Complex Masses of Mesons and Resonances In Relativistic Quantum Mechanics

TL;DR

This paper develops a relativistic quantum mechanics model for mesons and resonances, deriving a complex-mass formula and exploring the concept of distance-dependent particle mass to better understand hadron bound states.

Contribution

It introduces a novel approach using a two-particle wave equation with a coordinate-dependent coupling and mass, providing new asymptotic expressions and practical applications in hadron physics.

Findings

Derived exact asymptotic expressions for meson squared mass

Developed a complex-mass formula for mesons and resonances

Proposed a free particle hypothesis for quark-antiquark pairs

Abstract

Relativistic bound state problem in hadron physics is studied. Mesons and their resonance excitations in the framework of Relativistic Quantum Mechanics (RQM) are investigated. Two-particle wave equation for the Lorentz scalar QCD inspired funnel-type potential with the coordinate dependent strong coupling $\alpha_\S(r)$ is derived. The concept of distance dependent particle mass is developed. Two exact asymptotic expressions for the system's squared mass are obtained and used to derive the meson interpolating complex-mass formula. Free particle hypothesis for the bound state is developed: quark and antiquark move as free particles in of the bound system. Practical applications of the model are given.