Long-lived particles at the energy frontier: the MATHUSLA physics case.

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 [Formula: see text]m scale up to the Big Bang Nucleosynthesis limit of [Formula: see text] m. Neutral LLPs with lifetimes above [Formula: see text]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.

Natural gauge mediation with a Bino next-to-lightest supersymmetric particle at the LHC.

Natural models of supersymmetry with a gravitino lightest supersymmetric particle provide distinctive signatures at the LHC. For a neutralino next-to-lightest supersymmetric particle, sparticles can decay to two high energy photons plus missing energy. We use the ATLAS diphoton search with 4.8 b(-1) of data to place limits in both the top-squark-gluino and neutralino-chargino mass planes for this scenario. If the neutralino is heavier than 50 GeV, the lightest top squark must be heavier than 580 GeV, the gluino must be heavier than 1100 GeV, and charginos must be heavier than approximately 300-470 GeV. This provides the first nontrivial constraints in natural gauge mediation models with a neutralino next-to-lightest supersymmetric particle decaying to photons and implies a fine-tuning of at least a few percent in such models.

Dirac neutrino masses with planck scale lepton number violation.

It is shown how pure Dirac neutrino masses can naturally occur at low energies even in the presence of Planck scale lepton number violation. In a 5D setting this is achieved by explicitly breaking the lepton number on the Planck brane while the right-handed neutrino is localized on the TeV brane. A small wave function overlap then naturally leads to a small Dirac Yukawa coupling. In the 4D dual description the right-handed neutrino is identified as a composite CFT bound state and lepton number violation is highly suppressed by CFT operators with large anomalous dimensions.

Grand unified theory precursors and nontrivial fixed points in higher-dimensional gauge theories.

Within the context of traditional logarithmic grand unification at M(GUT) approximately equal to 10(16) GeV, we show that it is nevertheless possible to observe certain GUT states such as X and Y gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as "GUT precursors." These states offer an interesting alternative possibility for new physics at the TeV scale, and could be used to directly probe GUT physics even though the scale of gauge coupling unification remains high. Our results also give rise to a Kaluza-Klein realization of nontrivial fixed points in higher-dimensional gauge theories.

Anomaly-free brane worlds in seven dimensions.

We present an orbifold compactification of the minimal seven-dimensional supergravity. The vacuum is a slice of seven-dimensional anti-de Sitter space where six-branes of opposite tension are located at the orbifold fixed points. The cancellation of gauge and gravitational anomalies restricts the gauge group and matter content on the boundaries. In addition, anomaly cancellation fixes the boundary gauge couplings in terms of the gravitational constant, and the mass parameter of the Chern-Simons term.