This paper describes the physics case for a new fixed target facility at CERN SPS. The SHiP ( search for hidden particles ) experiment is intended to hunt for new physics in the largely unexplored domain of very weakly interacting particles with masses below the Fermi scale, inaccessible to the LHC experiments, and to study tau neutrino physics. The same proton beam setup can be used later to look for decays of tau-leptons with lepton flavour number non-conservation, τ → 3 μ and to search for weakly-interacting sub-GeV dark matter candidates. We discuss the evidence for physics beyond the standard model and describe interactions between new particles and four different portals —scalars, vectors, fermions or axion-like particles. We discuss motivations for different models, manifesting themselves via these interactions, and how they can be probed with the SHiP experiment and present several case studies. The prospects to search for relatively light SUSY and composite particles at SHiP are also discussed. We demonstrate that the SHiP experiment has a unique potential to discover new physics and can directly probe a number of solutions of beyond the standard model puzzles, such as neutrino masses, baryon asymmetry of the Universe, dark matter, and inflation.

The discovery of neutrino masses through the observation of oscillations boosted the importance of neutrinoless double beta decay (0νββ). In this paper, we review the main features of this process, underlining its key role from both the experimental and theoretical point of view. In particular, we contextualize the0νββin the panorama of lepton number violating processes, also assessing some possible particle physics mechanisms mediating the process. Since the0νββexistence is correlated with neutrino masses, we also review the state of the art of the theoretical understanding of neutrino masses. In the final part, the status of current0νββexperiments is presented and the prospects for the future hunt for0νββare discussed. Also, experimental data coming from cosmological surveys are considered and their impact on0νββexpectations is examined.

The Large Hadron Collider has the potential to probe the scale of left-right symmetry restoration and the associated lepton number violation. Moreover, it offers the hope of measuring the right-handed leptonic mixing matrix. We show how this, together with constraints from lepton flavor violating processes, can be used to make predictions for neutrinoless double beta decay. We illustrate this connection in the case of the type-II seesaw.

The hierarchy problem of the scalar sector of the standard model is reformulated, emphasizing the role of experimental facts that may suggest the existence of a new physics large mass scale, for instance, indications of the instability of matter or indications in favor of massive neutrinos. In the seesaw model for the neutrino masses a hierarchy problem arises if the mass of the right-handed neutrinos is larger than approximately ${10}^7\mathrm{GeV}:$ this problem, and its possible solutions, are discussed.