Limiting Equivalence Principle Violation and Long-Range Baryonic Force from Neutron-Antineutron Oscillation

We point out that if the baryon number violating neutron-antineutron oscillation is discovered, it would impose strong limits on the departure from Einstein's equivalence principle at a level of one part in $10^{19}$. If this departure owes its origin to the existence of long-range forces coupled to baryon number $B$ (or $B-L$), it would imply very stringent constraints on the strength of gauge bosons coupling to baryon number current. For instance, if the force mediating baryon number has strength $\alpha_B$ and its range is larger than a megaparsec, we find the limit to be $\alpha_B \leq 2\times 10^{-57}$, which is much stronger than all other existing bounds. For smaller range for the force, we get slightly weaker, but still stringent bounds by considering the potential of the Earth and the Sun.