  Long-lived particles (LLPs) are a common feature in many beyond the Standard
Model theories, including supersymmetry, and are generically produced in exotic
Higgs decays. Unfortunately, no existing or proposed search strategy will be
able to observe the decay of non-hadronic electrically neutral LLPs with masses
above $\sim$ GeV and lifetimes near the limit set by Big Bang Nucleosynthesis
(BBN), $c \tau \lesssim 10^7 - 10^8$~m. We propose the MATHUSLA surface
detector concept (MAssive Timing Hodoscope for Ultra Stable neutraL pArticles),
which can be implemented with existing technology and in time for the high
luminosity LHC upgrade to find such ultra-long-lived particles (ULLPs), whether
produced in exotic Higgs decays or more general production modes. We also
advocate for a dedicated LLP detector at a future 100 TeV collider, where a
modestly sized underground design can discover ULLPs with lifetimes at the BBN
limit produced in sub-percent level exotic Higgs decays.

High Energy Physics - Phenomenology;High Energy Physics - Experiment