine a fully consistent value and theoretical description of the pion-nucleon sigma term, \(\sigma_N\), given the differing results from lattice QCD, traditional analyses, and updated pion-nucleon scattering data.

Background

The nucleon mass form factor is decomposed into a dominant gluonic contribution and smaller quark-mass contributions, including the pion-nucleon sigma term $\sigma_N$. The value of $\sigma_N$ controls the weight of the long-range $\pi\pi$ cloud contribution in the decomposition of the nucleon mass radius.

The paper contrasts lattice-QCD and traditional determinations near 44–45 MeV with a larger value of approximately 56 MeV obtained from an updated analysis of pion-nucleon scattering data. Because this discrepancy affects the inferred separation between the compact gluonic core and the mesonic cloud, establishing a consistent determination remains unresolved.