Long-Lived Sleptons at the LHC and a 100 TeV Proton Collider

We study the prospects for long-lived charged particle (LLCP) searches at current and future LHC runs and at a 100 TeV pp collider, using Drell-Yan slepton pair production as an example. Because momentum measurements become more challenging for very energetic particles, we carefully treat the expected momentum resolution. At the same time, a novel feature of 100 TeV collisions is the significant energy loss of energetic muons in detectors. We use this to help discriminate between muons and LLCPs. We find that the 14 TeV LHC with an integrated luminosity of 3 ab$^{-1}$ can probe LLCP slepton masses up to 1.2 TeV, and a 100 TeV pp collider with 3 ab$^{-1}$ can probe LLCP slepton masses up to 4 TeV, using time-of-flight measurements. These searches will have striking implications for dark matter, with the LHC definitively testing the possibility of slepton-neutralino co-annihilating WIMP dark matter, and with the LHC and future hadron colliders having a strong potential for discovering LLCPs in models with superWIMP dark matter.