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

Abstract

We propose a model of Majorana fermions with quartic self-couplings. These Majorana fermions acquire masses via a type II seesaw mechanism in which the physical eigenstates are identified as a light Majorana fermion and another heavy Majorana fermion. On a physical basis, the quartic self-couplings involve axial currents of these Majorana fermions, and also the interaction of the axial current for the light particle with the heavy particle one. We introduce two auxiliaries gauge fields in this model, and we study the stability conditions of the correspondent effective potential of the model. The ground state of the effective potential introduces two 4-vectors as scales of vacuum expected values, and consequently, the dynamical Lorentz symmetry breaking (DLSB) emerges in the model. We use the expansion of the effective action to calculate the effective Lagrangian up to second order in the auxiliary fields as fluctuations around the ground state. This mechanism generates dynamics for the auxiliary gauge fields, mixed mass terms, longitudinal propagation, and Chern-Simons term through radiative corrections. After the diagonalization, the two gauge fields gain masses through an analogous type II seesaw mechanism in which 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 correspondent dispersion relations for the Majorana fermions and the gauge boson fields. Posteriorly, we analyze the neutrino's oscillations in the presence of a DLSB parameter, in the transition $\nu_{e} \rightarrow \nu_{\mu}$. We discuss the parameter space of this transition and show that the DLSB can conciliate the LSND and super-Kamiokande results.