Parity of the neutron consistent with neutron-antineutron oscillations

TL;DR

This paper demonstrates that both the $i\gamma^{0}$ and the standard $\gamma^{0}$ parity transformations are valid for analyzing neutron-antineutron oscillations, resolving recent debates by emphasizing careful treatment and the role of CP symmetry.

Contribution

It clarifies the validity of both parity definitions in neutron-antineutron oscillation analysis, showing they are equivalent when properly handled, and highlights the importance of CP symmetry in the process.

Findings

Both parity choices yield correct results with careful treatment.

CP symmetry plays a crucial role in mass diagonalization.

The Pauli-Gürsey transformation compensates for differences in parity definitions.

Abstract

In the analysis of neutron-antineutron oscillations, it has been recently argued in the literature that the use of the $i\gamma^{0}$ parity $n^{p}(t,-\vec{x})=i\gamma^{0}n(t,-\vec{x})$ which is consistent with the Majorana condition is mandatory and that the ordinary parity transformation of the neutron field $n^{p}(t,-\vec{x}) = \gamma^{0}n(t,-\vec{x})$ has a difficulty. We show that a careful treatment of the ordinary parity transformation of the neutron works in the analysis of neutron-antineutron oscillations. Technically, the CP symmetry in the mass diagonalization procedure is important and the two parity transformations, $i\gamma^{0}$ parity and $\gamma^{0}$ parity, are compensated for by the Pauli-G\"ursey transformation. Our analysis shows that either choice of the parity gives the correct results of neutron-antineutron oscillations if carefully treated.