Proton annihilation at hadron colliders and Kamioka: high-energy versus high-luminosity

We examine models and prospects for proton annihilation to dileptons, a process which violates baryon and lepton number each by two. We determine that currently Super-Kamiokande would place the most draconian bound on $pp \rightarrow \ell^+ \ell^+$,rulingoutnewphysicsbelowascaleof$\sim 1.6$ TeV. We also find present and future hadron collider sensitivity to these processes. While 8 TeV LHC data excludes new physics at a scale below $\sim 800$GeV,thereachofa14TeVLHCrunis$\sim 1.8$ TeV, putting it on par with the sensitivity of Super-Kamiokande. On the other hand, a 100 TeV proton-proton collider would be sensitive to proton annihilation at a scale up to 10 TeV, allowing it to far exceed the reach of both Super-Kamiokande and the projected 2 TeV reach of Hyper-Kamiokande. Constraints from neutron star observation and cosmological evolution are not competitive. Therefore, although high-luminosity water Cherenkov experiments currently place the leading bounds on baryon and lepton number violation, next generation high-energy hadron colliders will begin surpassing them in sensitivity to some $B\mathrm{/}L$-violating processes.