HEP
In the literature: open
Do neutrons oscillate into antineutrons?
In plain words
Some theories allow a neutron to turn into its own antiparticle, changing baryon number by two. This would not show up in proton decay searches.
Precise statement
Search for $\Delta B = 2$ neutron-antineutron oscillations with free-neutron oscillation time $\tau_{\mathrm{nnbar}} > 8.6e7\,\mathrm{s}$ (ILL, 1994) and bound-neutron limits converting to $\sim 4.7e8\,\mathrm{s}$ (Super-Kamiokande, 2021). An answer is a detection or a free-neutron limit improved by 1 to 3 orders of magnitude.
What would settle it
The proposed NNBAR experiment at the European Spallation Source and bound-neutron searches in DUNE and Hyper-Kamiokande.