Confining Bethe--Salpeter equation in QCD

Abstract

We derive a confining $ q \bar{q}$ Bethe--Salpeter equation starting from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion, the corresponding Wilson loop potential is recovered, spin--dependent and velocity--dependent terms included. We also show, that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.