Complex masses in the S-matrix

TL;DR

This paper introduces an empirical algebraic method to restore unitarity in the S-matrix when dealing with complex resonance masses, demonstrated through pion-pion scattering analysis.

Contribution

It presents a novel algebraic approach to maintain unitarity in S-matrix calculations involving complex masses, applicable to hadron decay processes.

Findings

Restores unitarity in S-matrix with complex resonance masses

Preserves symmetry of the S-matrix

Applied to pion-pion scattering with preliminary results

Abstract

Most excited hadrons have multiparticle strong decay modes, which can often be described as resulting from intermediate states containing one or two resonances. In a theoretical approach, such a description in terms of quasi-two-particle initial and final states leads to unitarity violations, because of the complex masses of the involved resonances. In the present paper, an empirical algebraic procedure is presented to restore unitarity of the S-matrix while preserving its symmetry. Preliminary results are presented in a first application to S-wave pion-pion scattering, in the framework of the Resonance-Spectrum Expansion.