Chiral oscillations in the non-relativistic regime

Victor A S V Bittencourt,Massimo Blasone,Alex E Bernardini

doi:10.1140/epjc/s10052-021-09209-2

Abstract

Massive Dirac particles are a superposition of left and right chiral components. Since chirality is not a conserved quantity, the free Dirac Hamiltonian evolution induces chiral quantum oscillations, a phenomenon related to the Zitterbewegung, the trembling motion of free propagating particles. While not observable for particles in relativistic dynamical regimes, chiral oscillations become relevant when the particle’s rest energy is comparable to its momentum. In this paper, we quantify the effect of chiral oscillations on the non-relativistic evolution of a particle state described as a Dirac bispinor and specialize our results to describe the interplay between chiral and flavor oscillations of non-relativistic neutrinos: we compute the time-averaged survival probability and observe an energy-dependent depletion of the quantity when compared to the standard oscillation formula. In the non-relativistic regime, this depletion due to chiral oscillations can be as large as 40%. Finally, we discuss the relevance of chiral oscillations in upcoming experiments which will probe the cosmic neutrino background.

Highlights

Ity cannot be an eigenvector of the massive Dirac Hamiltonian, the free evolution of such state will induce left-right chiral oscillations [5]
We quantify the effect of chiral oscillations on the nonrelativistic evolution of a particle state described as a Dirac bispinor and specialize our results to describe the interplay between chiral and flavor oscillations of non-relativistic neutrinos: we compute the time-averaged survival probability and observe an energy-dependent depletion of the quantity when compared to the standard oscillation formula
In this paper we have described dynamical features of chiral oscillations in the non-relativistic regime, both from a general perspective including their relation with Zitterbewegung, to the study of flavor oscillations for non-relativistic neutrinos

Summary

Introduction

The non-relativistic regime is interesting for exploring the connection between the Zitterbewegung effect and chiral oscillations. Since the chiral oscillation amplitude depends on the mass to energy ratio [13,14], the minimum survival probability of an initial state with definite chirality could be averaged out in the non-relativistic limit. In previous studies [17,18], it has been noticed that the expected event rate of CνB capture on tritium will exhibit a depletion We show that such a depletion for Dirac neutrinos can be understood as a manifestation of chiral oscillations and give a precise quantification of it. The chiral oscillations corrections are relevant when the particle’s momentum is comparable with the lightest neutrino mass and, in the non-relativistic regime, the maximum difference is 40%, a prediction consistent with the preliminary discussion pointed in [18] in connection with CνB detection. We focus on Dirac neutrinos, we discuss chiral oscillations effects in Majorana neutrinos and provide detailed calculations for the general Majorana-Dirac mass term in the appendix

Chirality and chiral oscillations in bispinor dynamics

Flavor mixing and chiral oscillations in non-relativistic regime

Chiral oscillations effect on the average flavor oscillation

Chiral oscillations and tests for Dirac and Majorana neutrinos

Conclusions