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 m scale up to the Big Bang Nucleosynthesis limit of 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.

In the conventional misalignment mechanism, the axion field has a constant initial field value in the early Universe and later begins to oscillate. We present an alternative scenario where the axion field has a nonzero initial velocity, allowing an axion decay constant much below the conventional prediction from axion dark matter. This axion velocity can be generated from explicit breaking of the axion shift symmetry in the early Universe, which may occur as this symmetry is approximate.

Despite growing interest and extensive effort to search for ultralight dark matter in the form of a hypothetical dark photon, how it fits into a consistent cosmology is unclear. Several dark photon dark matter production mechanisms proposed previously are known to have limitations, at least in certain mass regimes of experimental interest. In this paper, we explore a novel mechanism, where a coherently oscillating axionlike field can efficiently transfer its energy density to a dark photon field via a tachyonic instability. The residual axion relic is subsequently depleted via couplings to the visible sector, leaving only the dark photon as dark matter. We ensure that the cosmologies of both the axion and dark photon are consistent with existing constraints. We find that the mechanism works for a broad range of dark photon masses, including those of interest for ongoing experiments and proposed detection techniques.

We propose a mechanism called axiogenesis where the cosmological excess of baryons over antibaryons is generated from the rotation of the QCD axion. The Peccei-Quinn (PQ) symmetry may be explicitly broken in the early Universe, inducing the rotation of a PQ charged scalar field. The rotation corresponds to the asymmetry of the PQ charge, which is converted into the baryon asymmetry via QCD and electroweak sphaleron transitions. In the concrete model we explore, interesting phenomenology arises due to the prediction of a small decay constant and the connections with new physics at the LHC and future colliders and with axion dark matter.

The QCD axion is a good dark matter candidate. The observed dark matter abundance can arise from misalignment or defect mechanisms, which generically require an axion decay constant $f_a\sim \mathcal{O}({10}^{11})\mathrm{GeV}$ (or higher). We introduce a new cosmological origin for axion dark matter, parametric resonance from oscillations of the Peccei-Quinn symmetry breaking field, that requires $f_a\sim ({10}^8–{10}^{11})\mathrm{GeV}$. The axions may be warm enough to give deviations from cold dark matter in large scale structure.