Gauged B-L Number and Neutron--Antineutron Oscillation: Long-range Forces Mediated by Baryophotons

Transformation of neutron to antineutron is a small effect that has not yet been experimentally observed. %cite{Phillips:2014fgb}. In principle, it can occur with free neutrons in the vacuum or with bound neutrons inside the nuclear environment different for neutrons and antineutrons and for that reason in the latter case it is heavily suppressed. Free neutron transformation also can be suppressed if environmental vector field exists destinguishing neutron from antineutron. We consider here the case of a vector field coupled to $B-L$ charge of the particles ($B-L$ photons) and study a possibility of this to lead to the observable suppression of neutron to antineutron transformation. The suppression effect however can be removed by applying external magnetic field. If the neutron--antineutron oscillation will be discovered in free neutron oscillation experiments, this will imply limits on $B-L$ photon coupling constant and interaction radius few order of magnitudes stronger than present limits form the tests of the equivalence principle. If $n-bar n$ oscillation will be discovered via nuclear instability, but not in free neutron oscillations in corresponding level, this would indicate to the presence of fifth-forces mediated by such baryophotons.