Lorentz violating extension of the standard model and theβ-decay endpoint

Abstract

The standard model extension with additional Lorentz violating terms allows for redefining the equation of motion of a propagating left-handed fermionic particle. The obtained Dirac-type equation can be embedded in a generalized Lorentz-invariance-preserving algebra through the definition of Lorentz algebralike generators with a lightlike preferred axis. The resulting modification to the fermionic equation of motion introduces some novel ingredients to the phenomenological analysis of the cross section of the tritium $\ensuremath{\beta}$ decay. Assuming lepton number conservation, our formalism provides a natural explanation for the tritium $\ensuremath{\beta}$-decay end point via an effective neutrino mass term without the need of a sterile right-handed state.