Asymptotic scaling and infrared behavior of the gluon propagator

The Landau gauge gluon propagator for the pure gauge theory is evaluated on a ${32}^3\times 64$ lattice with a physical volume of ${(3.35\mathrm{}}^3\times 6.7){\mathrm{fm}}^4.$ Comparison with two smaller lattices at different lattice spacings allows an assessment of finite volume and finite lattice spacing errors. Cuts on the data are imposed to minimize these errors. Scaling of the gluon propagator is verified between $\beta =6.0\mathrm{}$ and $\beta =\mathrm{6.2.}\mathrm{}$ The tensor structure is evaluated and found to be in good agreement with the Landau gauge form, except at very small momentum values, where some small finite volume errors persist. A number of functional forms for the momentum dependence of the propagator are investigated. The form ${D(q}^2{)=D}_{\mathrm{IR}}{+D}_{\mathrm{UV}},$ where $D_{\mathrm{IR}}{(q}^2)\propto {(q}^2{+M}^2{)}^{-\eta }$ and $D_{\mathrm{UV}}$ is an infrared regulated one-loop asymptotic form, is found to provide an adequate description of the data over the entire momentum region studied — thereby bridging the gap between the infrared confinement region and the ultraviolet asymptotic region. The best estimate for the exponent $\eta$ is ${3.2}_{-0.2-0.3}^{+0.1+0.2\mathrm{}},$ where the first set of errors represents the uncertainty associated with varying the fitting range, while the second set of errors reflects the variation arising from different choices of infrared regulator in $D_{\mathrm{UV}}.$ Fixing the form of $D_{\mathrm{UV}},$ we find that the mass parameter M is $(1020\mathrm{}\pm 100)\mathrm{MeV}.$