Dispersive analysis of the scalar form factor of the nucleon

TL;DR

This paper develops a dispersive framework using Roy-Steiner equations to analyze the scalar form factor of the nucleon, incorporating K-bar K intermediate states to refine the sigma term extraction.

Contribution

It introduces a coupled integral equation approach for pion and kaon channels in nucleon scalar form factor analysis, advancing the dispersive methods in this area.

Findings

Updated the scalar form factor analysis with K-bar K states

Calculated the correction Delta_sigma for sigma term extraction

Provided a detailed dependence on subthreshold parameters

Abstract

Based on the recently proposed Roy-Steiner equations for pion-nucleon scattering, we derive a system of coupled integral equations for the pi pi --> N-bar N and K-bar K --> N-bar N S-waves. These equations take the form of a two-channel Muskhelishvili-Omnes problem, whose solution in the presence of a finite matching point is discussed. We use these results to update the dispersive analysis of the scalar form factor of the nucleon fully including K-bar K intermediate states. In particular, we determine the correction Delta_sigma=sigma(2M_pi^2)-sigma_{pi N}, which is needed for the extraction of the pion-nucleon sigma term from pi N scattering, as a function of pion-nucleon subthreshold parameters and the pi N coupling constant.