Classical Solutions of SU(2) and SU(3) Pure Yang-Mills Theories and Heavy Quark Spectrum

Abstract

In this paper we compute classical Minkowsky spacetime solutions of pure SU(2) and SU(3) gauge theories, in Landau gauge. The solutions are regular everywhere except at the origin and/or infinity, are characterized by a four momentum $k$ such that $k^2 = 0$ and resemble QED configurations. The classical solutions suggest a particle-independent description of hadrons, similarly to the Atomic and Nuclear energy levels, which is able to reproduce the heavy quarkonium spectrum with a precision below 10%. Typical errors in the theoretical mass prediction relative to the measured mass being of the order of 2-4%.