Mass spectra of gg, ggg and $$gq\bar q$$ states in a Bethe-Salpeter formalismstates in a Bethe-Salpeter formalism

Abstract

A covariant 3-D form (under the null-plane ansatz) of the Bethe-Salpeter equation with a Lorentz-invariant vector type (γμ(1)γμ(2)), confining 3 kernel, which had earlier successfully predicted the mass spectra of\(q\bar q\) (all flavours) and qqq (u, d, s, flavours) hadrons, is extended in natural way to make spectral predictions for low-lying gg, ggg and\(gq\bar q\) states, with no free parameters, except for an input constituent gluon mass (mg) playing the role ofmq. The sensitivity of the glueball spectra tomg is studied for both gg and ggg systems, and a sharp increase in the hadron mass,M withmg is found for these systems. The large spin content of the gluon (compared to the quark's) induces large mass depressions in the spectra of low-J glueball states, which in turn require a fairly large gluon mass as a sort of threshold (for low-J states) to ensure a real solution for the corresponding BSE. (This problem is absent for pure quark states as well as for hybrids characterized by lower spin splittings.) The locations of «exotic» glueball states are explored in some detail, both in terms of the «normal»S3-classifications usually employed for qqq systems and from additional [2, 1] symmetries (termed «abnormal» in the text) which are available in principle for 3-body states ofL=0. Comparison of the BS results (as a function ofmg) on all the three sectors is made with those of other models, where the available results are mostly limited to gg states. Quantitative comparison with available experimental candidates (with overlappingJPC and masses) is relegated to a more systematic BS formulation (in progress) of the transition amplitudes connecting gg etc. states with the conventional\(q\bar q\) states.