Quantization of Yang-Mills theory without Gribov copies: Perturbative renormalization

We calculate the one-loop correction to the gluon propagator for a pure Yang-Mills theory with a soft gauge fixing which avoids the problem of Gribov copies. It is found that the propagator reduces, in the limit in which the gauge-fixing parameter $M$ is taken to infinity, to the conventional one in the Landau gauge. The $M$-dependent propagator is then used to check that the gauge dependence disappears when calculating the vacuum expectation value (VEV) of gauge-invariant observables. These two facts are used to discuss how finite results might be obtained, beyond the tree level, for VEV's of gauge-invariant observables.