We examine the theoretical motivations for long-lived particle (LLP) signals at the LHC in a comprehensive survey of standard model (SM) extensions. LLPs are a common prediction of a wide range of theories that address unsolved fundamental mysteries such as naturalness, dark matter, baryogenesis and neutrino masses, and represent a natural and generic possibility for physics beyond the SM (BSM). In most cases the LLP lifetime can be treated as a free parameter from the µm scale up to the Big Bang Nucleosynthesis limit of ∼10 7 m. Neutral LLPs with lifetimes above ∼ 100 m are particularly difficult to probe, as the sensitivity of the LHC main detectors is limited by challenging backgrounds, triggers, and small acceptances. MATHUSLA is a proposal for a minimally instrumented, large-volume surface detector near ATLAS or CMS. It would search for neutral LLPs produced in HL-LHC collisions by reconstructing displaced vertices (DVs) in a low-background environment, extending the sensitivity of the main detectors by orders of magnitude in the long-lifetime regime. We study the LLP physics opportunities afforded by a MATHUSLA-like detector at the HL-LHC, assuming backgrounds can be rejected as expected. We develop a model-independent approach to describe the sensitivity of MATHUSLA to BSM LLP signals, and compare it to DV and missing energy searches at ATLAS or CMS. We then explore the BSM motivations for LLPs in considerable detail, presenting a large number of new sensitivity studies. While our discussion is especially oriented towards the long-lifetime regime at MATHUSLA, this survey underlines the importance of a varied LLP search program at the LHC in general. By synthesizing these results into a general discussion of the top-down and bottom-up motivations for LLP searches, it is our aim to demonstrate the exceptional strength and breadth of the physics case for the construction of the MATHUSLA detector.

The proposed LDMX experiment would provide roughly a meter-long region of instrumented tracking and calorimetry that acts as a beam stop for multi-GeV electrons in which each electron is tagged and its evolution measured. This would offer an unprecedented opportunity to access both collider-invisible and ultra-short lifetime decays of new particles produced in electron (or muon)-nuclear fixed-target collisions. In this paper, we show that the missing momentum channel and displaced decay signals in such an experiment could provide world-leading sensitivity to sub-GeV dark matter, millicharged particles, and visibly or invisibly decaying axions, scalars, dark photons, and a range of other new physics scenarios.

Large, non-standard neutrino self-interactions have been shown to resolve the ∼ 4σ tension in Hubble constant measurements and a milder tension in the amplitude of matter fluctuations. We demonstrate that interactions of the necessary size imply the existence of a force-carrier with a large neutrino coupling (> 10 −4 ) and mass in the keV -100 MeV range. This mediator is subject to stringent cosmological and laboratory bounds, and we find that nearly all realizations of such a particle are excluded by existing data unless it carries spin 0 and couples almost exclusively to τ -flavored neutrinos. Furthermore, we find that the light neutrinos must be Majorana, and that a UV-complete model requires a non-minimal mechanism to simultaneously generate neutrino masses and appreciable self-interactions.

A natural possibility for dark matter is that it is composed of the stable pions of a QCD-like hidden sector. Existing literature largely assumes that pion self-interactions alone control the early universe cosmology. We point out that processes involving vector mesons typically dominate the physics of dark matter freeze-out and significantly widen the viable mass range for these models. The vector mesons also give rise to striking signals at accelerators. For example, in most of the cosmologically favored parameter space, the vector mesons are naturally long-lived and produce standard model particles in their decays. Electron and proton beam fixed-target experiments such as HPS, SeaQuest, and LDMX can exploit these signals to explore much of the viable parameter space. We also comment on dark matter decay inherent in a large class of previously considered models and explain how to ensure dark matter stability.