Particles beyond the Standard Model (SM) can generically have lifetimes that are long compared to SM particles at the weak scale. When produced at experiments such as the Large Hadron Collider (LHC) at CERN, these long-lived particles (LLPs) can decay far from the interaction vertex of the primary proton–proton collision. Such LLP signatures are distinct from those of promptly decaying particles that are targeted by the majority of searches for new physics at the LHC, often requiring customized techniques to identify, for example, significantly displaced decay vertices, tracks with atypical properties, and short track segments. Given their non-standard nature, a comprehensive overview of LLP signatures at the LHC is beneficial to ensure that possible avenues of the discovery of new physics are not overlooked. Here we report on the joint work of a community of theorists and experimentalists with the ATLAS, CMS, and LHCb experiments—as well as those working on dedicated experiments such as MoEDAL, milliQan, MATHUSLA, CODEX-b, and FASER—to survey the current state of LLP searches at the LHC, and to chart a path for the development of LLP searches into the future, both in the upcoming Run 3 and at the high-luminosity LHC. The work is organized around the current and future potential capabilities of LHC experiments to generally discover new LLPs, and takes a signature-based approach to surveying classes of models that give rise to LLPs rather than emphasizing any particular theory motivation. We develop a set of simplified models; assess the coverage of current searches; document known, often unexpected backgrounds; explore the capabilities of proposed detector upgrades; provide recommendations for the presentation of search results; and look towards the newest frontiers, namely high-multiplicity ‘dark showers’, highlighting opportunities for expanding the LHC reach for these signals.

The lack of evidence for new physics beyond the standard model at the LHC points to a paucity of new particles near the weak scale. This suggests that the weak scale is tuned and that supersymmetry, if present at all, is realized at higher energies. The measured Higgs mass constrains the scalar sparticles to be below 10⁵TeV, while gauge coupling unification favors Higgsinos below 100 TeV. Nevertheless, in many models gaugino masses are suppressed and remain within reach of the LHC. Tuning the weak scale and the renormalization group evolution of the scalar masses constrain Split model building. Due to the small gaugino masses, either the squarks or the up-higgs often run tachyonic; in the latter case, successful electroweak breaking requires heavy higgsinos near the scalar sparticles. We discuss the consequences of tuning the weak scale and the phenomenology of several models of Split supersymmetry including anomaly mediation, U(1)_B−Lmediation, and Split gauge mediation.

We revisit the Twin Higgs scenario as a “dark” solution to the little hierarchy problem, identify the structure of a minimal model and its viable parameter space, and analyze its collider implications. In this model, dark naturalness generally leads to Hidden Valley phenomenology. The twin particles, including the top partner, are all Standard-Model-neutral, but naturalness favors the existence of twin strong interactions — an asymptotically-free force that confines not far above the Standard Model QCD scale — and a Higgs portal interaction. We show that, taken together, these typically give rise to exotic decays of the Higgs to twin hadrons. Across a substantial portion of the parameter space, certain twin hadrons have visible and often displaced decays, providing a potentially striking LHC signature. We briefly discuss appropriate experimental search strategies.

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

We lay out a comprehensive physics case for a future high-energy muon collider, exploring a range of collision energies (from 1 to 100 TeV) and luminosities. We highlight the advantages of such a collider over proposed alternatives. We show how one can leverage both the point-like nature of the muons themselves as well as the cloud of electroweak radiation that surrounds the beam to blur the dichotomy between energy and precision in the search for new physics. The physics case is buttressed by a range of studies with applications to electroweak symmetry breaking, dark matter, and the naturalness of the weak scale. Furthermore, we make sharp connections with complementary experiments that are probing new physics effects using electric dipole moments, flavor violation, and gravitational waves. An extensive appendix provides cross section predictions as a function of the center-of-mass energy for many canonical simplified models.

We assess the current state of searches at the LHC for additional Higgs bosons in light of both direct limits and indirect bounds coming from coupling measurements of the Standard Model-like Higgs boson. Given current constraints, we identify and study three LHC searches that are critical components of a comprehensive program to investigate extended electroweak symmetry breaking sectors: production of a heavy scalar or pseudoscalar with decay to \( t\overline{t} \); \( b\overline{b} \) and \( t\overline{t} \) associated production of a heavy scalar or pseudoscalar with decay to invisible final states; and \( t\overline{b} \) associated production of a charged Higgs with decay to \( t\overline{b} \). Systematic experimental searches in these channels would contribute to robust coverage of the possible single production modes of additional heavy Higgs bosons.