Limiting Lorentz Violation from Neutron--Antineutron Oscillation

We point out that if neutron–antineutron oscillation is observed in a free neutron oscillation experiment, it will put an upper limit on the strengths of Lorentz invariance violating (LIV) mass operators for neutrons at the level of ${10}^{-23}$ GeV or so, which would be the most stringent LIV limit for neutrons. We also study constraints on $\mathrm{\Delta }B=2$ LIV operators and find that for one particular operator degaussing is not necessary to obtain a visible signal. We also note that observation of $n-\bar{n}$ oscillation signal in the nucleon decay search experiment involving nuclei does not lead to any limit on LIV operators since the nuclear potential difference between neutron and antineutrons will mask any Lorentz violating effect.