Quark-antiquark Bethe-Salpeter formalism, spectrum and Regge Trajectories

Starting from a path integral representation of appropriate 4-point and 2-point gauge invariant Green functions and from the "Modified Area Law" model for the evaluation of the Wilson loop, a q \bar q Bethe-Salpeter like equation and a related Schwinger-Dyson equation can be obtained. From such equations an effective relativistic Hamiltonian can be derived by standard methods and then applied to the determination of the meson spectrum. The entire known heavy-heavy and heavy-light spectra and the lowest light-light Regge trajectories are rather well reproduced in terms of four parameters alone, the light quark masses being fixed a priori on typical current values.