Spectrum of heavy and light mesons from a unified covariant treatment of hyperfine splitting

We present a completely covariant description of a two-quark system interacting by the Cornell potential with a Breit term describing the hyperfine splitting. Using an appropriate numerical procedure to calculate the Breit correction, we find heavy meson masses in excellent agreement with experimental data. We also use our approach to investigate light quarks. Taking average values of the running coupling constant, we show that covariance properties and hyperfine splitting are sufficient to reproduce the light mesons spectrum with good accuracy . The fundamental role of a coherent relativistic formulation for quarkonia models is therefore evident and our unifiedtreatment for any mass of the constituent quarks proves to be a valuable and effective scheme to study potential models for mesons.