Finite Size Scaling and Low Mass Glueballs

We propose finite lattice effects as a probe of the glueball mass spectrum, and give an analysis of the recent SU(2) Monte Carlo data of Brower, Nauenberg and Schalk in terms of a gas of free glueballs. For Z 4 lattices with L = 4, 5, 6 fits are made to ~(m = 1/a~) which indicate a rather large effective number of degrees of freedom (i.e. statistical degeneracy where a spin J counts as 2J+ 1) from 5 to 15 states. As the degeneracy is increased, the central glueball mass increases from m =(1.3+0.2)~/~ at degeneracy 5 to about m =(1.9+0.2)~/K at degeneracy 15, relative to the SU(2) string tension ~/K. Recent Monte Carlo simulations for lattice quantum chromodynamics have come close to experimental confrontation for predicted mass ratios in the continuum limit. For SU(2) and SU(3) quantum chromodynamics without quarks, calculations of the ratio of the square root of the string tension (x/T) relative to the minimal subtracted A~ parameter of logarithmic scaling violations [1, 2] have given A~/x/-K = (1.3 + 0.2)(0.199) for SU(2), (1) A~/~/-K = (0.5 + 0.15)(0.289) for SU(3). In SU(3), with ~/~=420MeV, this is a suitable A parameter (A~-60 MeV); however, the experimental uncertainty for Am does not encourage much more streneous computations of this ratio. Within quarkless QCD, a more definitive test should be the prediction of the lowest mass glueball and its degeneracy (i.e. statistical weight 2J + 1 for spin J). After all, the glueball is a salient non-perturbative effect of QCD, absent in earlier quark models. Even a 10% bound on its mass could in principle prove fatal to the standard QCD theory.