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We propose a model of Majorana fermions with quartic self-couplings. TheseMajorana fermions acquire masses via a type II seesaw mechanism in which thephysical eigenstates are identified as a light Majorana fermion and anotherheavy Majorana fermion. On a physical basis, the quartic self-couplings involveaxial currents of these Majorana fermions, and also the interaction of theaxial current for the light particle with the heavy particle one. We introducetwo auxiliaries gauge fields in this model, and we study the stabilityconditions of the correspondent effective potential of the model. The groundstate of the effective potential introduces two 4-vectors as scales of vacuumexpected values, and consequently, the dynamical Lorentz symmetry breaking(DLSB) emerges in the model. We use the expansion of the effective action tocalculate the effective Lagrangian up to second order in the auxiliary fieldsas fluctuations around the ground state. This mechanism generates dynamics forthe auxiliary gauge fields, mixed mass terms, longitudinal propagation, andChern-Simons term through radiative corrections. After the diagonalization, thetwo gauge fields gain masses through an analogous type II seesaw mechanism inwhich a gauge boson has a light mass, and the other one acquires a heavy mass.In this scenario of Lorentz symmetry breaking, we obtain the correspondentdispersion relations for the Majorana fermions and the gauge boson fields.Posteriorly, we analyze the neutrino's oscillations in the presence of a DLSBparameter, in the transition $\nu_{e} \rightarrow \nu_{\mu}$. We discuss theparameter space of this transition and show that the DLSB can conciliate theLSND and super-Kamiokande results.

Reconciling LSND and super-Kamiokande data through the dynamical Lorentz symmetry breaking in a four-Majorana fermion model