Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos

Abstract

The current paper is a technical work that is focused on Lorentz violation for Dirac fermions as well as neutrinos, described within the nonminimal Standard-Model Extension. We intend to derive two theoretical results. The first is the full propagator of the single-fermion Dirac theory modified by Lorentz violation. The second is the dispersion equation for a theory of $N$ neutrino flavors that enables the description of both Dirac and Majorana neutrinos. As the matrix structure of the neutrino field operator is very involved for generic $N$, we will use sophisticated methods of linear algebra to achieve our objectives. Our main finding is that the neutrino dispersion equation has the same structure in terms of Lorentz-violating operators as that of a modified single-fermion Dirac theory. The results will be valuable for phenomenological studies of Lorentz-violating Dirac fermions and neutrinos.

17 pages

References in corpus (7)

• Electrodynamics with Lorentz-violating operators of arbitrary dimension
• Global three-parameter model for neutrino oscillations using Lorentz violation
• Perturbative Lorentz and CPT violation for neutrino and antineutrino oscillations
• Classical kinematics for Lorentz violation
• Neutrinos as probes of Lorentz invariance
• Testing Lorentz and CPT invariance with neutrinos
• Tests of Lorentz symmetry in single beta decay