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 $pp
\rightarrow \ell^+ \ell^+$, ruling out new physics below a scale of $\sim 1.6$
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, the reach of a 14 TeV LHC run is $\sim 1.8$ 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 $B/L$-violating
processes.
