Abstract
We calculate the low-lying glueball spectrum of the SU(3) lattice gauge theory in 3 + 1 dimensions for the range β ≤ 6.50 using the standard plaquette action. We do so for states in all the representations R of the cubic rotation group, and for both values of parity P and charge conjugation C . We extrapolate these results to the continuum limit of the theory using the confining string tension σ as our energy scale. We also present our results in units of the r0 scale and, from that, in terms of physical ‘GeV’ units. For a number of these states we are able to identify their continuum spins J with very little ambiguity. We also calculate the topological charge Q of the lattice gauge fields so as to show that we have sufficient ergodicity throughout our range of β, and we calculate the multiplicative renormalisation of Q as a function of β. We also obtain the continuum limit of the SU(3) topological susceptibility.
Highlights
On the theoretical side the spectrum represents the obvious challenge for attempts to obtain an analytic control of the gauge theory. (This is of indirect phenomenological importance since much of the difficulty in obtaining analytic control of the long distance physics of QCD arises from the non-perturbative physics of the underlying gauge theory.) To use the glueball spectrum as a test of theoretical approaches it is important to have a substantial number of states for a variety of spins J, parities P and charge conjugations C, with excited as well as ground states
In this paper we provide a new calculation of the glueball spectrum of SU(3) gauge theories which is designed to improve upon some limitations of earlier calculations
We perform high statistics calculations out to lattice spacings as small as a(β = 6.50) 0.042 fm, which both improves our control of our extrapolations to the continuum limit and gives us a finer resolution of the glueball correlators, which is useful for the heavier glueballs
Summary
In this case it can be convenient to use the vacuum-subtracted operator φ − φ , which will remove the contribution of the vacuum in eq (2.3), so that the lightest non-trivial state appears as the leading term in the expansion of states The accuracy of such a calculation of aEgs is constrained by the fact that the statistical errors are roughly independent of t (for pure gauge theories) while the desired ‘signal’ is decreasing exponentially with t. The correlator of a more massive state will disappear into the ‘noise’ at smaller t = ant and this may make ambiguous the judgement of whether it is dominated by a single exponential All this may provide an important source of systematic error. The lattice sizes next to these β values are the ones we use for our string tension and glueball mass calculations. We show the average plaquette at each value of β as well as the string tension (see section 3) and the mass gap (see section 4)
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