Development of Methods for Determining the Coordinates of Firing Positions of Roving Mortars by A Network of Counter-battery Radars

The mathematical formulation of the problem of determining the coordinates of targets in the network of counter-battery radars is formulated. It has been established that the problem of estimating the coordinates of targets in the network of counter-battery radars for an excessive number of estimates of primary coordinates should be considered as a statistical problem. The method for determining the coordinates of the firing positions of roving mortars has been improved, in which, in contrast to the known ones, the coordinates of targets on the flight trajectory are coordinated with space and time and the information is processed by a network of counter-battery radars. The developed simulation mathematical model for determining the coordinates of the firing positions of roving mortars by a network of counter-battery radars. Simulation modeling of the method for determining the coordinates of the firing positions of roving mortars by a network of counter-battery radars has been carried out. It has been established that the use of a network of radars makes it possible to increase the accuracy of determining the coordinates of the firing means on average from 23 % to 71 %, depending on the number of counter-battery radars in the network. It has also been found that the appropriate number of counter-battery warfare radars in the network is three or four. A further increase in the number of counter-battery warfare radars in the network does not lead to a significant increase in the accuracy of determining the coordinates of artillery and mortar firing positions. In carrying out further research, it is necessary to develop a method for the spatial separation of elements of a group of targets and interfering objects by a network of counter-battery warfare radar

Test of light-lepton universality in τ\tau decays with the Belle II experiment

International audienceWe present a measurement of the ratio $R_\mu = \mathcal{B}(\tau^-\to \mu^-\bar\nu_\mu\nu_\tau) / \mathcal{B}(\tau^-\to e^-\bar\nu_e\nu_\tau)$ of branching fractions $\mathcal{B}$ of the $\tau$ lepton decaying to muons or electrons using data collected with the Belle II detector at the SuperKEKB $e^+e^-$ collider. The sample has an integrated luminosity of 362 fb$^{-1}$ at a centre-of-mass energy of 10.58 GeV. Using an optimised event selection, a binned maximum likelihood fit is performed using the momentum spectra of the electron and muon candidates. The result, $R_\mu = 0.9675 \pm 0.0007 \pm 0.0036$, where the first uncertainty is statistical and the second is systematic, is the most precise to date. It provides a stringent test of the light-lepton universality, translating to a ratio of the couplings of the muon and electron to the $W$ boson in $\tau$ decays of $0.9974 \pm 0.0019$, in agreement with the standard model expectation of unity