Quarkonia in the Bethe-Salpeter formalism with background fields

Abstract

A QCD-oriented Bethe-Salpeter (BS) equation for a {ital q{bar q}} system is formulated in which the quark 4-momenta {ital p}{sub {mu}} are modified as {ital p}{sub {mu}}{r arrow}{ital p}{sub {mu}}{minus}{ital gA}{sub {mu}}({ital x}) in the inverse propagators therein, and a Fock-Schwinger (FS) gauge expansion is employed for the gluon fields {ital A}{sub {mu}}({ital x}). The first term ({similar to}{ital x}{sub {mu}}) of the FS representation yields a harmonic kernel when the BS equation is reduced to a 3-dimensional level via the null-plane ansatz (NPA). It also generates a spin-dependent interaction proportional to ({bold j}{sub 1}+{bold s}{sub 1}){center dot}({bold j}{sub 2}+{bold s}{sub 2}), in close parallel to a {bold J}{center dot}{bold S} term generated by a vector-like ({gamma}{sup (1)}{gamma(2)}) harmonic model for the {ital q{bar q}} interaction proposed earlier by the Delhi Group. A possible mechanism for confinement in an asymptotically linear scene is proposed within the BS framework, taking cue partly from the suggestions of multiple correlation effects (Shifman), and partly from the postulation of stochastic fields (Simonov).