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 -> l(+)l(+), ruling out new physics below a scale of similar to 1.6 TeV. We also find present and future hadron collider sensitivity to these processes. While 8 TeV LHC data exclude new physics at a scale below similar to 800 GeV, the reach of a 14 TeV LHC run is similar to 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/L-violating processes.