Neutral Fermion Phenomenology With Majorana Spinors

Abstract

We ask the question whether neutrino physics with momentum space Majorana spinors, the eigenvectors of the particle--antiparticle conjugation operator, C=i\gamma_2 K (with K standing for complex conjugation), is different but physics with Dirac spinors. First we analyze properties of Majorana spinors in great detail. We show that four dimensional, (4d), Majorana spinors are unsuited for the construction of a local quantum field because C invariance does not allow for a covariant propagation in four spinor dimensions, a conduct due to \gamma_2\gamma_\mu= -\gamma_\mu * \gamma_2. The way out of this dilemma is finding one more discrete symmetry that respects C invariance and gives rise to covariant propagators. We construct such a symmetry in observing that the parity operator, \gamma_0, ``ladders'' between (4d) rest-frame Majorana spinors, which takes us to eight dimensional spinor spaces. We build up two types of (8d) spaces-- one with a symmetric- and an other with an anti-symmetric off diagonal metric and calculate traces of single beta-- and neutrinoless double beta (0\nu\beta \beta) decays there. We find physics with (8d) Majorana spinors in the former space to be equivalent to physics with Dirac spinors in four dimensions. In the latter space we make the rare observation that in effect of cancellations triggered by the anti-symmetric off diagonal (8d) metric, the neutrino mass drops from the single beta decay trace but reappears in 0\nu \beta\beta, without the neutrino being massless in its free equation-- a curious and in principle experimentally testable signature for a non-trivial impact of Majorana framework.