  In this article we derive the integral equation that controls the momentum
dependence of the effective gluon mass in the Landau gauge. This is
accomplished by means of a well-defined separation of the corresponding
"one-loop dressed" Schwinger-Dyson equation into two distinct contributions,
one associated with the mass and one with the standard kinetic part of the
gluon. The entire construction relies on the existence of a longitudinally
coupled vertex of nonperturbative origin, which enforces gauge invariance in
the presence of a dynamical mass. The specific structure of the resulting mass
equation, supplemented by the additional requirement of a positive-definite
gluon mass, imposes a rather stringent constraint on the derivative of the
gluonic dressing function, which is comfortably satisfied by the large-volume
lattice data for the gluon propagator, both for SU(2) and SU(3). The numerical
treatment of the mass equation, under some simplifying assumptions, is
presented for the aforementioned gauge groups, giving rise to a gluon mass that
is a non-monotonic function of the momentum. Various theoretical improvements
and possible future directions are briefly discussed.
