Density of States of a Coupled-Channel System

TL;DR

This paper derives an effective density of states from the S-matrix in coupled-channel systems, revealing how poles, phase, and Riemann sheets influence the dynamics of resonant and non-resonant interactions.

Contribution

It introduces a method to compute the density of states from the S-matrix, highlighting the role of phase and complex structures in coupled-channel scattering.

Findings

Density of states computed for $\pi\pi$, $Kar{K}$ channels.

Phase of the S-matrix determinant encodes key dynamical information.

Analysis of poles, roots, branch cuts, and Riemann sheets impacts the density of states.

Abstract

We demonstrate how an effective density of states can be derived from the S-matrix describing a coupled-channel system. Besides the locations of poles, the phase of the determinant of the S-matrix encodes essential details in characterizing the dynamics of resonant and non-resonant interactions. The density of states is computed for the two channel scattering problem ($\pi\pi, K \bar{K}$, S-wave), and the influences from the various dynamical structures: poles, roots, branch cuts, and Riemann sheets, are examined.