Search

The cross section for the $e^+e^-\to K_SK_L$ process is measured in the center-of-mass energy range from 1000 MeV to 1100 MeV in the experiment with the SND detector at the VEPP-2000 $e^+e^-$ collider. The measurement is carried out in the $K_S\to 2\pi^0$ decay mode. Data with an integrated luminosity of 20 pb$^{-1}$ recorded in 2018 at 18 energy points are used in the analysis. The systematic uncertainty in the measured cross section at the maximum of the $\phi$ resonance is 0.9%. The mass, width of the $\phi$ meson, and the product of the branching fractions $B(\phi\to K_SK_L)B(\phi\to e^+e^-)$ are determined from the fit to the cross-section energy dependence., Comment: 14 pages, 12 figures

The $e^+e^-\to n\bar{n}$ cross section was measured at center of mass (c.m.) energies from the threshold to 1908 MeV. The experiment to measure the cross section has been carried out at the VEPP-2000 $e^+e^-$ collider in 13 energy points. The SND detector is used to detect the produced neutron-antineutrons ($n\bar{n}$) events. A special time measurement system on the calorimeter was used to select the time-delayed $n\bar{n}$ events. The measured $e^+e^-\to n\bar{n}$ cross section is 0.4--0.6 nb. The neutron effective timelike form factor in the energy range under study varies from 0.3 to 0.6., Comment: arXiv admin note: substantial text overlap with arXiv:2309.05241

The results of the search for the $e^+e^-\to\eta^{\prime}\gamma$ process in the center-of-mass energy range from 1.075 to 2 GeV are presented. We analyze data with an integral luminosity of 746 pb$^{-1}$ accumulated with the SND detector at the $e^+e^-$ collider VEPP-2000 in 2010--2024. The $\eta^{\prime}\to\eta\pi^0\pi^0$ decay is used in the analysis, with the subsequent $\eta$ and $\pi^0$ decays into $\gamma\gamma$. Upper limits not exceeding 13 pb have been set on the $e^+e^-\to\eta^{\prime}\gamma$ cross section at the 90\% confidence level., Comment: 5 pages, 2 figures. arXiv admin note: text overlap with arXiv:2306.12734

A Thorne-\.{Z}ytkow object can be formed when a neutron star is absorbed by the envelope of its giant companion star, spirals toward the center of the giant star due to the drag from the surrounding envelope, and merges with the star's core. During in-spiral, dynamical friction is the main drag force acting on a neutron star inside the star envelope. However, dynamical friction is caused by the neutron star's gravitational interaction with its own gravitationally induced wake. Therefore, exactly the same gravitational drag force will act on a mirror neutron star, and if a significant part of the dark matter is in the form of mirror matter, then we expect the formation of Thorne-\.{Z}ytkow objects with a mirror neutron star inside. We explore the plausibility of the existence of such exotic Thorne-\.{Z}ytkow objects., Comment: 13 pages, 1 figure, version to be published in Modern Physics Letters A

The results of the measurement of the $e^+e^- \to n \bar{n}$ cross section and effective neutron timelike form factor are presented. The data taking was carried out in 2020-2021 at the VEPP-2000 $e^+e^-$ collider in the center-of-mass energy range from 1891 to 2007 MeV. The general purpose nonmagnetic detector SND is used to detect neutron-antineutron events. The event selection is performed using the time-of-flight technique. The measured cross section is 0.4-0.6 nb. The neutron form factor in the energy range under study varies from 0.3 to 0.2., Comment: 13 pages, 8 figures

The process $e^+e^- \to \omega\pi^0 \to \pi^+\pi^-\pi^0\pi^0$ is studied in the center-of-mass energy region $1.05-2.00$ GeV using data with an integral luminosity of about 35 pb$^{-1}$ collected with the SND detector at the VEPP-2000 $e^+e^-$ collider. In the energy range under study, the value of the measured Born cross section varies from 0.7 to 18 nb. The statistical uncertainty of the cross section is $2-23$%, while the systematic uncertainty is in the range of $3.0-14.2$%. The results are consistent with previous measurements but have better accuracy., Comment: 13 pages, 11 figures

The advent of arXiv has revolutionized scientific communication. However, its cultural significance goes far beyond simply accelerating scholarly communication. The arXiv gave a powerful impetus to the democratization of science, freeing young scientists and not only, especially from totalitarian countries, from authoritarian oppression. Many of arXiv's innovative features have been blurred by the introduction of a moderation system. Without a doubt, a moderation system is essential to maintain the quality of arXiv content. However, I believe that it can be improved in line with arXiv's original intentions, using the very successful experience of the MathOverflow moderation system., Comment: 11 pages, no figures, version published in Journal of Informetrics

