Lorentz violation dispersion relation and its application

TL;DR

This paper derives a modified dispersion relation in Lorentz-violating QED, explores its implications for neutrino oscillations, and sets a stringent bound on Lorentz violation parameters using ultrahigh energy cosmic rays.

Contribution

It introduces a new MDR in Lorentz-violating QED, links Lorentz violation to spin-gravity coupling, and proposes a neutrino oscillation mechanism with tight experimental bounds.

Findings

Derived a modified dispersion relation in Lorentz-violating QED.

Proposed a neutrino oscillation mechanism induced by Lorentz violation.

Set a bound of approximately 10^{-25} on Lorentz violation parameters from cosmic ray data.

Abstract

We derive a modified dispersion relation (MDR) in the Lorentz violation extension of quantum electrodynamics (QED) sector in the standard model extension (SME) framework. Based on the extended Dirac equation and corresponding MDR, we observe the resemblance of the Lorentz violation coupling with spin-gravity coupling. We also develop a neutrino oscillation mechanism induced by the presence of nondiagonal terms of Lorentz violation couplings in 2-flavor space in a 2-spinor formalism by explicitly assuming neutrinos to be Marjorana fermions. We also obtain a much stringent bound ($\backsim10^{-25}$) on one of the Lorentz violation parameters by applying MDR to the ultrahigh energy cosmic ray (UHECR) problem.