Improved dispersive analysis of the scalar form factor of the nucleon

TL;DR

This paper develops a coupled integral equation approach to analyze the scalar form factor of the nucleon, incorporating Kbar K intermediate states, to improve the extraction of the pion-nucleon sigma term.

Contribution

It introduces a novel coupled system of integral equations derived from Roy-Steiner equations for a more accurate dispersive analysis of the nucleon's scalar form factor.

Findings

Determined the corrections Delta_sigma and Delta_D for sigma term extraction.

Found the difference Delta_D - Delta_sigma to be approximately -1.8 MeV, insensitive to input parameters.

Enhanced understanding of Kbar K contributions in nucleon scalar form factors.

Abstract

We present a coupled system of integral equations for the pi pi --> Nbar N and Kbar K --> Nbar N S-waves derived from Roy-Steiner equations for pion-nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili-Omnes problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including Kbar K intermediate states. In particular, we determine the corrections Delta_sigma and Delta_D, which are needed for the extraction of the pion-nucleon sigma term from pi N scattering, and show that the difference Delta_D - Delta_sigma=(-1.8 +/- 0.2) MeV is insensitive to the input pi N parameters.