The $e^+e^-\to\eta\gamma$ cross section is measured in the center-of-mass energy range from 1.07 to 2.00 GeV in the decay channel $\eta\to 3\pi^0$, $\pi^0\to\gamma\gamma$. The data set with an integrated luminosity of 242 pb$^{-1}$ accumulated in the experiment with the SND detector at the VEPP-2000 $e^+e^-$ collider is analyzed., Comment: 12 pages, 3 figures

The process $e^+e^-\to n\bar n$ is studied in the experiment at the VEPP-2000 $e^+e^-$ collider with the SND detector. The technique of the time measurements in the multichannel NaI(Tl) electromagnetic calorimeter is used to select nnbar events. The value of the measured cross section in the center-of-mass energy range from 1.894 to 2 GeV varies from 0.5 to 0.35 nb. The effective neutron timelike form factor is derived from the measured cross section and compared with the proton form factor. The ratio of the neutron electric and magnetic form factors is obtained from the analysis of the antineutron polar angle distribution and found to be consistent with unity., Comment: 13 pages, 17 figures, 19 references

In this article, we present MuMuPy, a computational library and cloud-based tool for calculating cross sections for the interaction of dimuonium (true muonium) with matter. MuMuPy calculates corresponding form factors and allows one to find the probabilities of dimuonium transitions in the electric field of the nucleus. MuMuPy was developed in the context of the $\mu\mu$-tron facility, the project of a low-energy electron-positron collider for production and experimental study of dimuonium, proposed in our home institute, Budker Institute of Nuclear Physics. The reliability of MuMuPy was verified by three independent methods, one of which was developed by the authors earlier., Comment: Accepted in Computer Physics Communications Added one new reference in this version

The process $e^+e^-\to\eta\eta\gamma$ is studied in the center-of-mass energy range 1.17-2.00 GeV using data with an integrated luminosity of 201 pb$^{-1}$collected by the SND detector at the VEPP-2000 $e^+e^-$ collider. The $e^+e^-\to\eta\eta\gamma$ cross section is measured for the first time. It is shown that the dominant mechanism of this reaction is the transition through the $\phi\eta$ intermediate state. Our result on the $e^+e^-\to\eta\eta\gamma$ cross section is consistent with the $e^+e^-\to\phi\eta$ measurement in the $\phi\to K^+ K^-$ mode. The search for radiative processes contributing to the $e^+e^-\to\eta\eta\gamma$ cross section is performed, and no significant signal is observed., Comment: 6 pages, 3 figures, to be submitted to European Physical Journal C. arXiv admin note: text overlap with arXiv:2006.05465

Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete-discrete transition form factors for hydrogen-like atoms. For comparison, an overview is also given of two other commonly used methods., Comment: 14 pages, no figures, version to be published in Acta Physica Polonica B

It is widely known in quantum mechanics that solutions of the Schr\"{o}inger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein's principle of equivalence. What is usually not so widely known is that solutions of the Schr\"{o}dinger equation with harmonic potential can also be mapped to the solutions of the free Schr\"{o}dinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric., Comment: 28 pages, 1 figure, version to be published in Annals of Physics

Dark photons and mirror matter are well-motivated dark matter candidates. It is possible that both of them arose during the compactification and symmetry breaking scenario of the heterotic $E_8\times E_8$ string theory and are related to each other. In this case, dark photons can become a natural portal into the mirror world. Unfortunately, the expected magnitude of the induced interactions of ordinary matter with mirror matter is too small to be of phenomenological interest., Comment: 9 pages, no figures, revtex4, version to be published in Modern Physics Letters A

We investigate the influence of a dark photon on the Casimir effect and calculate the corresponding leading contribution to the Casimir energy. For expected magnitudes of the photon - dark photon mixing parameter, the influence turns out to be negligible. The plasmon dispersion relation is also not noticeably modified by the presence of a dark photon., Comment: 20 pages, no figures, revtex4. Version to be published in International Journal of Theoretical Physics

The fact that repulsive Rutherford scattering casts a paraboloidal shadow is rarely exploited in introductory mechanics textbooks. Another rarely used construction in such textbooks is the Hamilton vector, a cousin of the more famous Laplace-Runge-Lenz vector. We will show how the latter (Hamilton's vector) can be used to explain and clarify the former (paraboloidal shadow)., Comment: 8 pages, 2 figures, to be published in European Journal of Physics

