Since its approval in 2016, NA64 has pioneered Light Dark Matter (LDM) searches with electron [1], positron [2], muon [3], and hadron [4] beams. The experiment has successfully met its primary objectives, as outlined in the EPPS input (2018), and even exceed them producing results that demonstrate its ability to operate in a near background-free environment. The Physics Beyond Collider (PBC) initiative at CERN recognizes NA64’s contributions as complementary and worthy of continued exploration. Its key advantage over beam dump approaches is that the signal rate scales as (coupling)² rather than (coupling)⁴, reducing the required beam particles for the same sensitivity.
To fully exploit the NA64 physics potential, an upgrade during LS3 will enable NA64 to run in background-free mode at higher SPS beam rates. Planned upgrades include (a) improved detector hermeticity with a new veto hadron calorimeter, (b) enhanced particle identification with a synchrotron radiation detector, and (c) increased beam rates via upgraded electronics.
With the recently strengthened NA64 collaboration, stable operations and timely data analysis are planned for LHC Run 4. The expected ∼ 10¹³ electrons, ∼ 10¹¹ positrons (40 and 60 GeV), and ∼ 2×10¹³ muons on target will allow NA64 to explore new light dark matter regions, with the potential for discovery or conclusive exclusion of many well-motivated LDM models.

Ten years ago, in a paper [1], a brief historical survey of the research activity in the Sector “Supersymmetry” at the Bogoliubov Laboratory of Theoretical Physics (BLTP) for more than 50 years of its existence has been given. Here, in commemoration of the 70th jubilee of the Joint Institute for Nuclear Research, we review some recent sound advancements in this area. Specifically, we consider the issues of constructing the superfield quantum effective actions in 6D, N = (1, 0) supersymmetry and off-shell unconstrained superfield formulations of N = 2 higher spins. In both cases, the harmonic superspace approach plays the decisive role.

The study of the interaction of colloidal solution components with microfiltration membranes is of continuing interest, both in the development of composite porous materials and in the numerous applications of membranes for separating suspensions. This study investigates the transport of silver nanoparticles through track-etched membranes under conditions where the nanoparticles and the membrane surface possess opposite charges. The objective was to establish patterns of nanoparticle deposition based on the membranes structural parameters and the solution flow rate.
A simple criterion was derived to determine nanoparticle retention efficiency by considering convection and diffusion within the pores. This criterion was tested through experiments using polyethylene terephthalate track-etched membranes with pore diameters ranging from 0.1 to 7.1 µm, while the average nanoparticle diameter was 24 nm. By varying the pressure drop, the flow rate of the colloidal solution through the membrane pores was varied.
Nanoparticle retention efficiency was determined using optical spectroscopy and energy-dispersive X-ray analysis. The distribution of nanoparticles on the membrane surface was examined using scanning electron microscopy. It was found that the proposed criterion satisfactorily predicts the transition from nearly complete particle retention to complete transmission when key parameters — pore diameter, membrane thickness, and pressure drop — are varied.
The obtained results provide insights into the controlled immobilization of nanoparticles on membrane surface, which is essential for creating functional nanocomposite devices, such as sensors.

The development of the unique cryogenic source of polarized deuterons, POLARIS, in the late 1970s was very fruitful and significantly enhanced JINR’s instrumental base for studies of nucleon-nucleon interactions as well as interactions of lightest nuclei with heavier nuclei.

Experimental data on polarization-dependent effects, obtained at the Synchrophasotron and the Nuclotron, significantly influenced the worldwide understanding of strong interactions between hadrons as well as the structure of lightest nuclei (the deuteron, first of all) at short inter-nucleon distances.

Experiments with polarized deuteron, proton and neutron beams at intermediate (several GeV) energies resulted in creation of wide collaborations between VBLHEP of JINR and other world centers (in the USSR and Russia, France, the USA, Germany, Japan, China). Many new and unexpected experimental results were obtained by those collaborations. In particular, many new unique results were obtained for the nucleon electromagnetic formfactors of nucleons, thanks to results of works within the ALPOM/ALPOM2 project. In addition, new ways became opened for experimental investigations with polarized ³He beams. In this direction, new unique results were obtained.

The necessary developments of the techniques for the spin program at the Nuclotron/NICA are discussed in the paper.

Refracton of particles (nucleons, nuclei, γ-quanta) in matter with polarized protons (nuclei) results in revealing coherent quasi-optical phenomenon of nuclear spin precession of particles (nuclei) in the pseudomagnetic field of matter with polarized spins and the phenomenon of birefringence of particles (nuclei) with spin S ⩾ 1. These phenomena can be observed and studied at the Nuclotron-M/NICA complex. The similar effects for γ-quanta could be observed at the LINAC accelerator.Quasi-optical coherent phenomena of spin rotation and dichroism are not caused by strong interactions only, the T-odd P-odd, T-odd P-even, and T-even P-odd interactions also contribute. Limits on the values of these contributions at the energies available at the Nuclotron-M/NICA complex can be obtained by investigating all these phenomena. When studying polarized particle collisions, it is necessary to consider possible influences of quasi-optical phenomena of spin rotation and spin dichroism caused by nuclear precession and birefringence.

The theory of spin effects (with the particular emphasis on T-odd ones) in QCD and its development in JINR is reviewed, including some personal recollections on the joint work with A.V. Efremov. The analysis of the sources of imaginary phases and respective cuts in hadronic kinematic variables leads to the effective character (non-universality) of T-odd distribution functions, contrary to universality of T-odd fragmentation functions. In particular, the model calculations of DIS with explicit T-violations can be used to predict the oscillations of T-odd polarizing fragmentation function. The comparison of polarization effects in hadronic and heavy-ion collisions is addressed.