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We examine models and prospects for proton annihilation to dileptons, aprocess which violates baryon and lepton number each by two. We determine thatcurrently Super-Kamiokande would place the most draconian bound on $pp\rightarrow \ell^+ \ell^+$, ruling out new physics below a scale of $\sim 1.6$TeV. We also find present and future hadron collider sensitivity to theseprocesses. While 8 TeV LHC data excludes new physics at a scale below $\sim800$ GeV, the reach of a 14 TeV LHC run is $\sim 1.8$ TeV, putting it on parwith the sensitivity of Super-Kamiokande. On the other hand, a 100 TeVproton-proton collider would be sensitive to proton annihilation at a scale upto 10 TeV, allowing it to far exceed the reach of both Super-Kamiokande and theprojected 2 TeV reach of Hyper-Kamiokande. Constraints from neutron starobservation and cosmological evolution are not competitive. Therefore, althoughhigh-luminosity water Cherenkov experiments currently place the leading boundson baryon and lepton number violation, next generation high-energy hadroncolliders will begin surpassing them in sensitivity to some $B/L$-violatingprocesses.

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