Gauged B - L number and neutron-antineutron oscillation: long-range forces mediated by baryophotons

Transformation of a neutron to an antineutron n -> (n) over tilde has not yet been experimentally observed. In principle, it can occur with free neutrons in the vacuum or with neutrons bound inside the nuclei. In a nuclear medium the neutron and the antineutron have different potentials and for that reason n-(n) over tilde conversion in nuclei is heavily suppressed. This transformation can also be suppressed for free neutrons in the presence of an environmental vector field that distinguishes the neutron from the antineutron. We consider the case of a gauge field coupled to the B - L charge of the particles (B - L photon), and we show that discovery of n-(n) over tilde oscillation in experiment will lead to few order of magnitudes stronger limits on its coupling constant than present limits from the tests of the equivalence principle. If n-(n) over tilde oscillation will be discovered via nuclear instability, but not in free neutron oscillations at a corresponding level, this would indicate the presence of such environmental fifth forces. In the latter case the B - L potential can be measurable by varying the external magnetic field for achieving the resonance conditions for n-(n) over tilde conversion. As for neutron-mirror neutron oscillation, such potentials should have no effect once the fifth forces are associated to a common quantum number (B - L) - (B' - L') shared by the ordinary and mirror particles.