The Instantaneous Breit Equation with an Application to Charmonium

TL;DR

This paper solves the instantaneous Breit equation for two spin-1/2 particles, applies it to charmonium with a Cornell potential, and explores how different Lorentz structures affect bound state energies.

Contribution

It introduces a method to solve the Breit equation with an instantaneous potential for pseudoscalar states and analyzes the impact of Lorentz structure mixing on charmonium masses.

Findings

Calculated masses of charmonium states below charm threshold.

Showed how vector-scalar mixing influences bound state energies.

Provided insights into the Lorentz nature of the confining potential.

Abstract

The solution of the Breit equation with an instantaneous potential for the case of two spin-1/2 particles in a pseudoscalar bound state is considered. This is then applied to charmonium using a potential of the Cornell type. The masses of the two JP = 0^- states below charm threshold are calculated in this model. We allow different mixtures of the Lorentz nature (vector or scalar) of the linear confining term and investigate the effect of these on the bound-state energies. Some general comments are made on the issue of how the bound nature of these states depends on the vector-scalar mix.