Thetexpansion and SU(3) lattice gauge theory

This paper presents the first results obtained by applying the t expansion to the case of an SU(3) lattice gauge theory in 3+1 space-time dimensions. We apply to this problem the same techniques which have been successfully used in the analysis of the SU(2) theory. We test their effectiveness first on the one-plaquette SU(3) problem, and conclude that even a moderate series in t suffices to reach the weak-coupling domain. We then compute the t expansion of the vacuum energy density to order $t^8$ and find from our analysis the behavior of this quantity as a function of the coupling constant. From the same series we obtain the mass M of the lowest-lying $0^{++}$ glueball to order $t^6$. Evaluating the string tension σ to the same order we construct the ratio R=$M^2$/σ which allows us to obtain a dimensional result for M which is consistent with Monte Carlo analyses.