  The dynamically generated effective gluon mass is known to depend
non-trivially on the momentum, decreasing sufficiently fast in the deep
ultraviolet, in order for the renormalizability of QCD to be preserved. General
arguments based on the analogy with the constituent quark masses, as well as
explicit calculations using the operator-product expansion, suggest that the
gluon mass falls off as the inverse square of the momentum, relating it to the
gauge-invariant gluon condensate of dimension four. In this article we
demonstrate that the power-law running of the effective gluon mass is indeed
dynamically realized at the level of the non-perturbative Schwinger-Dyson
equation. We study a gauge-invariant non-linear integral equation involving the
gluon self-energy, and establish the conditions necessary for the existence of
infrared finite solutions, described in terms of a momentum-dependent gluon
mass. Assuming a simplified form for the gluon propagator, we derive a
secondary integral equation that controls the running of the mass in the deep
ultraviolet. Depending on the values chosen for certain parameters entering
into the Ansatz for the fully-dressed three-gluon vertex, this latter equation
yields either logarithmic solutions, familiar from previous linear studies, or
a new type of solutions, displaying power-law running. In addition, it
furnishes a non-trivial integral constraint, which restricts significantly (but
does not determine fully) the running of the mass in the intermediate and
infrared regimes. The numerical analysis presented is in complete agreement
with the analytic results obtained, showing clearly the appearance of the two
types of momentum-dependence, well-separated in the relevant space of
parameters. Open issues and future directions are briefly discussed.
