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The leptonic decay widths of heavy quarkonia are complementary observables to the semileptonic decays of heavy mesons and provide additional insight into the possible lepton flavor universality breaking. We analyze the former in the framework of the covariant confined quark model, introducing a novel approach for the description of the radially excited quarkonia states, which is based on constituent quark mass running and the orthogonality of the states. We are able to describe the experimental observations by our approach within the Standard model, which does not support new physics explanations.

The damped oscillating structures (OS) were recently revealed in the proton "effective" form factor (FF) data. For the time being they can be neither confirmed nor disproved by investigations of timelike data on the individual proton electric and proton magnetic FFs because their precision and reliability (especially of the proton electric FF data) has not achieved required level for this aim. On the other hand, conjectures that the OS are direct manifestations of the quark-gluon structure of the proton indicate that they must not be specific only for the proton and neutron, but that they should be present also for other hadrons. This opens a plausibility to find damped oscillatory structures also from the EM FFs data of such hadrons, for which adequate EM FFs data exist, by using the same procedure as for the proton. Consequently in this paper damped oscillatory structures are investigated in the EM FFs data of the charged and neutral $K$-mesons to be extracted from the corresponding production cross sections, $\sigma^{bare}_{tot}(e^+e^-\to K^+ K^-)$ measured from the threshold up to 64 GeV$^2$ and $\sigma^{bare}_{tot}(e^+e^-\to K_s K_L)$ measured from the threshold up to 9.5 GeV$^2$ of the total c.m. energy squared. The following results have been obtained. If the charged and neutral K-meson EM FFs timelike data are described by the three parametric formula by means of which OS have been revealed from the "effective" proton FF data then OS appear. If physically well founded Unitary and Analytic model of the K-meson EM structure is used for a description of the charged K-meson EM FFs data, no OS are visible. However, in the case of the neutral K-meson EM FF data one cannot make a definite decision. The overall results indicate that OS obtained from the "effective" proton FF data are likely an artefact of the three parametric formula which does not describe these data well.

The aim of this text to present the covariant confined quark model (CCQM) and review its applications to the decays of $B$ mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we review also. The physics principles are in detail exposed for the CCQM, the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering successively three categories of decay processes: leptonic, semileptonic and non-leptonic.

Very precise satellite photometry has revealed a large number of variable stars whose variability is caused either by surface spots or by binarity. Detailed studies of such variables provide insights into the physics of these objects. We study the nature of the periodic light variability of the white dwarf EPIC 206197016 that was observed by the K2 mission. We obtain phase-resolved medium-resolution spectroscopy of EPIC 206197016 using XSHOOTER spectrograph at VLT to understand the nature of the white dwarf variability. We use NLTE model atmospheres to determine stellar parameters at individual phases. EPIC 206197016 is a hot DA white dwarf with $T_\text{eff}=78\,$kK. The analysis of the spectra reveals periodic radial velocity variations that can result from gravitational interaction with an invisible secondary whose mass corresponds to a red dwarf. The close proximity of the two stars where the semimajor axis is about $3\,R_\odot$ results in the irradiation of the companion with temperatures more than twice as high on the illuminated side compared to the nonilluminated hemisphere. This effect can explain the observed light variations. The spectra of the white dwarf show a particular feature of the Balmer lines called the Balmer line problem, where the observed cores of the lower Balmer lines are deeper than predicted. This can be attributed to either weak pollution of hydrogen in the white dwarf atmosphere by heavy elements or to the presence of a circumstellar cloud or disk., Comment: 8 pages, accepted for publication in Astronomy & Astrophysics

Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented ideas may have applications in numerical mathematics.

Decay processes $B\rightarrow D_{\left(s\right)}^{\left(*\right)}h$ ($h=\pi,\rho$) are studied in the framework of the confined covariant quark model using the na\"{i}ve factorization assumption. We observe that the theoretical results on branching fractions have tendency to systematically exceed the experimental numbers. Such a behavior has already been seen for similar processes by other authors.

Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that $c_n^f = \mathcal{C}_n \left(\mathcal{A}_N^f \right)$. All known approximations can be interpreted in this way and we review some of them. In addition, we construct several new expansion types including three rational approximations.

Ultraprecise space photometry enables us to reveal light variability even in stars that were previously deemed constant. A large group of such stars show variations that may be rotationally modulated. This type of light variability is of special interest because it provides precise estimates of rotational rates. We aim to understand the origin of the light variability of K2 targets that show signatures of rotational modulation. We used phase-resolved medium-resolution XSHOOTER spectroscopy to understand the light variability of the stars KIC~250152017 and KIC~249660366, which are possibly rotationally modulated. We determined the atmospheric parameters at individual phases and tested the presence of the rotational modulation in the spectra. KIC 250152017 is a HgMn star, whose light variability is caused by the inhomogeneous surface distribution of manganese and iron. It is only the second HgMn star whose light variability is well understood. KIC 249660366 is a He-weak, high-velocity horizontal branch star with overabundances of silicon and argon. The light variability of this star is likely caused by a reflection effect in this post-common envelope binary., Comment: 8 pages, accepted for publication in Astronomy & Astrophysics

We treat the $Y(4260)$ resonance as a four-quark state in the framework of the covariant confining quark model. We study two choices of the interpolating current, either the molecular-type current which effectively corresponds to the product of $D$ and $\bar D_1$ quark currents or tetraquark one. In both cases we calculate the widths of decays $Y(4260)\to Z_c(3900)+\pi$ and $Y(4260)\to D^{(\ast)}+\bar D^{(\ast)}$. It is found that in both approches the mode $Y\to Z^+_c + \pi^-$ is enhanced compared with the open charm modes. However the absolute value of the $Y\to Z^+_c + \pi^-$ decay width obtained in molecular picture is arguably too large. On the other hand the value obtained in tetraquark picture is reasonable., Comment: 12 pages, 1 figure

Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which use one-dimensional integrals is presented together with some interesting non-analytic weight functions., Comment: 8 pages

We study the rare radiative leptonic decays $B_s\to\ell^+\ell^-\gamma$ ($\ell=e,\mu,\tau$) within the Standard Model, considering both the structure-dependent amplitude and bremsstrahlung. In the framework of the covariant confined quark model developed by us, we calculate the form factors characterizing the $B_s\to\gamma$ transition in the full kinematical region of the dilepton momentum squared and discuss their behavior. We provide the analytic formula for the differential decay distribution and give predictions for the branching fractions in both cases: with and without long-distance contributions. Finally, we compare our results with those obtained in other approaches., Comment: 22 pages, 8 figures, 6 tables, more references and material added, a version to appear on PRD

In the wake of recent measurements of the decays $B_c^+\to J/\psi D^+_s$ and $B_c^+\to J/\psi D^{\ast\,+}_s$ performed by the LHCb and ATLAS Collaborations, we recalculate their branching fractions in the framework of the covariant confined quark model. We compare the obtained results with available experimental data, our previous findings and numbers from other approaches., Comment: 15 pages, 2 figures

If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution, interpreted as the value of the quantity of interest, can be determined with better precision than what is the precision provided by a single algorithm. Often, with lack of enough independent algorithms, one can proceed differently: many practical algorithms introduce a bias using a parameter, e.g. a small but finite number to compute a limit or a large but finite number (cutoff) to approximate infinity. One may vary such parameter of a single algorithm and interpret the resulting numbers as generated by several algorithms. A numerical evidence for the validity of this approach is shown for differentiation.

