Dispersive analysis of the scalar form factor of the nucleon

A bstractBased on the recently proposed Roy-Steiner equations for pion-nucleon (πN) scattering [1], we derive a system of coupled integral equations for the $ \pi \pi \to \overline N N $ and $ \overline K K \to \overline N N $S-waves. These equations take the form of a two-channel Muskhelishvili-Omnès 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 $ \overline K K $ intermediate states. In particular, we determine the correction $ {\Delta_{\sigma }} = \sigma \left( {2M_{\pi }^2} \right) - {\sigma_{{\pi N}}} $, which is needed for the extraction of the pion-nucleon σ term from πN scattering, as a function of pion-nucleon subthreshold parameters and the πN coupling constant.