arXiv subjects
Publications and source records attributed to Z. K. Silagadze.
Some time ago Wastlund reformulated the Basel problem in terms of a physical system using the proportionality of the apparent brightness of a star to the inverse square of its distance. Inspired by this approach, we give another physical interpretation which, in our opinion, is simpler, natural enough, and very Eulerian in its spirit.
Ulmer and Kaissl formulas for the deconvolution of one-dimensional Gaussian kernels are generalized to the three-dimensional case. The generalization is based on the use of the scalar version of the Grad's multivariate Hermite polynomials which can be expressed through ordinary Hermite polynomials.
The process $e^+e^- \to π^+π^-π^0η$ is studied in the center-of-mass energy region below 2 GeV with the SND detector at the VEPP-2000 $e^+e^-$ collider. The four intermediate states contribute to this process: $ωη$, $ϕη$, $a_0(980)ρ$, and a structureless $π^+π^-π^0η$ state. We measure the total $e^+e^- \to π^+π^-π^0η$ cross section and the cross sections for its components: $ωη$, $ϕη$, and a sum of $a_0(980)ρ$ and the structureless state. Our results are in agreement with previous measurements and have comparable or better accuracies.
This is the second of a series of popular lectures on quantum chromodynamics. The first (introductory) lecture can be found here: https://scfh.ru/blogs/O_fizike_i_fizikah/polet-nad-kvantovoy-khromodinamikoy/ The lecture deals with the one of the main pillars of quantum chromodynamics --- quantum mechanics . Non-physicists usually consider quantum mechanics as an extremely weird subject far from the everyday common sense. Partly this is true. However we will try to argue in this lecture that in its essence quantum mechanics is, in a some sense, even more natural than classical mechanics, and it is not so far from the common sense as a layman usually assumes.
The process $e^+e^- \to π^0γ$ is studied with the SND detector at the VEPP-2000 $e^+e^-$ collider. Basing on data with an integrated luminosity of 41 pb$^{-1}$ recorded in 2010-2012 we measure the $e^+e^- \to π^0γ$ cross section in the center-of-mass energy range from 1.075 up to 2 GeV. In the range 1.4-2.0 GeV the process $e^+e^- \to π^0γ$ is studied for the first time.
A search for the rare decay $η\rightarrow e^+e^-$ is performed using the inverse process $e^+e^- \rightarrow η$ in the decay mode $η\toπ^0π^0π^0 $. We analyze data with an integrated luminosity of 654 nb$^{-1} $ accumulated at the VEPP-2000 $e^+e^-$ collider with the SND detector at the center-of-mass energy $E=m_ηc ^2\approx 548 $ MeV, and set the upper limit $ {\cal B} (η\rightarrow e^+ e^-) < 7 \times 10^{-7} $ at the 90\% confidence level.
The manual contains (in Russian) solutions of 230 problems that were used by the author for a number of years at the tutorial seminars in the first year undergraduate course in Mechanics and special relativity at Novosibirsk State University. The manual consists of 36 chapters - according to the number of seminars in this course. In each chapter, from 5 to 10 problems are dealt with. Where possible, several solutions of the same problem are given in order the students to become used to treating physical phenomena from different points of view. Most problems are taken from the problem book Yu.I. Belchenko, E.A. Gilev, Z.K. Silagadze, V.G. Sokolov, Collection of problems in the mechanics of particles and bodies, Novosibirsk: NSU, 2000. For such problems, the corresponding number in the problem book is indicated in parentheses.
The $e^+e^- \rightarrow K_S K_L π^0$ cross section is measured in the center-of-mass energy range $\sqrt{s}=1.3-2.0$ GeV. The analysis is based on the data sample with an integrated luminosity of 33.5 pb$^{-1}$ collected with the SND detector at the VEPP-2000 $e^+e^-$ collider.
Schumann resonance transients which propagate around the globe can potentially generate a correlated background in widely separated gravitational wave detectors. We show that due to the distribution of lightning hotspots around the globe these transients have characteristic time lags, and this feature can be useful to further suppress such a background, especially in searches of the stochastic gravitational-wave background. A brief review of the corresponding literature on Schumann resonances and lightnings is also given.