We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of diffusion in the velocity space are demonstrated in both non-relativistic and relativistic regimes., Comment: 8 pages, 1 figures, to be published in Modern Physics Letters A

A fast leading-order Monte Carlo generator for the process $e^+e^-\to\mu^+\mu^-\gamma$ is described. In fact, using the $e^+e^-\to\mu^+\mu^-\gamma $ process as an example, we provide a pedagogical demonstration of how a Monte Carlo generator can be created from scratch. The $e^+ e^- \to \mu^+ \mu^- \gamma$ process was chosen, since in this case we are not faced with either too trivial or too difficult a task. Matrix elements are calculated using the helicity amplitude method. Monte Carlo algorithm uses the acceptance-rejection method with an appropriately chosen simplified distribution that can be generated using an efficient algorithm. We provide a detailed pedagogical exposition of both the helicity amplitude method and the Monte Carlo technique, which we hope will be useful for high energy physics students., Comment: 28 pages, uses FEYNMAN.tex file for drawing Feynman diagrams, version to be published in The European Physical Journal Plus

In 1995, a team of physicists from the Budker Institute of Nuclear Physics in Novosibirsk was able to observe the splitting of a photon in the Coulomb field of an atomic nucleus for the first time, and reported the preliminary results of this experiment at two conferences. This was an extremely difficult experiment as the probability of the process is very small. It took another seven years to publish the final results. This story has been further developed recently. The ATLAS detector at the Large Hadron Collider observed in ultra-peripheral heavy ion collisions a process related to the photon splitting - light by light scattering. In addition, a team of Italian, Polish and British astrophysicists obtained the first observational evidence of the existence of vacuum birefringence in the magnetic field of an isolated neutron star - another physical phenomenon also related to the photon splitting. These new developments triggered this essay, written several years ago., Comment: 10 pages, in Russian

We estimate the expected magnitudes of the Schumann resonance fields immediately after the Chicxulub impact and show that they exceed their present-day values by about $5\times 10^4$ times. Long-term distortion of the Schumann resonance parameters is also expected due to the enviromental impact of the Chicxulub event. If Schumann resonances play a regulatory biological role, as some studies indicate, it is possible that the excitation and distortion of Schumann resonances as a result of the asteroid/comet impact was a possible stress factor, which, among other stress factors associated with the impact, contributed to the demise of dinosaurs., Comment: 26 pages, no figures, version to be published in Physics Letters A

The dynamics of the process $ e^+e^- \to \pi^+\pi^-\pi^0 $ is studied in the energy region from 1.15 to 2.00 GeV using data accumulated with the SND detector at the VEPP-2000 $e^+e^-$ collider. The Dalitz plot distribution and $\pi^+\pi^-$ mass spectrum are analyzed in a model including the intermediate states $\rho(770)\pi$, $\rho(1450)\pi$, and $\omega\pi^0$. As a result, the energy dependences of the $\rho(770)\pi$ and $\rho(1450)\pi$ cross sections and the relative phases between the $\rho(770)\pi$ amplitude and the $\rho(1450)\pi $ and $\omega\pi^0$ amplitudes are obtained. The $\rho(1450)\pi$ cross section has a peak in the energy region of the $\omega(1650)$ resonance (1.55-1.75 GeV). In this energy range the contributions of the $\rho(770)\pi$ and $\rho(1450)\pi$ states are of the same order of magnitude. No resonance structure near 1.65 GeV is observed in the $\rho(770)\pi$ cross section. We conclude that the intermediate state $\rho(1450)\pi$ gives a significant contribution to the decay of $\omega (1650)\to\pi^+\pi^-\pi^0$, whereas the $\rho(770)\pi$ mechanism dominates in the decay $\omega(1420)\to\pi^+\pi^-\pi^0$., Comment: 9 pages, 7 figures, 3 tables

The process $e^+e^-\to K^+K^-\pi^0$ is studied with the SND detector at the VEPP-2000 $e^+e^-$ collider. Basing on data with an integrated luminosity of 26.4~pb$^{-1}$ we measure the $e^+e^-\to K^+K^-\pi^0$ cross section in the center-of-mass energy range from 1.28 up to 2 GeV. The measured mass spectrum of the $K\pi$ system indicates that the dominant mechanism of this reaction is the transition through the $K^{\ast}(892)K$ intermediate state. The cross section for the $\phi\pi^0$ intermediate state is measured separately. The SND results are consistent with previous measurements in the BABAR experiment and have comparable accuracy. We study the effect of the interference between the $\phi\pi^0$ and $K^\ast K$ amplitudes. It is found that the interference gives sizable contribution to the measured $e^+e^- \to \phi \pi^0\to K^+K^-\pi^0$ cross section below 1.7 GeV.

