Neutrino helicity reversal and fundamental symmetries

Abstract

A rather elusive helicity reversal occurs in a gedanken experiment in which a massive left-handed Dirac neutrino, traveling at a velocity u < c, is overtaken on a highway by a speeding vehicle (traveling at velocity v with u < v < c). Namely, after passing the neutrino, looking back, one would see a right-handed neutrino (which has never been observed in nature). The Lorentz-invariant mass of the right-handed neutrino is still the same as before the passing. The gedanken experiment thus implies the existence of right-handed, light neutrinos, which are not completely sterile. Furthermore, overtaking a bunch of massive right-handed Dirac neutrinos leads to gradual de-sterilization. We discuss the helicity reversal and the concomitant sterilization and de-sterilization mechanisms by way of an illustrative example calculation, with a special emphasis on massive Dirac and Majorana neutrinos. We contrast the formalism with a modified Dirac neutrino described by a Dirac equation with a pseudoscalar mass term proportional to the fifth current.

Calculation of the decay rate of tachyonic neutrinos against charged-lepton-pair and neutrino-pair Cerenkov radiation

“…35)]. Our approach relies on a consistent formalism developed for the fundamental tachyonic bispinor solutions, as reported in various recent investigations [6][7][8][9][10].…”

“…We base our treatment on a Lorentz-covariant theory of tachyonic (faster-than-light) spin-1/2 particles, i.e., on the tachyonic Dirac (not Majorana) equation [1][2][3][4][5]. Solutions of this equation [6][7][8][9][10] fulfill the Lorentz covariant dispersion relation E = ( k 2 − m 2 ν ) 1/2 , where E is the energy and k is the spatial momentum vector, while m ν is the tachyonic parameter, corresponding to a negative Lorentz-invariant mass square −m 2 ν . The quantity p µ p µ = E 2 − k 2 = −m 2 ν is Lorentz invariant.…”

Ultrarelativistic decoupling transformation for generalized Dirac equations

“…This observation is intimately linked to the fact that massless Dirac spinors describe particles which always move at the speed of light; it is impossible to "overtake" the particle, which otherwise leads to a helicity flip (see Ref. [24]). …”

“…The algbraic structures underlying the tachyonic spin-1/2 equation have recently been studied in greater depth (see Refs. [20][21][22][23][24] and references therein). Pertinent potentially relevant astrophysical observations have recently been recorded in Refs.…”

“…This amounts to the exact ultrarelativistic decoupling transformation of the free tachyonic Hamiltonian, in the helicity ("Weyl") basis which has been shown to lead to a very efficient description of the tachyonic bispinor solutions [19,24,36]. The Taylor series expansion of H TD gives rise to the terms…”