2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221394We study the Standard-Model extensions that have the following features: they violate Lorentz invariance explicitly at high energies; they are unitary, local, polynomial and renormalizable by weighted power counting; they contain the vertex (LH)^2, which gives Majorana masses to the neutrinos after symmetry breaking, and possibly four fermion interactions; they do not contain right-handed neutrinos, nor other extra fields. We study the simplest CPT invariant Standard-Model extension of this type in detail and prove the cancellation of gauge anomalies. We investigate the low-energy recovery of Lorentz invariance and comment on other types of extensions.26 pages; v2: more references and comments, PRDHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext