We show how a mass mixing matrix can be generated dynamically, for two massless fermion flavors coupled to a Lorentz invariance violating (LIV) gauge field. The LIV features play the role of a regulator for the gap equations, and the nonanalytic dependence of the dynamical masses, as functions of the gauge coupling, allows us to consider the limit where the LIV gauge field eventually decouples from the fermions. Lorentz invariance is then recovered, to describe the oscillation between two free fermion flavors, and we check that the finite dynamical masses are the only effects of the original LIV theory. We also discuss briefly a connection of our results with the case of Majorana neutrinos in both, the standard model, where only left-handed (active) neutrinos are considered, and extensions thereof, with sterile right-handed neutrinos.

• Received 6 May 2013

DOI:https://doi.org/10.1103/PhysRevD.87.125029