  We present the general derivation of the full nonperturbative equation that
governs the momentum evolution of the dynamically generated gluon mass, in the
Landau gauge. The gluon mass originates from the inclusion of longitudinally
coupled vertices containing massless poles of non-perturbative origin, which
preserve the form of the fundamental Slavnov-Taylor identities of the theory.
The equation is obtained within the PT-BFM formalism, where the corresponding
Schwinger-Dyson equation involves a reduced number of fully dressed diagrams.
The resulting homogeneous integral equation is solved numerically for the
entire range of physical momenta, yielding positive-definite and monotonically
decreasing gluon masses, in agreement with a variety of less formal
considerations.
