All‐dielectric nanophotonics attracts ever increasing attention nowadays due to the possibility of controlling and configuring light scattering on high‐index semiconductor nanoparticles. It opens a room of opportunities for designing novel types of nanoscale elements and devices, and paves the way for advanced technologies of light energy manipulation. One of the exciting and promising prospects is associated with utilizing the so‐called toroidal moment, being the result of poloidal currents excitation, and anapole states, corresponding to the interference of dipole and toroidal electric moments. Here, higher‐order toroidal moments of both types (up to the electric octupole toroidal moment) are presented and investigated in detail via the direct Cartesian multipole decomposition allowing new near‐ and far‐field configurations to be obtained. Poloidal currents can be associated with vortex‐like distributions of the displacement currents inside nanoparticles, revealing the physical meaning of the high‐order toroidal moments and the convenience of the Cartesian multipoles as an auxiliary tool for analysis. High‐order nonradiating anapole states accompanied by the excitation of intense near‐fields are demonstrated. It is believed that the results are of high importance for both the fundamental understanding of light scattering by high‐index particles and a variety of nanophotonics applications and light governing on nanoscale.

Heavy Neutral Leptons (HNLs) are hypothetical particles predicted by many extensions of the Standard Model. These particles can, among other things, explain the origin of neutrino masses, generate the observed matter-antimatter asymmetry in the Universe and provide a dark matter candidate. The SHiP experiment will be able to search for HNLs produced in decays of heavy mesons and travelling distances ranging between O(50 m) and tens of kilometers before decaying. We present the sensitivity of the SHiP experiment to a number of HNL's benchmark models and provide a way to calculate the SHiP's sensitivity to HNLs for arbitrary patterns of flavour mixings. The corresponding tools and data files are also made publicly available.

The Search for Hidden Particles (SHiP) Collaboration has shown that the CERN SPS accelerator with its 400 GeV/c proton beam offers a unique opportunity to explore the Hidden Sector [1–3]. The proposed experiment is an intensity frontier experiment which is capable of searching for hidden particles through both visible decays and through scattering signatures from recoil of electrons or nuclei. The high-intensity experimental facility developed by the SHiP Collaboration is based on a number of key features and developments which provide the possibility of probing a large part of the parameter space for a wide range of models with light long-lived super-weakly interacting particles with masses up to 𝒪(10) GeV/c2 in an environment of extremely clean background conditions. This paper describes the proposal for the experimental facility together with the most important feasibility studies. The paper focuses on the challenging new ideas behind the beam extraction and beam delivery, the proton beam dump, and the suppression of beam-induced background.

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