preprints.org > physical sciences > mathematical physics > doi: 10.20944/preprints202002.0346.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 21 February 2020 / Approved: 24 February 2020 / Online: 24 February 2020 (05:21:43 CET)

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.

Dirac equation; superluminal neutrino; mass oscillation; Zitterbewegung

Physical Sciences, Mathematical Physics

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