The process $e^+e^-\to\eta\pi^0\gamma$ is studied in the center-of-mass energy range 1.05-2.00 GeV using data with an integrated luminosity of 94.5 pb$^{-1}$ collected by the SND detector at the VEPP-2000 $e^+e^-$ collider. The $e^+e^-\to\eta\pi^0\gamma$ cross section is measured for the first time. It is shown that the dominant mechanism of this reaction is the transition through the $\omega\eta$ intermediate state. The measured cross section of the subprocess $e^+e^-\to\omega\eta\to\eta\pi^0\gamma$ is consistent with previous measurements in the $e^+e^-\to\pi^+\pi^-\pi^0\eta$ mode. It is found, with a significance of 5.6$\sigma$, that the process $e^+e^-\to\eta\pi^0\gamma$ is not completely described by hadronic vector-pseudoscalar intermediate states. The cross section of this missing contribution, which can originate from radiation processes, e. g. $e^+e^-\to a_{0}(1450)\gamma$, is measured. It is found to be 15-20 pb in the wide energy range from 1.3 to 1.9 GeV., Comment: 10 pages, 6 figures, to be submitted to European Physical Journal C

We calculate the electrostatic potential and electric field of a uniformly charged disk everywhere in space. This electrostatic problem was solved long ago, and its gravitational analogue - even earlier. However, it seems that physics students are not aware of the solution, because it is not presented in textbooks. The purpose of the present article is to fill this gap in the pedagogical literature., Comment: 14 pages, 6 figures, to be published in European Journal of Physics

The cross section of the process $e^+ e^-\to\pi^+\pi^-$ has been measured in the Spherical Neutral Detector (SND) experiment at the VEPP-2000 $e^+e^-$ collider VEPP-2000 in the energy region $525 <\sqrt[]{s} <883$ MeV. The measurement is based on data with an integrated luminosity of about 4.6 pb$^{-1}$. The systematic uncertainty of the cross section determination is 0.8 % at $\sqrt{s}>0.600$ GeV. The $\rho$ meson parameters are obtained as $m_\rho = 775.3\pm 0.5\pm 0.6$ MeV, $\Gamma_\rho = 145.6\pm 0.6\pm 0.8$ MeV, $B_{\rho\to e^+ e^-}\times B_{\rho\to\pi^+\pi^-} = (4.89\pm 0.02\pm 0.04)\times 10^{-5}$, and the parameters of the $e^+ e^-\to\omega\to\pi^+\pi^-$ process, suppressed by $G$-parity, as $B_{\omega\to e^+ e^-}\times B_{\omega\to\pi^+\pi^-}= (1.32\pm 0.06\pm 0.02)\times 10^{-6} $ and $\phi_{\rho\omega} = 110.7\pm 1.5\pm1.0$ degrees.

ISIM(2) symmetry group of Cohen and Glashow's very special relativity is unstable with respect to small deformations of its underlying algebraic structure and according to Segal's principle cannot be a true symmetry of nature. However, like special relativity, which is a very good description of nature thanks to the smallness of the cosmological constant, which characterizes the deformation of the Poincare group, the very special relativity can also be a very good approximation thanks to the smallness of the dimensionless parameter characterizing the deformation of ISIM(2)., Comment: 6 pages, revtex4, to be published in Modern Physics Letters A. The article is heavily based on arXiv:1609.08647

We consider a problem of finding the maximum attainable energy at a cyclotron as an exercise in the introductory relativity course and comment on some subtle points of the solution., Comment: 7 pages, revtex4, to be published in Eur. J. Phys

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., Comment: 11 pages, to be published in The Mathematical Intelligencer

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., Comment: 12 pages, to be published in Physics Letters A

A search for direct production of the $f_1(1285)$ resonance in $e^+e^-$ annihilation is performed with the SND detector at the VEPP-2000 $e^+e^-$ collider. The analysis is based on data with an integrated luminosity of 15.1 pb$^{-1}$ accumulated in the center-of-mass energy range 1.2--1.4 GeV. Two $e^+e^-\to f_1(1285)$ candidate events are found at the peak of the resonance and zero events beyond the resonance. The significance of the $e^+e^-\to f_1(1285)$ signal is $2.5\sigma$. The cross section at the maximum of the resonance is found to be $\sigma(e^+e^-\to f_1)=45^{+33}_{-24}$ pb. The corresponding branching fraction $B(f_1(1285)\to e^+e^-)=(5.1^{+3.7}_{-2.7})\times 10^{-9}$. We consider this result as a first indication of the process $e^+e^-\to f_1(1285)$. The measured branching fraction is consistent with the theoretical prediction., Comment: 11 pages, 4 figures