The $e^+e^- \to ηπ^+π^-$ cross section is measured at the SND detector in the $η$ decay mode $η\to 3π^0$. The analysis is based on the data sample with an integrated luminosity of 32.7 pb$^{-1}$ collected at the VEPP-2000 $e^+e^-$ collider in the center-of-mass energy range $\sqrt{s}=1.075-2.000$ GeV. The data obtained in the $η\to 3π^0$ decay mode are found to be in agreement with the previous SND measurements in the $η\to γγ$ mode. Therefore the measurements in the two modes are combined.
We comment on the Friedmann and Hagen's quantum mechanical derivation of the Wallis formula for $π$. In particular, we demonstrate that not only the Gaussian trial function, used by Friedmann and Hagen, but also the Lorentz trial function can be used to get the Wallis formula. The anatomy of the integrals leading to the appearance of the Wallis ratio is carefully revealed.
We analyze a 37 pb$^{-1}$ data sample collected with the SND detector at the VEPP-2000 $e^+e^-$ collider in the center-of-mass energy range 1.05--2.00 GeV and present an updated measurement of the $e^+e^- \to ωπ^0 \to π^0π^0γ$ cross section. In particular, we correct the mistake in radiative correction calculation made in our previous measurement based on a part of the data. The measured cross section is fitted with the vector meson dominance model with three $ρ$-like states and used to test the conserved vector current hypothesis in the $τ^-\toωπ^-ν_τ$ decay.
New results on exclusive hadron production in $e^+e^-$ annihilation obtained in experiments with the SND detector at the VEPP-2M and VEPP-2000 $e^+e^-$ colliders are presented.
The $e^+e^-\to K^+K^-$ cross section is measured in the center-of-mass energy range $1.05-2.00$ GeV at the SND detector. The measurement is based on data with an integrated luminosity of 35 pb$^{-1}$ collected at the VEPP-2000 $e^+e^-$-collider. The obtained results are consistent with the previous most accurate data obtained in the BABAR experiment and have a comparable accuracy.
The process $e^+e^-\toωηπ^0$ is studied in the energy range $1.45-2.00$ GeV using data with an integrated luminosity of 33 pb$^{-1}$ accumulated by the SND detector at the $e^+e^-$ collider VEPP-2000. The $e^+e^-\toωηπ^0$ cross section is measured for the first time. The cross section has a threshold near 1.75 GeV. Its value is about 2 nb in the energy range $1.8-2.0$ GeV. The dominant intermediate state for the process $e^+e^- \to ωηπ^0$ is found to be $ωa_0(980)$.
The cross section for the process $e^+e^- \to ωη$ is measured in the center-of-mass energy range 1.34--2.00 GeV. The analysis is based on data collected with the SND detector at the VEPP-2000 $e^+e^-$ collider. The measured $e^+e^- \to ωη$ cross section is the most accurate to date. A significant discrepancy is observed between our data and previous BABAR measurement.
The process $e^+e^- \to π^0γ$ has been studied in the experiment with the SND detector at the VEPP-2M $e^+e^-$ collider. The $e^+e^- \to π^0γ$ cross section has been measured in the center-of-mass energy range from 0.60 to 1.38 GeV. The cross section is well described by the vector meson dominance model. From the fit to the cross section data we have determined the branching fractions $B(ρ\toπ^0γ)=(4.20\pm0.52)\times10^{-4}$, $B(ω\toπ^0γ)=(8.88\pm0.18)\%$, $B(ϕ\toπ^0γ)=(1.367\pm0.072)\times10^{-3}$, and the relative phase between the $ρ$ and $ω$ amplitudes $φ_ρ=(-12.7\pm4.5)^\circ$. Our data on the process $e^+e^- \to π^0γ$ are the most accurate to date.
We comment on the recent paper "Note on the perihelion/periastron advance due to cosmological constant" by H. Arakida (Int. J. Theor. Phys. 52 (2013) 1408-1414, arXiv:1212.6289) and provide simple derivations both of the main result of this paper and of the Adkins-McDonnell's precession formula, on which this main result is based.