Lorentz invariant CPT breaking in the Dirac equation

TL;DR

This paper introduces a Lorentz invariant, non-local CPT breaking modification to the Dirac equation that results in a mass splitting between particles and antiparticles, with potential implications for neutrino physics.

Contribution

It presents a novel Lorentz invariant CPT breaking term in the Dirac equation, constructed explicitly in coordinate space, and discusses its possible impact on neutrino-antineutrino mass differences.

Findings

Mass splitting of particle and antiparticle eigenvalues by Δm

Lorentz invariance preserved despite CPT breaking

Non-locality at Planck scale in the modification

Abstract

If one modifies the Dirac equation in momentum space to $[\gamma^{\mu}p_{\mu}-m-\Delta m(\theta(p_{0})-\theta(-p_{0})) \theta(p_{\mu}^{2})]\psi(p)=0$, the symmetry of positive and negative energy eigenvalues is lifted by $m\pm \Delta m$ for a small $\Delta m$. The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations $\theta(\pm p_{0})\theta(p_{\mu}^{2})$ with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but non-local at a distance scale of the Planck length. The application of this Lorentz invariant CPT breaking mechanism to the possible mass splitting of the neutrino and antineutrino in the Standard Model is briefly discussed.