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 introduction of T parity dramatically improves the consistency of Little Higgs models with precision electroweak data, and renders the lightest T-odd particle (LTP) stable. In the Littlest Higgs model with T parity, the LTP is typically the T-odd heavy photon, which is weakly interacting and can play the role of dark matter. We analyze the relic abundance of the heavy photon, including its coannihilations with other Todd particles, and map out the regions of the parameter space where it can account for the observed dark matter. We evaluate the prospects for direct and indirect discovery of the heavy photon dark matter. The direct detection rates are quite low and a substantial improvement in experimental sensitivity would be required for observation. A substantial flux of energetic gamma rays is produced in the annihilation of the heavy photons in the galactic halo. This flux can be observed by the GLAST telescope, and, if the distribution of dark matter in the halo is favorable, by ground-based telescope arrays such as VERITAS and HESS.

Composite Higgs models can trivially satisfy precision-electroweak and flavour constraints by simply having a large spontaneous symmetry breaking scale, f 10 TeV. This produces a 'split' spectrum, where the strong sector resonances have masses greater than 10 TeV and are separated from the pseudo Nambu-Goldstone bosons, which remain near the electroweak scale. Even though a tuning of order 10 −4 is required to obtain the observed Higgs boson mass, the big hierarchy problem remains mostly solved. Intriguingly, models with a fully-composite right-handed top quark also exhibit improved gauge coupling unification. By restricting ourselves to models which preserve these features we find that the symmetry breaking scale cannot be arbitrarily raised, leading to an upper bound f 100-1000 TeV. This implies that the resonances may be accessible at future colliders, or indirectly via rare-decay experiments. Dark matter is identified with a pseudo NambuGoldstone boson, and we show that the smallest coset space containing a stable, scalar singlet and an unbroken SU(5) symmetry is SU(7)/SU(6)×U(1). The colour-triplet pseudo Nambu-Goldstone boson also contained in this coset space is metastable due to a residual symmetry. It can decay via a displaced vertex when produced at colliders, leading to a distinctive signal of unnaturalness.

We investigate the LHC signals of a minimal supersymmetric hidden valley. Our theory consists of the supersymmetric Standard Model along with a light hidden U (1) x gauge multiplet and a pair of hidden chiral superfields that spontaneously break the new Abelian gauge symmetry near a GeV. The visible and hidden sectors interact exclusively through supersymmetric gauge kinetic mixing. We perform a thorough examination of the hidden decay cascades initiated by the lightest Standard Model superpartner and we study the range of LHC signals they can produce. In particular, we find parameter regions that give rise to missing energy, single and multiple lepton jets, and displaced vertices. Given the simplicity of the underlying theory and the broad range of collider signals it can produce, we propose that this model is a useful benchmark for LHC studies of (supersymmetric) hidden valleys.