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 conclusions of the Physics Working Group of the International Scoping Study of a future Neutrino Factory and super-beam facility (the ISS) are presented. The ISS was carried out by the international community between NuFact05, (the 7th International Workshop on Neutrino Factories and Super-beams, Laboratori Nazionali di Frascati, Rome, 21-26 June 2005) and NuFact06 (Ivine, CA, 24-30 August 2006). The physics case for an extensive experimental programme to understand the properties of the neutrino is presented and the role of high-precision measurements of neutrino oscillations within this programme is discussed in detail. The performance of second-generation super-beam experiments, beta-beam facilities and the Neutrino Factory are evaluated and a quantitative comparison of the discovery potential of the three classes of facility is presented. High-precision studies of the properties of the muon are complementary to the study of neutrino oscillations. The Neutrino Factory has the potential to provide extremely intense muon beams and the physics potential of such beams is discussed in the final section of the report.

We derive the general counting rules for a quantum effective field theory (EFT) in d dimensions. The rules are valid for strongly and weakly coupled theories, and they predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of the cross sections is controlled by the power counting of EFT, not by chiral counting, even for chiral perturbation theory (χ PT). The relation between and f is generalized to d dimensions. We show that the naive dimensional analysis 4π counting is related toh counting. The EFT counting rules are applied to χ PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.

We explore whether the axion which solves the strong CP problem can naturally be much lighter than the canonical QCD axion. The $$ {Z}_{\mathcal{N}} $$ Z N symmetry proposed by Hook, with $$ \mathcal{N} $$ N mirror and degenerate worlds coexisting in Nature and linked by the axion field, is considered in terms of generic effective axion couplings. We show that the total potential is safely approximated by a single cosine in the large $$ \mathcal{N} $$ N limit, and we determine the analytical formula for the exponentially suppressed axion mass. The resulting universal enhancement of all axion interactions relative to those of the canonical QCD axion has a strong impact on the prospects of axion-like particle experiments such as ALPS II, IAXO and many others: experiments searching for generic axion-like particles have in fact discovery potential to solve the strong CP problem. The finite density axion potential is also analyzed and we show that the $$ {Z}_{\mathcal{N}} $$ Z N asymmetric background of high-density stellar environments sets already significant model-independent constraints: 3 ≤ $$ \mathcal{N} $$ N ≲ 47 for an axion scale fa ≲ 2.4 × 1015 GeV, with tantalizing discovery prospects for any value of fa and down to $$ \mathcal{N} $$ N ∼ 9 with future neutron star and gravitational wave data, down to the ultra-light mass region. In addition, two specific ultraviolet $$ {Z}_{\mathcal{N}} $$ Z N completions are developed: a composite axion one and a KSVZ-like model with improved Peccei-Quinn quality.