A Lattice Study of the Gluon Propagator in Momentum Space

Abstract

We consider pure glue QCD at beta=5.7, beta=6.0 and beta=6.3. We evaluate the gluon propagator both in time at zero 3-momentum and in momentum space. From the former quantity we obtain evidence for a dynamically generated effective mass, which at beta=6.0 and beta=6.3 increases with the time separation of the sources, in agreement with earlier results. The momentum space propagator G(k) provides further evidence for mass generation. In particular, at beta=6.0, for k less than 1 GeV, the propagator G(k) can be fit to a continuum formula proposed by Gribov and others, which contains a mass scale b, presumably related to the hadronization mass scale. For higher momenta Gribov's model no longer provides a good fit, as G(k) tends rather to follow an inverse power law. The results at beta=6.3 are consistent with those at beta=6.0, but only the high momentum region is accessible on this lattice. We find b in the range of three to four hundred MeV and the exponent of the inverse power law about 2.7. On the other hand, at beta=5.7 (where we can only study momenta up to 1 GeV) G(k) is best fit to a simple massive boson propagator with mass m. We argue that such a discrepancy may be related to a lack of scaling for low momenta at beta=5.7. {}From our results, the study of correlation functions in momentum space looks promising, especially because the data points in Fourier space turn out to be much less correlated than in real space.