Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay

TL;DR

This paper explores the theoretical challenges of incorporating tachyonic particles into quantum field theory, proposing a formulation that allows for localizable neutrinos with implications for neutrinoless double beta decay and superluminal neutrino propagation.

Contribution

It introduces a field-theoretic approach for localizable tachyonic particles, addressing previous issues and deriving a compact neutrino propagator with natural chirality properties.

Findings

Derived a compact neutrino propagator form

Showed natural left-handedness of neutrinos and right-handedness of antineutrinos

Discussed implications for neutrinoless double beta decay and superluminal neutrino propagation

Abstract

The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packets in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, we conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix, and we write down field operators with unrestricted momenta. We find that once these choices have been made, the propagator for the neutrino field can be given in a compact form, and the left-handedness of the neutrino as well as the right-handedness of the antineutrino follow naturally. Consequences for neutrinoless double beta decay and superluminal propagation of neutrinos are briefly discussed.