Neutron–antineutron oscillation and discrete symmetries

Abstract

We analyze status of [Formula: see text], [Formula: see text] and [Formula: see text] discrete symmetries in application to neutron–antineutron transitions breaking conservation of baryon charge [Formula: see text] by two units. At the level of free particles, all these symmetries are preserved. This includes [Formula: see text] reflection in spite of the opposite internal parities usually ascribed to neutron and antineutron. Explanation, which goes back to the 1937 papers by Majorana and Racah, is based on a definition of parity satisfying [Formula: see text], instead of [Formula: see text], and ascribing [Formula: see text] to both, neutron and antineutron. We apply this to [Formula: see text], [Formula: see text] and [Formula: see text] classification of six-quark operators with [Formula: see text]. It allows to specify operators contributing to neutron–antineutron oscillations. Remaining operators contribute to other [Formula: see text] 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.