The process $e^+e^- \to \pi^+\pi^-\pi^0\eta$ 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: $\omega\eta$, $\phi\eta$, $a_0(980)\rho$, and a structureless $\pi^+\pi^-\pi^0\eta$ state. We measure the total $e^+e^- \to \pi^+\pi^-\pi^0\eta$ cross section and the cross sections for its components: $\omega\eta$, $\phi\eta$, and a sum of $a_0(980)\rho$ and the structureless state. Our results are in agreement with previous measurements and have comparable or better accuracies., Comment: 17 pages, 11 figures, 3 tables. arXiv admin note: text overlap with arXiv:1607.00371

Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the canonical commutation relations and hence quantum mechanics at the Planck scale. The corresponding modification of classical mechanics is usually considered by replacing modified quantum commutators by Poisson brackets suitably modified in such a way that they retain their main properties (antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that there exists an alternative interesting possibility. Koopman-Von Neumann's Hilbert space formulation of classical mechanics allows, as Sudarshan remarked, to consider the classical mechanics as a hidden variable quantum system. Then the Planck scale modification of this quantum system naturally induces the corresponding modification of dynamics in the classical substrate. Interestingly, it seems this induced modification in fact destroys the classicality: classical position and momentum operators cease to be commuting and hidden variables do appear in their evolution equations., Comment: 39 pages, ws-ijmpd, version to be published in Int. J. Mod. Phys. D

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., Comment: 23 pages, in Russian

This is a popular lecture about the history of gravitational wave research. Without any doubt, the discovery of gravitational waves is the most important event in the physics of the last decade along with the discovery of the Higgs boson. This landmark discovery is another confirmation of the general theory of relativity, on the basis of which Albert Einstein predicted the existence of gravitational waves in 1916. However, the history of gravitational wave research includes, besides Einstein, many other important players. The author thanks Mikhail Korobko for pointing out the inaccuracy in the first version of the manuscript and Olga Chashchina for her kind help with the text of the manuscript. Any remaining errors and inaccuracies are solely the fault of the author., Comment: 30 pages, in Russian. Incorrectly identified photo has been replaced. Thanks to Mikhail Korobko for pointing out this inaccuracy

The process $e^+e^- \to \pi^0\gamma$ 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 $e^+e^- \to \pi^0\gamma$ 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 $e^+e^- \to \pi^0\gamma$ is studied for the first time., Comment: 7 pages, 5 figures. arXiv admin note: text overlap with arXiv:1601.08061

A search for the rare decay $\eta \rightarrow e^+e^-$ is performed using the inverse process $e^+e^- \rightarrow \eta$ in the decay mode $\eta\to\pi^0\pi^0\pi^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_\eta c ^2\approx 548 $ MeV, and set the upper limit $ {\cal B} (\eta \rightarrow e^+ e^-) < 7 \times 10^{-7} $ at the 90\% confidence level., Comment: 9 pages, 4 figures

The $e^+e^- \to \eta\pi^+\pi^-$ cross section is measured at the SND detector in the $\eta$ decay mode $\eta\to 3\pi^0$. 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 $\eta\to 3\pi^0$ decay mode are found to be in agreement with the previous SND measurements in the $\eta\to \gamma\gamma$ mode. Therefore the measurements in the two modes are combined., Comment: 8 pages, 5 figures

The $e^+e^- \rightarrow K_S K_L \pi^0$ 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., Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. D

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., Comment: 260 pages, 174 figures, in Russian

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., Comment: 5 pages, revtex4, one table, version to be published in Modern Physics Letters A

We comment on the Friedmann and Hagen's quantum mechanical derivation of the Wallis formula for $\pi$. 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., Comment: 11 pages, no figures, version to appear in Physics Letters A

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 $e^+e^- \to \omega \pi^0 \to \pi^0\pi^0\gamma$ 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 $\rho$-like states and used to test the conserved vector current hypothesis in the $\tau^-\to\omega\pi^-\nu_{\tau}$ decay., Comment: 7 pages, 3 figures, 3 tables