
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 entire construction hinges crucially on the inclusion of longitudinally coupled vertices containing massless poles of nonperturbative origin, which preserve the form of the fundamental SlavnovTaylor identities of the theory. The mass equation is obtained from a previously unexplored version of the SchwingerDyson equation for the gluon propagator, particular to the PTBFM formalism, which involves a reduced number of 'twoloop dressed' diagrams, thus simplifying the calculational task considerably. The twoloop contributions turn out to be of paramount importance, modifying the qualitative features of the full mass equation, and enabling the emergence of physically meaningful solutions. Specifically, the resulting homogeneous integral equation is solved numerically, subject to certain approximations, for the entire range of physical momenta, yielding positivedefinite and monotonically decreasing gluon masses.
