  We consider Yang-Mills theories in a recently proposed family of nonlinear
covariant gauges that consistently deals with the issue of Gribov ambiguities.
Such gauges provide a generalization of the Curci-Ferrari-Delbourgo-Jarvis
gauges which can be formulated as an extremization procedure and might be
implemented in numerical calculations. This would allow for nonperturbative
studies of Yang-Mills correlators in a broad class of covariant gauges
continuously connected to the well-studied Landau gauge. We compute the ghost
and gluon propagators in the continuum formulation at one-loop order in
perturbation theory and we study their momentum dependence down to the deep
infrared regime, with and without renormalization group improvement. In
particular, we show that the theory admits infrared-safe renormalization-group
trajectories with no Landau pole. Both the gluon and the ghost behave as
massive fields at low energy, and the gluon propagator is transverse even away
from the Landau gauge limit. We compare our results to those obtained in the
usual Curci-Ferrari model, which allows us to pinpoint the specific effects
arising from our treatment of Gribov copies.

High Energy Physics - Theory;High Energy Physics - Lattice