Our article is devoted to the study of the rare $B_s\to \phi \ell^+\ell^-$ decay where $\ell=\mu,\tau$. We compute the relevant form factors in the framework of the covariant quark model with infrared confinement in the full kinematical momentum transfer region. The calculated form factors are used to evaluate branching fractions and polarization observables in the cascade decay $B\to \phi(\to K^+K^-)\ell^+\ell^-$. We compare the obtained results with available experimental data and the results from other theoretical approaches., Comment: 16 pages, 13 figures. arXiv admin note: text overlap with arXiv:1511.04887

Our article is devoted to the study of the rare $B\to K^\ast \ell^+\ell^-$~decay where $\ell=e,\mu,\tau$. We compute the relevant form factors in the framework of the covariant quark model with infrared confinement in the full kinematical momentum transfer region. The calculated form factors are used to evaluate branching fractions and polarization observables in the cascade decay $B\to K^\ast(\to K\pi)\ell^+\ell^-$. We compare the obtained results with available experimental data and the results from other theoretical approaches., Comment: 39 pages, 11 figures. References and discussion added. Accepted by Few-Body Systems for publication. arXiv admin note: text overlap with arXiv:hep-ph/0608015 by other authors

The pion scalar form factor along with all existing S-wave iso-scalar $\pi\pi$-scattering phase shift data in the elastic region up to $1 {\rm GeV}^2$ are applied for a determination of the $f_0(500)$ and $f_0(980)$ meson parameters $m_{f_0(500)}=(360\pm33){\rm MeV}$, $\Gamma_{f_0(500)}=(587\pm 85){\rm MeV}$ and $m_{f_0(980)}=(957\pm77) {\rm MeV}$, $\Gamma_{f_0(980)}=(164\pm142){\rm MeV}$ in a model independent way., Comment: 13 pages, 3 figures, submitted to Phys.Rev.D

The covariant quark model represents an appropriate theoretical framework to describe the recent results on $B_{s}\rightarrow J/\psi+\eta$ and $B_{s}\rightarrow J/\psi+\eta'$ decays from the Belle collaboration. In this article we present the main features of he covariant quark model together with details on some of its aspects and methods, which we consider to be important. Further we apply the model specifically to the studied decay processes and give numerical results on decay widths as they follow from the odel. We conclude that the model, with most of its parameters previously fixed from different processes, is able to incorporate the new measurements from the Belle experiment., Comment: 14 pages, 1 figure; v2: more discussions and references are added, version accepted for publication in PRD

New precise experimental information on $\sigma_{tot}(e^+e^- \to \pi^+ \pi^-)$ is transferred into the space-like region, by taking advantage of the analyticity. As a result a rigorous pion electromagnetic form factor behavior is obtained. The latter with some existing model predictions is compared., Comment: 8 pages, 3 eps figures

By means of the universal unitary and analytic model of electromagnetic structure of hadrons the two-photon decay rates of P=pi^0, eta, eta' mesons are determined in an alternative way from data on their transition form factors., Comment: 7 pages, 6 eps figures. Lecture given at Hadron Structure and QCD: from LOW to HIGH energies, Gatchina, Russia, July 5 - July 9, 2010

We use the unitary and analytic model of the pion electromagnetic form factor in order to evaluate in the lowest order the $e^{+}e^{-}\to\pi^{+}\pi^{-}$ contribution into the muon magnetic anomaly. We demonstrate, that this technique enables us to reduce the uncertainty of the theoretical prediction importantly in comparison to usual approaches, where the measured data are integrated directly., Comment: 5 Latex pages,1 figure. Talk at the HSQCD 2009 Int. Conference, Tatranska Strba, 29.8.3.9.2009, Slovak Republic

The present situation on a comparison of theoretical evaluation of the muon anomalous magnetic moment with experimental one is roughly reviewed. Then by means of a recently elaborated unitary and analytic model of the meson transition form factors the contributions of $e^+e^-\to P(S) \gamma$ processes to muon $g-2$ is estimated., Comment: 12 pages, 9 figures. Contribution presented at Pisa SIGHAD03, Workshop on Hadronic Cross Section at Low Energy, October 8-10, 2003, Italy