Heavy and heavy-light mesons and the Lorentz structure of the quark-antiquark interaction

TL;DR

This paper solves a Minkowski-space integral equation for heavy and heavy-light mesons within the Covariant Spectator Theory, exploring how the Lorentz structure of the quark-antiquark interaction influences the meson spectrum.

Contribution

It introduces a covariant model with a mixed Lorentz structure for the confining potential and fits the mixing parameter to meson spectra to determine the interaction's nature.

Findings

The model successfully describes heavy meson spectra.

The Lorentz structure of the confining potential can be constrained by spectral fits.

The mixing parameter influences the meson mass predictions.

Abstract

We solve a Minkowski-space integral equation, derived in the Covariant Spectator Theory, for quark-antiquark bound states describing heavy and heavy-light mesons. The equation's kernel contains a one-gluon exchange interaction and a covariant generalization of a linear confining potential with a mixed scalar, pseudoscalar, and vector Lorentz structure, characterized by a continuous mixing parameter. We investigate to what extent the Lorentz structure of the confining kernel can be determined by fitting the mixing parameter to the meson spectrum.