Dispersive analysis of the scalar form factor of the nucleon

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.