The COMET experiment at J-PARC, Japan, aims to search for muon to electron conversion with aluminum nuclei, achieving a sensitivity four orders of magnitude higher than the current upper limit at a 90 % confidence level. The proton beam line has recently been completed, and muons have been successfully transported through the curved solenoid during the Phase-alpha of the experiment. In this paper, the current status of the experiment is presented.

In order to improve the energy and coordinate resolution of the neutral trigger of the СMD-3 detector, it is proposed to use a clustering algorithm based on overlapping “windows” of trigger cells. The window of 2 × 2 crystals is considered to be a single trigger cell, and its signal amplitude value is sent for processing by the trigger system. Based on MonteCarlo simulation, the optimal number of trigger cells to assign to the cluster for energy reconstruction of particles hitting the calorimeter in real time was determined.

The conversion decay w® p0e+e- with the CMD-3 detector on the VEPP-2000 electron-positron collider VEPP-2000 at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences was investigated. The data from the first scan were used in the work, which corresponded to an integral brightness of around 10 pb–1 in the energy range of 660 to 840 MeV in the center of mass system. The 1113 ± 37 signal events were detected. The product of the relative decay probability and ω-meson width G(w® e+e- ) × Br(w® p0e+e- ) = (4, 20 ± 0,12 ± 0, 25) ×10-7 MeV, as well branching ratio Br(w® p0e+e- ) = (6, 78 ± 0,19 ± 0, 40) ×10-4 are measured with better precision than the world average.

The measurement of the cross-section of the processp(+)p???????(-)p(???????0) ??????? with the CMD-3 detector at the electron-positron collider VEPP-2000 in the energy region below 1 GeV in c.m.s. based on a part of the collected statistics with an integrated luminosity of about 16.35 pb(-1) is presented. The measured cross-section has been analyzed in the framework of the vector meson dominance model taking into account the interference of ?, ?, f, ?' , ?" resonances. PACS numbers: 12.40.Vv

The theory of quantum mechanical scattering in hyperbolic space is developed. General formulas based on usage of asymptotic form of the solution of the Shrödinger equation in hyperbolic space are derived. The concept of scattering length in hyperbolic space, a convenient measurable in describing low-energy nuclear interactions is introduced. It is shown that, in the limit of the flat space, i.e., when ρ→∞, the obtained expressions for quantum mechanical scattering in hyperbolic space transform to corresponding formulas in three-dimensional Euclidean space.

The cross section of the process e+ e– → π+ π– π0 was measured with the CMD-3 detector at the electron-positron collider VEPP-2000 in the ω meson energy region based on the data collected in 2013–2018 and corresponding to an integrated luminosity of 40 pb–1. The parameters of the ω-meson: Mω = 782.67 ± 0.01 ± 0.1 MeV, Γω = 8.56 ± 0.02 ± 0.07 MeV, σ0(ω → π+ π– π) = 1629 ± 3 ± 36 nb with the precision match or even exceeding the previous data are obtained.

In this paper, we propose a method for the rejection of the background from the superposition of signals from different, almost simultaneously occurring events in the calorimeter for the COMET experiment. The basic idea is to use the chi-squared distribution obtained from fitting the recorded shape of the signal with an average waveform. The elaborated method is applied for the reconstruction of events with overlapping signals from the electron and radiative capture of neutrons by the 175 Lu nucleus, as well as overlapping signals from two electrons born as a result of the decay of muons in the bound state with an aluminum nucleus with impulses causing a “false” signal of the μ – e conversion. The method showed a good ability to separate events, meanwhile, the separation time is significantly less than the FWHM of the pulse shape.

The cross section of the process e+ e– → π+ π– π0 was measured with the CMD-3 detector at the electron-positron collider VEPP-2000 in the energy region from 750 MeV to 800 MeV in c.m.s. This measurement was based on the data collected in 2013 and related to an integrated luminosity of about 7.8 pb–1. The procedure for obtaining the Born cross section and determining the parameters of the ω-meson was worked out. The preliminary ω-meson parameters mω = 782.70 ± 0.02 ± ± 0.11 MeV, Гω = 8.74 ± 0.05 ± 0.22 MeV, σ0(ω → π+ π– π) = 1545 ± 4 ± 39 nb were obtained. The results were compared with previous data and proven to demonstrate a good agreement with them.

In this paper, based on the definition of the center of mass given in [1, 2], its immobility is postulated in spaces with a constant curvature, and the problem of two particles with an internal interaction, described by a potential depending on the distance between points on a three-dimensional sphere, is considered. This approach, justified by the absence of a principle similar to the Galileo principle on the one hand and the property of isotropy of space on the other, allows us to consider the problem in the map system for the center of mass. It automatically ensures dependence only on the relative variables of the considered points. The Hamilton – Jacobi equation of the problem is formulated, its solutions and the equations of trajectories are found. It is shown that the reduced mass of the system depends on the relative distance. Given this circumstance, a modified system metric is written out.

In this paper, on the basis of the Monte-Carlo simulation results a signal processing algorithm for determination of the energy deposited in real time by incident particles has been developed and implemented in the created electronics prototype of the trigger system for an electromagnetic calorimeter of the COMET experiment. The energy thresholds for trigger cells are determined which make it possible to select signal events – an electron with a momentum of 105 MeV/c, and significantly reduce a rate of background events. The electronics prototype of the trigger system has been verified by testbench measurements and electron beam experiments. The obtained results satisfy the key requirement of the calorimeter – the energy resolution in real time is better than 5 % for the signal electron energy.

Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three-dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of the separation of center mass and relative motion variables for action of two particles into biquaternionic form is formulated. We showed that the algebraic nature of these nonseparable variables follows from the fact that algebra of biquaternions is noncommutative. Some special cases of separation of center mass and relative motion variables are considered.

Some classical and quantum-mechanical problems previously studied in Lobachevsky space are generalized to the extended Lobachevsky space (unification of the real, imaginary Lobachevsky spaces and absolute). Solutions of the Schrödinger equation with Coulomb potential in two coordinate systems of the imaginary Lobachevsky space are considered. The problem of motion of a charged particle in the homogeneous magnetic field in the imaginary Lobachevsky space is treated both classically and quantum mechanically. In the classical case, Hamilton-Jacoby equation is solved by separation of variables, and constraints for integrals of motion are derived. In the quantum case, solutions of Klein-Fock-Gordon equation are found.

We consider the production of magnetic monopoles via γγ fusion at high energy pp collisions. In the assumption that the monopole spin is equal 0, 1/2, 1, the monopole–antimonopole pair production cross-section by this mechanism at LHC energies is estimated and analyzed.