Abstract: It is well known that the scotogenic model for neutrino mass generation can explain correctly the relic abundance of cold dark matter. There have been claims in the literature that an important part of the parameter space of the simplest scotogentic model can be constrained by the requirement that no Z(2)-breaking must occur in the early universe. Here we show that this requirement does not give any constraints on the underlying parameter space at least in those parts, where we can trust perturbation theory. To demonstrate this, we have taken into account the proper decoupling of heavy degrees of freedom in both the thermal potential and in the RGE evolution.

Abstract: According to the “Black Box” theorem the experimental confirmation of neutrinoless double beta decay (0 nu 2 beta) would imply that at least one of the neutrinos is a Majorana particle. However, a null 0 nu 2 beta signal cannot decide the nature of neutrinos, as it can be suppressed even for Majorana neutrinos. In this letter we argue that if the null 0 nu 2 beta decay signal is accompanied by a 0 nu 2 beta quadruple beta decay signal, then at least one neutrino should be a Dirac particle. This argument holds irrespective of the underlying processes leading to such decays.

Abstract: 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 similar to 10(7) m. Neutral LLPs with lifetimes above similar to 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.