Single β and Double 0υββ Decays with Majorana Spinors

Abstract

We first show that the Majorana spinors which are eigenspinors to the charge conjugation operator, C =iγ₂ K, with K standing for complex conjugation, are completely different species but the Dirac spinors which are eigenspinors to the parity operator, P = γ0- The difference is that while P eigenspinors propagate in accord with the Dirac equation, C eigenspinors are static. This is due to the fact that while upon boost γ0 transforms as $B(p)\gamma _0 B(p)^{ - 1} = \tfrac{p} {m}$, under same transformation C remains static because of B(p)γ2KB(p) ^-1 = γ2. In order to escape above dilemma one has two options. To either give up the concept of C eigenspinors and restrict calculus to two dimensional Weyl spinors with Grassmann number components, a path pursued by the literature, or, exploit the fact that in eight spinorial dimensions, (8d), one can construct commuting C and P operators and achieve Majorana spinor propagation there, a path taken by the present work. We express (8d) Majorana traces of single β and double 0μββ decays in terms of standard Dirac traces and find the neutrino mass to drop from the single β, and re-appear in the 0μββ trace, an intriguing and in principle experimentally testable footprint of Majorana-ness of massive neutrino.