The time-dependent Hartree–Fock equation is solved by the Wigner function moments method taking into account spin degrees of freedom. Energies and reduced transition probabilities of K^π = 0⁻, 1⁻ and 2⁻ excitations are calculated taking ¹⁶⁴Dy as an example. The spin degrees of freedom give rise to the electric spin dipole resonance. Its properties and interplay with the giant dipole resonance are investigated. The deformation-induced splitting of the spin M2 resonance is discussed. The results of calculations are compared with the experimental data and other theoretical studies.

To ensure anomaly cancellation, the E₆ inspired U(1) extensions of the Minimal Supersymmetric (SUSY) Standard Model (MSSM) involve extra exotic matter. The lightest exotic neutralino in these models can be stable contributing to the cold dark matter density. We consider the interactions of such neutralino with nucleons within a specific extension of the MSSM with an additional U(1)_N gauge symmetry (SE₆SSM). The constraints on the couplings of this state, which are set by the present experimental bounds caused by the direct detection experiments, are examined. The obtained results can be generalised to other E₆ inspired SUSY models with extra U(1) gauge symmetry.

Nowadays, the Standard Model Effective Field Theory (SMEFT) provides a standard framework to parameterize potential deviations from the Standard Model and to combine information from multiple processes in global analyses. This review summarizes dedicated studies that constrain dimension-six Wilson coefficients using three top-quark and four top-quark production processes. We highlight the complementarity of these channels, as well as summarize the main problems and prospects in the area. A concise introduction to the SMEFT formalism and a discussion of the problem of potential perturbative unitarity violation are also provided.

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.