Quark--Antiquark Bethe--Salpeter Equation in QCD

Abstract

We review our recent results \cite{bsult} on the derivation of a B-S equation in QCD in a Wilson loop context. We work in a second order formalism, use the Feynman--Schwinger path integral representation for a quark in external field and obtain a similar expression for a quark--antiquark amplitude in which the gauge fields appears only through the Wilson loop integral $W$. A $ q \bar{q}$ B-S equation is obtained starting from this expression under the assumption, already used in the derivation of heavy quark potential, that $i \ln W$ can be expressed as the sum of a perturbative contribution and an area term. The intrinsically nonperturbative derivation method is first discussed on the simpler case of two spinless particles interacting through a scalar field. The $q \bar{q}$ semirelativistic potential is reobtained in the large quark mass limit.