First principle quadratic and linear mass operators, quarkonium spectrum and Regge trajectories

Abstract

In previous works, a squared mass operator M^2 and a more common centre of frame Hamiltonian H_CM for the quark-antiquark system were obtained by using the only assumption that ln W (W being the Wilson loop correlator) can be written in QCD as the sum of its perturbative expression and an area term. We evaluated the spectrum of these operators by neglecting all the spin-dependent terms but for a spin-spin term. We succeeded in reproducing rather well the entire meson spectrum and for the light-light systems we found straight Regge trajectories with the right slope and intercepts. A first attempt to study the contribution of the spin dependent terms has been made.