Renormalization of massless fields in the $(1,0)\oplus (0,1)$ representation

We study the one-loop renormalization of self-interacting massless fields in the $(1,0)\oplus (0,1)$ representation of the Restricted Lorentz Group. We work with a general model that represents the entire class of parity-invariant self-interacting massless theories that can be defined in this representation. It consists of a general free Lagrangian that reproduces the massless limit of three theories previously studied in the literature: the Joos-Weinberg, the Shay-Good/Hammer-McDonald-Pursey, and the Klein-Gordon-like one, as particular cases; along with an interacting Lagrangian containing all the independent dimension-4 parity-invariant self-interactions available in this representation. The model is found to be renormalizable.