  In this work we explore the applicability of a special gluon mass generating
mechanism in the context of the linear covariant gauges. In particular, the
implementation of the Schwinger mechanism in pure Yang-Mills theories hinges
crucially on the inclusion of massless bound-state excitations in the
fundamental nonperturbative vertices of the theory. The dynamical formation of
such excitations is controlled by a homogeneous linear Bethe-Salpeter equation,
whose nontrivial solutions have been studied only in the Landau gauge. Here,
the form of this integral equation is derived for general values of the
gauge-fixing parameter, under a number of simplifying assumptions that reduce
the degree of technical complexity. The kernel of this equation consists of
fully-dressed gluon propagators, for which recent lattice data are used as
input, and of three-gluon vertices dressed by a single form factor, which is
modelled by means of certain physically motivated Ans\"atze. The
gauge-dependent terms contributing to this kernel impose considerable
restrictions on the infrared behavior of the vertex form factor; specifically,
only infrared finite Ans\"atze are compatible with the existence of nontrivial
solutions. When such Ans\"atze are employed, the numerical study of the
integral equation reveals a continuity in the type of solutions as one varies
the gauge-fixing parameter, indicating a smooth departure from the Landau
gauge. Instead, the logarithmically divergent form factor displaying the
characteristic "zero crossing", while perfectly consistent in the Landau gauge,
has to undergo a dramatic qualitative transformation away from it, in order to
yield acceptable solutions. The possible implications of these results are
briefly discussed.
