Parity-doublet representation of Majorana fermions and neutron oscillation

TL;DR

This paper introduces a parity-doublet theorem for Majorana fermions, providing a new criterion for neutron-antineutron oscillation within a BCS-like effective theory, and explores CP violation effects.

Contribution

It develops a parity-doublet theorem for Majorana fermions and applies it to neutron oscillation, offering a novel theoretical framework and analysis method.

Findings

Parity-doublet theorem for Majorana fermions established

Criterion for neutron-antineutron oscillation derived

CP violation effects on oscillation are negligible in leading order

Abstract

We present a parity-doublet theorem for the representation of the intrinsic parity of Majorana fermions, which is expected to be useful also in condensed matter physics, and it is illustrated to provide a criterion of neutron-antineutron oscillation in a BCS-like effective theory with $\Delta B=2$ baryon number violating terms. The CP violation in the present effective theory causes no direct CP violating effects in the oscillation itself, which is demonstrated by the exact solution, although it influences the neutron electric dipole moment in the leading order of small $\Delta B=2$ parameters. An analogue of Bogoliubov transformation, which preserves P and CP, is crucial in the analysis.