Roy-Steiner equations for pi N scattering

TL;DR

This paper derives and solves Roy-Steiner equations for pion-nucleon scattering using dispersion relations, crossing symmetry, and unitarity, providing insights into the partial wave amplitudes relevant for nucleon form factors.

Contribution

It introduces a systematic approach to solve Roy-Steiner equations for pi N scattering, including the t-channel subsystem using Muskhelishvili-Omnès techniques, which is a novel application.

Findings

Solution of the t-channel subsystem via Muskhelishvili-Omnès methods.

Results for P-waves relevant to nucleon electromagnetic form factors.

Demonstration of the full Roy-Steiner system's potential for pi N scattering analysis.

Abstract

Starting from hyperbolic dispersion relations for the invariant amplitudes of pion-nucleon scattering together with crossing symmetry and unitarity, one can derive a closed system of integral equations for the partial waves of both the s-channel (pi N --> pi N) and the t-channel (pi pi --> Nbar N) reaction, called Roy-Steiner equations. After giving a brief overview of the Roy-Steiner system for pi N scattering, we demonstrate that the solution of the t-channel subsystem, which represents the first step in solving the full system, can be achieved by means of Muskhelishvili-Omn\`es techniques. In particular, we present results for the P-waves featuring in the dispersive analysis of the electromagnetic form factors of the nucleon.