Baryon number violation in supersymmetry: n - (n)over-bar oscillations as a probe beyond the LHC

We summarize the current status of baryon number violation in supersymmetry and provide prospects for going beyond the present reach by means of a new search for neutron-antineutron oscillations. The main motivation is the recently proposed neutron-antineutron oscillation experiment at the European Spallation Source in Lund, Sweden, which is projected to be able to improve the current bound on the transition probability in the quasi-free regime by three orders of magnitude. We consider various processes involving superpartners that give rise to neutron-antineutron oscillations and extract the corresponding simplified models, including only the most relevant superpartners and couplings. In terms of these models we recast and determine the exclusion limits from LHC searches as well as from searches for flavor transitions, CP violation and di-nucleon decays. We find that, for certain regions of the parameter space, the proposed neutron-antineutron experiment has a reach that goes beyond all other experiments, as it can probe gluino and squark masses in the multi-TeV range