Infrared gluon dynamics from an ordinary differential equation

In this talk, we present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an exactly solvable ordinary differential equation, whose origin is the fundamental Slavnov-Taylor identity satisfied by the three-gluon vertex, evaluated in a particular kinematic limit.  The differential equation solution is expressed in terms of a well-known projection of the three-gluon vertex, simulated on the lattice, and a specific derivative of the ghost-gluon kernel, whose approximate form is derived from a standard Schwinger-Dyson equation.  In addition, the physical requirement of a pole-free answer fixes the initial boundary condition. We will show that if one has previous knowledge of the gluon propagator computed from the lattice, this formalism allows for the extraction of the momentum-dependent effective gluon mass.