Solvable Two-Body Dirac Equation as a Potential Model of Light Mesons

TL;DR

This paper develops an exactly solvable two-body Dirac equation model with specific potentials to describe light mesons, calculating their mass spectrum and comparing it with experimental data.

Contribution

It introduces a class of linear plus Coulomb potentials allowing exact solutions of the two-body Dirac equation for light mesons.

Findings

Derived relativistic potential model for light mesons

Calculated meson mass spectrum matching experimental data

Identified potentials enabling exact solvability

Abstract

The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular structure is found, for which the equation is exactly solvable. On this ground a relativistic potential model of light mesons is constructed and the mass spectrum is calculated. It is compared with experimental data.