The Riemann Surface of a Static Dispersion Model and Regge Trajectories

TL;DR

This paper analyzes the Riemann surface structure of a static dispersion model's S-matrix, explicitly deriving Regge trajectories for meson scattering with spin, revealing insights into the analytic properties of scattering amplitudes.

Contribution

It provides an explicit analysis of the Riemann surface and Regge trajectories in a finite-order dispersion model with crossing symmetry, specifically for meson scattering with arbitrary angular momentum.

Findings

Explicit Regge trajectories derived for the model

Finite order N S-matrix with crossing symmetry analyzed

Analytic structure of the S-matrix characterized

Abstract

The S-matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy $\omega$ in the plane with cuts $(-\infty,-1],[+1,+\infty)$. In the elastic case it reduces to N functions $S_{i}(\omega)$ connected by the crossing symmetry matrix A. The scattering of a neutral pseodoscalar meson with an arbitrary angular momentum l at a source with spin 1/2 is considered (N=2). The Regge trajectories of this model are explicitly found.