  In this work we use two different but complementary approaches in order to
study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the
linear covariant gauges, focusing on its dependence on the gauge-fixing
parameter $\xi$ in the deep infrared. In particular, we first solve the
Schwinger-Dyson equation that governs the dynamics of the ghost propagator,
using a set of simplifying approximations, and under the crucial assumption
that the gluon propagators for $\xi>0$ are infrared finite, as is the case in
the Landau gauge $(\xi=0)$. Then we appeal to the Nielsen identities, and
express the derivative of the ghost propagator with respect to $\xi$ in terms
of certain auxiliary Green's functions, which are subsequently computed under
the same assumptions as before. Within both formalisms we find that for $\xi>0$
the ghost dressing function approaches zero in the deep infrared, in sharp
contrast to what happens in the Landau gauge, where it known to saturate at a
finite (non-vanishing) value. The Nielsen identities are then extended to the
case of the gluon propagator, and the $\xi$-dependence of the corresponding
gluon masses is derived using as input the results obtained in the previous
steps. The result turns out to be logarithmically divergent in the deep
infrared; the compatibility of this behavior with the basic assumption of a
finite gluon propagator is discussed, and a specific Ansatz is put forth, which
readily reconciles both features.
