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.

We show that the relaxion generically stops its rolling at a point that breaks CP leading to relaxion-Higgs mixing. This opens the door to a variety of observational probes since the possible relaxion mass spans a broad range from sub-eV to the GeV scale. We derive constraints from current experiments (fifth force, astrophysical and cosmological probes, beam dump, flavour, LEP and LHC) and present projections from future experiments such as NA62, SHiP and PIXIE. We find that a large region of the parameter space is already under the experimental scrutiny. All the experimental constraints we derive are equally applicable for general Higgs portal models. In addition, we show that simple multiaxion (clockwork) UV completions suffer from a mild fine tuning problem, which increases with the number of sites. These results favour a cut-off scale lower than the existing theoretical bounds.

Composite Higgs Models are often constructed including fermionic top partners with a mass around the TeV scale, with the top partners playing the role of stabilizing the Higgs potential and enforcing partial compositeness for the top quark. A class of models of this kind can be formulated in terms of fermionic strongly coupled gauge theories. A common feature they all share is the presence of specific additional scalar resonances, namely two neutral singlets and a colored octet, described by a simple effective Lagrangian. We study the phenomenology of these scalars, both in a model independent and model dependent way, including the bounds from all the available searches in the relevant channels with di-boson and di-top final states. We develop a generic framework which can be used to constrain any model containing pseudo-scalar singlets or octets. Using it, we find that such signatures provide strong bounds on the compositeness scale complementary to the