Relativistic Wave Equation and Mass Spectrum of Gluonium

Abstract

A relativistic wave equation is derived for gauge-invariant $J=0\mathrm{}$ gluonium amplitudes, and show that its reduced eigenvalue equation is identical with that for a quark-antiquark system in ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ states. Analyzing relations between potentials in the two respective systems, I obtain an upper limit of 2 GeV to the ground-state mass if I take light quarkonium as a reference system, whereas I estimate the ground state to lie between 2.5 and 3 GeV if I use charmonium potential parameters. The scalar and the pseudoscalar gluonium states are degenerate in the present approach.