Mass spectra of gg, ggg and gqq̅ states in a Bethe-Salpeter formalismstates in a Bethe-Salpeter formalism

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 qq̅ (all flavours) and qqq (u, d, s, flavours) hadrons, is extended in natural way to make spectral predictions for low-lying gg, ggg and gqq̅ states, with no free parameters, except for an input constituent gluon mass (mg) playing the role of mq. The sensitivity of the glueball spectra to mg is studied for both gg and ggg systems, and a sharp increase in the hadron mass,M with mg 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 of L=0. Comparison of the BS results (as a function of mg) 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 overlapping JPC and masses) is relegated to a more systematic BS formulation (in progress) of the transition amplitudes connecting gg etc. states with the conventional qq̅ states