Tachyonic Field Theory and Neutrino Mass Running

TL;DR

This paper explores superluminal neutrino decay via Cerenkov radiation, properties of tachyonic Dirac equations, and proposes a model with a Yukawa interaction that could explain neutrino mass variations observed experimentally.

Contribution

It introduces a model Lagrangian with a Yukawa interaction to account for neutrino mass running and analyzes tachyonic neutrino decay and equations.

Findings

Decay rate depends on the tachyonic mass and dispersion relation shape.

Properties of tachyonic Dirac solutions are discussed in context of superluminal neutrinos.

A model Lagrangian suggests a mechanism for neutrino mass running via scalar interactions.

Abstract

In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii) We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations.