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Let R be a commutative associative ring with 1, and let G = GL( n , R ) be the general linear group of degree n ≥ 3 over R . Further, let I ⊴ R be an ideal of R . In the present note, which is a marginalia to the paper of Alexei Stepanov and the second author (2000), explicit expressions of the elementary transvection gt ij (ξ) g − 1 , where 1 ≤ i ≠ j ≤ n , ξ ∈ I and g ∈ G , are obtained as products of the Stein–Tits–Vaserstein generators of the relative elementary group E ( n,R, I ) .

New NICA accelerator complex at JINR (Dubna), based on the existing upgraded Nuclotron accelerator, will allow conducting all types of research in the field of high-energy physics. The main tasks of this project are study of the properties of the deconfinement phase transition, experimental investigation on medium modification of vector mesons, and search for the QCD critical end point. Thus, two interaction points are foreseen in the NICA collider: one for studying the collision of heavy ions on the Multipurpose detector MPD, the other for polarized beams for the experiment on the SPD installation. The ambitious physical goals of MPD require excellent particle identification at the maximum possible range of phase space. Identification of charged hadrons is achieved by combining time-of-flight measurements and energy loss measurements from the time-projection camera TPC. The Time-of-Flight system is based on multigap resistive plate chambers (MRPC), which are successfully used to identify particles in similar experiments around the world. A production site has been organized at the Laboratory of High Energy Physics of JINR for serial production of TOF MPD modules including 10 MRPCs. This site includes the entire cycle of work from preparing materials for the assembly of detectors to testing the assembled modules on cosmic radiation. This report presents the structure of the TOF system, its main parameters, the current state and the results of decoding and processing data obtained at the module testing facility.

A detector for adjusting the convergence of beams at the point of interaction of the MPD (multi-purpose detector) installation at the NICA collider (nuclotron-based ion collider facility) is discussed. Simulation of the detector operation for Au Au collisions at GeV is calculated. It is shown that background events from scattering on residual gas give a negligible contribution to the detector’s samples. It is discussed how to use a detector to adjust beam alignment. The calibration procedure for obtaining absolute luminosity in the MPD interaction zone with the help of this detector is considered.

— A new time-of-flight (ToF) system of the NA61/SHINE hadron spectrometer at the extracted beam of the Super Hadron Synchrotron in CERN has been developed in 2019–2022 by the staff of the Laboratory of High-Energy Physics of the Joint Institute for Nuclear Research. The new ToF system is based on Multigap Resistive Plate Chambers (MRPCs) technology. The previous system consisting of scintillation counters was substituted with the new ToF system. This paper presents the overview of the new NA61/SHINE ToF system.

Particle knockout scattering experiments1,2 are fundamental for mapping the structure of atomic nuclei2–6, but their interpretation is often complicated by initial- and final-state interactions of the incoming and scattered particles1,2,7–9. Such interactions lead to reduction in the scattered particle flux and distort their kinematics. Here we overcome this limitation by measuring the quasi-free scattering of 48 GeV c–112C ions from hydrogen. The distribution of single protons is studied by detecting two protons at large angles in coincidence with an intact 11B nucleus. The 11B detection suppresses the otherwise large distortions of reconstructed single-proton distributions induced by initial- and final-state interactions. By further detecting residual 10B and 10Be nuclei, we also identified short-range correlated nucleon–nucleon pairs9–13 and provide direct experimental evidence for separation of the pair wavefunction from that of the residual many-body nuclear system9,14. All measured reactions are well described by theoretical calculations that include no distortions from the initial- and final-state interactions. Our results showcase the ability to study the short-distance structure of short-lived radioactive nuclei at the forthcoming Facility for Antiproton and Ion Research (FAIR)15 and Facility for Rare Isotope Beams (FRIB)16 facilities, which is relevant for understanding the structure and properties of nuclei far from stability and the formation of visible matter in the Universe.Initial- and final-state interactions distort the kinematics in particle knockout scattering experiments, complicating their interpretation. These effects are suppressed by detecting 11B nuclei in quasi-free scattering of 12C ions from hydrogen.

