A Constraint to the Parity-Conserving Parameter of the Neutron-Antineutron Oscillations

The phenomenology of neutrino oscillations is extended to the neutron-antineutron oscillations predicted by the grand unified theories. There are six parameters in general describing the one-flavor oscillations: two real Majorana masses (of opposite signs), three Euler’s angles, and a phase multiplier χ. The sum of the Majorana masses, treated as a small parity-violating parameter ǫ, induces the nuclear decays (A,Z) → (A − 2, Z) and determines the oscillation rate of neutrons in the vacuum. We derive a constraint to a small parity-conserving parameter ǫ representing a combination of two Euler’s angles. This parameter gives no significant contribution to the neutron oscillation rate in the vacuum, while contributes to the nuclear decay rate. The nuclear stability implies |ǫ| < 1yr−1. Absence of the vacuum neutron oscillations together with existence of the nuclear decays (A,Z) → (A− 2, Z) would become simplest manifestation of the ǫ 6= 0. PACS: 12.10.-g; 21.90.+f