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 discuss gauge mediation models where the doublet messengers and Higgs doublets are allowed to mix through a "charged" coupling. The charged coupling replaces messenger parity as a means of suppressing flavor changing neutral currents without introducing any unwanted CP violation. As a result of this mixing between the Higgs doublets and the messengers, relatively large A-terms are generated at the messenger scale. These large A-terms produce a distinct weak scale mass spectrum. Particularly, we show that the lightest Higgs boson mass is enhanced and can be as heavy as 125 GeV for a gluino mass as light as 2 TeV. We also show that the stops are heavier than that predicted by conventional gauge mediation models. It is also shown that these models have a peculiar slepton mass spectrum. arXiv:1107.3006v2 [hep-ph]

We revisit minimal supersymmetric SU(5) grand unification (GUT) models in which the soft supersymmetrybreaking parameters of the minimal supersymmetric Standard Model (MSSM) are universal at some input scale, M in , above the supersymmetric gauge-coupling unification scale, M GUT . As in the constrained MSSM (CMSSM), we assume that the scalar masses and gaugino masses have common values, m 0 and m 1/2 , respectively, at M in , as do the trilinear soft supersymmetry-breaking parameters A 0 . Going beyond previous studies of such a super-GUT CMSSM scenario, we explore the constraints imposed by the lower limit on the proton lifetime and the LHC measurement of the Higgs mass, m h . We find regions of m 0 , m 1/2 , A 0 and the parameters of the SU(5) superpotential that are compatible with these and other phenomenological constraints such as the density of cold dark matter, which we assume to be provided by the lightest neutralino. Typically, these allowed regions appear for m 0 and m 1/2 in the multi-TeV region, for suitable values of the unknown SU(5) GUTscale phases and superpotential couplings, and with the ratio of supersymmetric Higgs vacuum expectation values tan β 6.

We consider two potential non-accelerator signatures of generalizations of the well-studied constrained minimal supersymmetric standard model (CMSSM). In one generalization, the universality constraints on soft supersymmetry-breaking parameters are applied at some input scale below the grand unification (GUT) scale , a scenario referred to as ‘sub-GUT’. The other generalization we consider is to retain GUT-scale universality for the squark and slepton masses, but to relax universality for the soft supersymmetry-breaking contributions to the masses of the Higgs doublets. As with other CMSSM-like models, the measured Higgs mass requires supersymmetric particle masses near or beyond the TeV scale. Because of these rather heavy sparticle masses, the embedding of these CMSSM-like models in a minimal SU(5) model of grand unification can yield a proton lifetime consistent with current experimental limits, and may be accessible in existing and future proton decay experiments. Another possible signature of these CMSSM-like models is direct detection of supersymmetric dark matter. The direct dark matter scattering rate is typically below the reach of the LUX-ZEPLIN (LZ) experiment if is close to , but it may lie within its reach if  GeV. Likewise, generalizing the CMSSM to allow non-universal supersymmetry-breaking contributions to the Higgs offers extensive possibilities for models within reach of the LZ experiment that have long proton lifetimes.