Dynamics of Neutrino Wave Packet in the Tachyon-like Dirac Equation

TL;DR

This paper analytically solves the tachyon-like Dirac equation for superluminal neutrinos, revealing their pseudo-tachyon behavior, Zitterbewegung motion, and similar oscillation probabilities to ordinary neutrinos, challenging their distinguishability in experiments.

Contribution

It provides the first analytical Gaussian wave packet solutions for superluminal neutrinos using the tachyon-like Dirac equation, demonstrating their pseudo-tachyon nature and oscillation characteristics.

Findings

Superluminal neutrinos behave as pseudo-tachyons with imaginary mass.

Zitterbewegung occurs for superluminal neutrinos with subluminal oscillation velocity.

Neutrino oscillation probabilities are similar for tachyonic and ordinary neutrinos.

Abstract

In this study the tachyon-like Dirac equation, formulated by Chodos to describe superluminal neutrino, is solved. The analytical solutions are Gaussian wave packets obtained using the envelope method. It is shown that the superluminal neutrino behaves like a pseudo-tachyon, namely a particle with subluminal velocity and pure imaginary mass that fulfils the energy-momentum relation typical of classical tachyons. The obtained results are used to prove that the trembling motion of the particle position around the median, known as Zitterbewegung, also takes place for the superluminal neutrino, even if the oscillation velocity is always lower than the speed of light. Finally, the pseudo-tachyon wave packet is used to calculate the probability of oscillation between mass states, obtaining a formula analogous to the one obtained for the ordinary neutrino. This suggest that in the experiments concerning neutrino oscillation is not possible to distinguish tachyonic neutrinos from ordinary ones.