This paper reports measurements of two-pion femtoscopic correlations in Be+Be collisions at a beam momentum of 150 A GeV / c  (energy available in the center-of-mass system for nucleon pair s NN = 16.84 GeV) by the NA61/SHINE experiment at the CERN SPS accelerator. The obtained momentum space correlation functions can be well described by a Lévy distributed source model. The transverse mass dependence of the Lévy source parameters is presented, and their possible theoretical interpretations are discussed. The results show that the Lévy exponent α is approximately constant as a function of m T  , and far from both the Gaussian case of α = 2 or the conjectured value at the critical endpoint, α = 0.5 . The radius scale parameter R shows a slight decrease in m T  , which can be explained as a signature of transverse flow. Finally, an approximately constant trend of the intercept parameter λ as a function of m T  was observed, similar to previous NA44 S + Pb results (obtained with a Gaussian approximation, but unlike RHIC results).

The NA61/SHINE experiment at the CERN Super Proton Synchrotron studies the onset of deconfinement in strongly interacting matter through a beam energy scan of particle production in collisions of nuclei of varied sizes. This paper presents results on inclusive double-differential spectra, transverse momentum and rapidity distributions and mean multiplicities of π ± , K ± , p and p ¯ produced in 40 Ar+ 45 Sc collisions at beam momenta of 13 A , 19 A , 30 A , 40 A , 75 A and 150 A   Ge V / c . The analysis uses the 10% most central collisions, where the observed forward energy defines centrality. The energy dependence of the K ± / π ± ratios as well as of inverse slope parameters of the K ± transverse mass distributions are placed in between those found in inelastic p + p and central Pb + Pb collisions. The results obtained here establish a system-size dependence of hadron production properties that so far cannot be explained either within statistical or dynamical models.

Strong interactions preserve an approximate isospin symmetry between up ( u ) and down ( d ) quarks, part of the more general flavor symmetry. In the case of K meson production, if this isospin symmetry were exact, it would result in equal numbers of charged ( K + and K − ) and neutral ( K 0 and K ¯ 0 ) mesons produced in collisions of isospin-symmetric atomic nuclei. Here, we report results on the relative abundance of charged over neutral K meson production in argon and scandium nuclei collisions at a center-of-mass energy of 11.9 GeV per nucleon pair. We find that the production of K + and K − mesons at mid-rapidity is (18.4 ± 6.1)% higher than that of the neutral K mesons. Although with large uncertainties, earlier data on nucleus-nucleus collisions in the collision center-of-mass energy range 2.6 < s N N < 200 GeV are consistent with the present result. Using well-established models for hadron production, we demonstrate that known isospin-symmetry breaking effects and the initial nuclei containing more neutrons than protons lead only to a small (few percent) deviation of the charged-to-neutral kaon ratio from unity at high energies. Thus, they cannot explain the measurements. The significance of the flavor-symmetry violation beyond the known effects is 4.7 σ when the compilation of world data with uncertainties quoted by the experiments is used. New systematic, high-precision measurements and theoretical efforts are needed to establish the origin of the observed large isospin-symmetry breaking. Strong interaction is blind to quark flavor, so collisions of nuclei with the same number of protons and neutrons should generate the same number of charged and neutral kaons. Here, instead, the authors show a significant excess of charged over neutral kaon production in Ar+Sc nuclei collisions, compatibly with earlier measurements which however suffered from larger uncertainties, and show that known effects cannot explain the result.

The critical point of strongly interacting matter is searched for at the CERN SPS by the NA61/SHINE experiment in central 40 Ar +  45 Sc collisions at 13  A , 19  A , 30  A , 40  A , and 75  A  GeV/ c . The dependence of the second-order scaled factorial moments of proton multiplicity distributions on the number of subdivisions in transverse momentum space is measured. The intermittency analysis uses statistically independent data sets for every subdivision in transverse and cumulative-transverse momentum variables. The results obtained do not indicate the searched intermittent pattern. An upper limit on the fraction of correlated protons and the intermittency index is obtained based on a comparison with the Power-law Model.

A bstract Results of the BM@N experiment at the Nuclotron/NICA complex on the production of protons, deuterons and tritons in interactions of an argon beam of 3.2 A GeV with fixed targets of C, Al, Cu, Sn and Pb are presented. Transverse mass spectra, rapidity distributions and multiplicities of protons, deuterons and tritons are measured. The results are treated within a coalescence approach and compared with predictions of theoretical models and with other measurements.