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, [Formula: see text] 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 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.

Probing the origin of neutrino mass by disentangling the seesaw mechanism is one of the central issues of particle physics. We address it in the minimal left-right symmetric model and show how the knowledge of light and heavy neutrino masses and mixings suffices to determine their Dirac Yukawa couplings. This in turn allows one to make predictions for a number of high and low energy phenomena, such as decays of heavy neutrinos, neutrinoless double beta decay, electric dipole moments of charged leptons and neutrino transition moments. We also discuss a way of reconstructing the neutrino Dirac Yukawa couplings at colliders such as the LHC.

We give exact formulas for the right-handed analog of the CKM matrix in the minimal Left-Right symmetric theory, for the case when the Left-Right symmetry is generalized Parity as in the original version of the theory. We derive its explicit form and give a physical reason for the known and surprising fact that the right-handed mixing angles are close in value to the CKM ones, in spite of the Left-Right symmetry being badly broken in nature. We exemplify our results on the production of the right-handed charged gauge boson and the computation of KL − KS mass difference.I. Introduction. The Left-Right (LR) symmetric theory [1] prophetically implied non-vanishing neutrino mass whose smallness, through the seesaw mechanism [2-4], is related [2,3] to parity violation at low energies. The theory leads to neutrinoless double beta decay [5] through both left handed (LH) and heavy right handed (RH) neutrinos [3]. One can in principle observe lepton number violation at hadronic colliders and probe directly the Majorana nature of heavy neutrinos through the so-calleed KS process [6]. Moreover, the knowledge of neutrino masses allows one to predict the Dirac Yukawa couplings [7] and the associated decays of RH neutrinos.The small K L − K S mass difference implies a lower limit [8] on the LR scale in the minimal model around 3 TeV [9], and the LHC has come close to it for some channels [10]. This limit could go up to 20 TeV [11], but that depends on the UV completion of the theory.Detailed studies [12] support the feasibility of the KS process at the LHC connected to neutrinoless double beta decay and lepton flavor violation [13]. Recently CMS reported a 2.8 sigma excess [10] in the KS process that could be a manifestation of the LR symmetry [14]. It would require, however, the RH gauge coupling to be appreciably smaller that the LH one, not discussed here.In the limit of unbroken LR symmetry, left and right mixings are equal. The situation after the LR symmetry breaking depend on its nature, which can be either generalized charge conjugation C or generalized parity P. In the case of C, quark mass matrices are symmetric and the mixing angles remain the same, the only difference lying in phases.In the case of P, quark mass matrices are neither symmetric nor hermitian in general, yet it turns out that the left and right mixing angles are close to each other, as shown first numerically in a portion of the parameter space in [15]. An analytical study in the same approximation was made in [16], and [17] established this result over the entire parameter space by combining analytical and numerical computations.In this Letter we shed new light on this old issue by finding the explicit form of the right-handed quark mixing matrix, essential for high precision phenomenological studies of the theory. In the process we offer a physical explanation behind the approximate equality of left and

In a recent Letter we determined analytically the right-handed quark mixing matrix in the minimal Left-Right symmetric theory with generalized Parity. We derived its explicit form as a series expansion in a small parameter that measures the departure from hermiticity of quark mass matrices. Here we analyze carefully the convergence of the series by including higher order terms and by comparing with numerical results. We apply our findings to some phenomenological applications such as the production and decays of the right-handed gauge boson WR, the neutrinoless double beta decay, the decays of the heavy scalar doublet, the strong CP parameter and the theoretical limits on the new mass scale from the K and B-meson physics. In particular, we demonstrate that the relevant coupling for the production of the WR gauge boson at hadronic colliders and for the neutrinoless double beta decay equals its left-handed counterpart, within a percent. We also demonstrate that the stability of the theoretical lower limit on the WR mass from the K-meson physics is due to a partial cancellation of the external phases of the right-handed mixing matrix.