We review the collider phenomenology of neutrino physics and the synergetic aspects at energy, intensity and cosmic frontiers to test the new physics behind the neutrino mass mechanism. In particular, we focus on seesaw models within the minimal setup as well as with extended gauge and/or Higgs sectors, and on supersymmetric neutrino mass models with seesaw mechanism and with Rparity violation. In the simplest type-I seesaw scenario with sterile neutrinos, we summarize and update the current experimental constraints on the sterile neutrino mass and its mixing with the active neutrinos. We also discuss the future experimental prospects of testing the seesaw mechanism at colliders and in related low-energy searches for rare processes, such as lepton flavor violation and neutrinoless double beta decay. The implications of the discovery of lepton number violation at the Large Hadron Collider for leptogenesis are also studied.

Neutrinoless double beta decay is the most powerful tool to probe not only for Majorana neutrino masses but for lepton number violating physics in general. We discuss relations between lepton number violation, double beta decay and neutrino mass, review a general Lorentz invariant parametrization of the double beta decay rate, highlight a number of different new physics models showing how different mechanisms can trigger double beta decay, and finally discuss possibilities to discriminate and test these models and mechanisms in complementary experiments.

Physics at the Large Hadron Collider (LHC) and the International e + e − Linear Collider (ILC) will be complementary in many respects, as has been demonstrated at previous generations of hadron and lepton colliders. This report addresses the possible interplay between the LHC and ILC in testing the Standard Model and in discovering and determining the origin of new physics. Mutual benefits for the physics programme at both machines can occur both at the level of a combined interpretation of Hadron Collider and Linear Collider data and at the level of combined analyses of the data, where results obtained at one machine can directly influence the way analyses are carried out at the other machine. Topics under study comprise the physics of weak and strong electroweak symmetry breaking, supersymmetric models, new gauge theories, models with extra dimensions, and electroweak and QCD precision physics. The status of the work that has been carried out within the LHC / LC Study Group so far is summarised in this report. Possible topics for future studies are outlined.4

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.

High-precision analyses of supersymmetry parameters aim at reconstructing the fundamental supersymmetric theory and its breaking mechanism. A well defined theoretical framework is needed when higher-order corrections are included. We propose such a scheme, Supersymmetry Parameter Analysis SPA, based on a consistent set of conventions and input parameters. A repository for computer programs is provided which connect parameters in different schemes and relate the Lagrangian parameters to physical observables at LHC and high energy e + e − linear collider experiments, i.e., masses, mixings, decay widths and production cross sections for supersymmetric particles. In addition, programs for calculating high-precision low energy observables, the density of cold dark matter (CDM) in the universe as well as the cross sections for CDM search experiments are included. The SPA scheme still requires extended efforts on both the theoretical and experimental side before data can be evaluated in the future at the level of the desired precision. We take here an initial step of testing the SPA scheme by applying the techniques involved to a specific supersymmetry reference point.

We discuss a supersymmetric inverse seesaw model in which lepton flavour violating decays can be enhanced either by flavour violating slepton contributions or by the non-unitarity of the charged current mixing matrix. As an example we calculate Br(µ → eγ) taking into account both heavy lepton exchange as well as supersymmetric diagrams in a minimal supergravity framework. We find that the for the same parameters the rate can be enhanced with respect to seesaw model expectations, with or without supersymmetry.

The possibility to probe new physics scenarios of light Majorana neutrino exchange and right-handed currents at the planned next generation neutrinoless double β decay experiment SuperNEMO is discussed. Its ability to study different isotopes and track the outgoing electrons provides the means to discriminate different underlying mechanisms for the neutrinoless double β decay by measuring the decay half-life and the electron angular and energy distributions.a

We discuss lepton flavour violating processes induced in the production and decay of heavy right-handed neutrinos at the LHC. Such particles appear in left-right symmetrical extensions of the Standard Model as the messengers of neutrino mass generation, and can have masses at the TeV scale. We determine the expected sensitivity on the right-handed neutrino mixing matrix, as well as on the righthanded gauge boson and heavy neutrino masses. By comparing the sensitivity of the LHC with that of searches for low energy LFV processes, we identify favourable areas of the parameter space to explore the complementarity between LFV at low and high energies.