Mesons and Resonances in Relativistic Quantum Mechanics For the Lorentz-Scalar Potential

TL;DR

This paper develops a relativistic quantum mechanical model for mesons using a Lorentz-scalar potential, deriving wave equations and mass formulas to calculate meson spectra, bridging theoretical derivation with phenomenological results.

Contribution

It introduces a relativistic two-body wave equation with a Lorentz-scalar potential and derives a universal meson mass formula, advancing meson spectroscopy modeling.

Findings

Derived exact asymptotic expressions for meson squared masses.

Calculated light and heavy meson mass spectra.

Established a relativistic framework consistent with QCD-inspired potentials.

Abstract

Mesons as bound states of quark and anti-quark in the framework of a relativistic potential model are studied. Interaction of constituents in bound state is described by the Lorentz-scalar QCD inspired funnel-type potential with the coordinate dependent strong coupling, {\alpha}S(r). Lagrangian relativistic mechanics is used to derive the main dynamic two particle equation of motion. On this basis, relativistic two body wave equation is derived. Solution of the equation for the system in the form of a standing wave is obtained. Two exact asymptotic expressions for the meson squared mass are obtained and used to derive the meson universal mass formula. Light and heavy meson mass spectra are calculated.