How to construct self/anti-self charge conjugate states for higher spins?

TL;DR

This paper develops a framework for constructing self/anti-self charge conjugate states for higher spins within quantum field theory, analyzing their symmetries, equations, and experimental implications, especially for neutrino physics.

Contribution

It introduces a method to construct Majorana-like states for higher spins and examines their properties, symmetries, and physical consequences, extending previous spin-1/2 results.

Findings

Constructed self/anti-self charge conjugate states for higher spins.

Analyzed discrete symmetries and dynamical equations of these states.

Discussed experimental implications for neutrinoless double beta decay.

Abstract

We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2, 0)+(0, 1/2) representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. The corresponding dynamical equations are presented. In the (1/2, 0)+(0, 1/2) representation they obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The particular attention has been paid to the questions of chirality and helicity (two concepts which are frequently confused in the literature) for Dirac and Majorana states. We further review several experimental consequences which follow from the previous works of M.Kirchbach et al. on neutrinoless double beta decay, and G.J.Ni et al. on meson lifetimes.