Neutron--Antineutron Oscillations: Discrete Symmetries and Quark Operators

TL;DR

This paper examines how discrete symmetries like C, P, and T relate to neutron-antineutron oscillations, clarifying the role of parity and classifying operators that contribute to baryon number violation.

Contribution

It introduces a novel classification of six-quark operators based on a specific parity definition, clarifying their role in neutron-antineutron oscillations and other baryon-violating processes.

Findings

All discrete symmetries are preserved at the free particle level.

External magnetic fields do not induce new neutron-antineutron mixing operators.

Operators contributing to oscillations are distinguished from those causing nuclei instability.

Abstract

We analyze status of ${\bf C}$, ${\bf P}$ and ${\bf T}$ discrete symmetries in application to neutron-antineutron transitions breaking conservation of baryon charge ${\cal B}$ by two units. At the level of free particles all these symmetries are preserved. This includes ${\bf P}$ reflection in spite of the opposite internal parities usually ascribed to neutron and antineutron. Explanation, which goes back to the 1937 papers by E. Majorana and by G. Racah, is based on a definition of parity satisfying ${\bf P}^{2}=-1$, instead of ${\bf P}^{2}=1$, and ascribing $ {\bf P}=i$ to both, neutron and antineutron. We apply this to ${\bf C}$, ${\bf P}$ and ${\bf T}$ classification of six-quark operators with $|\Delta {\cal B} |=2$. It allows to specify operators contributing to neutron-antineutron oscillations. Remaining operators contribute to other $|\Delta {\cal B} |=2$ processes and, in particular, to nuclei instability. We also show that presence of external magnetic field does not induce any new operator mixing the neutron and antineutron provided that rotational invariance is not broken.