Relativistic Description of Exclusive Semileptonic Decays of Heavy Mesons

Using quasipotential approach, we have studied exclusive semileptonic decays of heavy mesons with the account of relativistic effects. Due to more complete relativistic description of the $s$ quark more precise expressions for semileptonic form factors are obtained. Various differential distributions in exclusive semileptonic decays of heavy mesons are calculated. It is argued that consistent account of relativistic effects and HQET motivated choice of the parameters of quark-antiquark potential allow to get reliable value for the ratio $A_2(0)/A_1(0)$ in the $D\to K^*l\nu_l$ decay as well as the ratio~$\Gamma(D\to K^*l\nu_l)/\Gamma(D\to Kl\nu_l)$. All calculated branching ratios are in accord with available experimental data.Comment: 18 pages, LATEX, 2 figures inclosed + 4 Postscript figure

Quark-antiquark potential with retardation and radiative contributions and the heavy quarkonium mass spectra

The charmonium and bottomonium mass spectra are calculated with the systematic account of all relativistic corrections of order v^2/c^2 and the one-loop radiative corrections. Special attention is paid to the contribution of the retardation effects to the spin-independent part of the quark-antiquark potential, and a general approach to accounting for retardation effects in the long-range (confining) part of the potential is presented. A good fit to available experimental data on the mass spectra is obtained.Comment: 20 pages, revtex, 2 Postscript figure

Exclusive semileptonic B decays to radially excited D mesons

Exclusive semileptonic B decays to radially excited charmed mesons are investigated at the first order of the heavy quark expansion. The arising leading and subleading Isgur-Wise functions are calculated in the framework of the relativistic quark model. It is found that the 1/m_Q corrections play an important role and substantially modify results. An interesting interplay between different corrections is found. As a result the branching ratio for the B-> D'e\nu decay is essentially increased by 1/m_Q corrections, while the one for B-> D*'e\nu is only slightly influenced by them.Comment: 19 pages, revtex, 6 figures, uses rotating.st

Collective modes for an array of magnetic dots in the vortex state

The dispersion relations for collective magnon modes for square-planar arrays of vortex-state magnetic dots, having closure magnetic flux are calculated. The array dots have no direct contact between each other, and the sole source of their interaction is the magnetic dipolar interaction. The magnon formalism using Bose operators along with translational symmetry of the lattice, with the knowledge of mode structure for the isolated dot, allows the diagonalization of the system Hamiltonian giving the dispersion relation. Arrays of vortex-state dots show a large variety of collective mode properties, such as positive or negative dispersion for different modes. For their description, not only dipolar interaction of effective magnetic dipoles, but non-dipolar terms common to higher multipole interaction in classical electrodynamics can be important. The dispersion relation is shown to be non-analytic as the value of the wavevector approaches zero for all dipolar active modes of the single dot. For vortex-state dots the interdot interaction is not weak, because, the dynamical part (in contrast to the static magnetization of the vortex state) dot does not contain the small parameter, the ratio of vortex core size to the dot radius. This interaction can lead to qualitative effects like the formation of modes of angular standing waves instead of modes with definite azimuthal number known for the insolated vortex state dot

Relativistic Description of Exclusive Heavy-to-Light Semileptonic Decays B→π(ρ)eνB\to\pi(\rho)e\nu

The method of calculating electroweak decay matrix elements between heavy-heavy and heavy-light meson states is developed in the framework of relativistic quark model based on the quasipotential approach in quantum field theory. This method is applied for the study of exclusive semileptonic $B\to\pi(\rho)$ decays. It is shown that the large value of the final $\pi(\rho)$ meson recoil momentum allows for the expansion in inverse powers of $b$-quark mass of the decay form factors at $q^2=0$, where $q^2$ is a momentum carried by the lepton pair. This $1/m_b$ expansion considerably simplifies the analysis of these decays and is carried out up to the second order. The $q^2$-dependence of the form factors is investigated. It is found that the $q^2$-behaviour of the axial form factor $A_1$ is different from the other form factors. It is argued that the ratios $\Gamma(B\to\rho e\nu)/\Gamma(B\to\pi e\nu)$ and $\Gamma_L/\Gamma_T$ are sensitive probes of the $A_1$ $q^2$-dependence, and thus their experimental measurement may discriminate between different approaches. We find $\Gamma(B\to\pi e\nu)=(3.0\pm0.6) \times|V_{ub}|^2\times10^{12}$s$^{-1}$ and $\Gamma(B\to\rho e\nu) =(5.4\pm 1.2)\times|V_{ub}|^2\times10^{12}$s$^{-1}$. The relation between semileptonic and rare radiative $B$-decays is discussed.Comment: 20 pages, two figures included, LATE

Solvent effect on kinetics and mechanism of the phospha-michael reaction of tertiary phosphines with unsaturated carboxylic acids

In aprotic solvents, kinetics of the reaction of triphenylphosphine with acrylic acid is second order in the acid and first order in the phosphine. To find the most suitable model to describe the solvent effect on this reaction, the third-order rate constants in a series of 16 aprotic solvents were analyzed using one- and multiparameter regressions within the framework of the Kamlet-Taft, the Catalán, the Gutmann-Mayer, and the Koppel-Palm equations. The best result gives a two-parameter model constructed on the basis of the Reichardt polarity ET and the basicity B from the Koppel-Palm equation, with the weak positive effect of the ET parameter on the reaction rate and very strong negative effect of the B parameter. The results obtained give further evidence to the previously suggested a stepwise mechanism, which involves the initial formation of a zwitterionic intermediate, followed by the proton transfer from the second molecule of acrylic acid to the generated carbanionic center in the rate-determining step. © 2014 Wiley Periodicals, Inc

Weak decays of the B_c meson to charmonium and D mesons in the relativistic quark model

Semileptonic and nonleptonic decays of the B_c meson to charmonium and D mesons are studied in the framework of the relativistic quark model. The decay form factors are explicitly expressed through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The relativistic meson wave functions are used for the calculation of the decay rates. The obtained results are compared with the predictions of other approaches.Comment: 27 pages, 17 figures, 1 figure and 1 reference added, version to appear in Phys. Rev.

Nonlinear viscosity and velocity distribution function in a simple longitudinal flow

A compressible flow characterized by a velocity field $u_x(x,t)=ax/(1+at)$ is analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook kinetic model. The sign of the control parameter (the longitudinal deformation rate $a$) distinguishes between an expansion ($a>0$) and a condensation ($a<0$) phenomenon. The temperature is a decreasing function of time in the former case, while it is an increasing function in the latter. The non-Newtonian behavior of the gas is described by a dimensionless nonlinear viscosity $\eta^*(a^*)$, that depends on the dimensionless longitudinal rate $a^*$. The Chapman-Enskog expansion of $\eta^*$ in powers of $a^*$ is seen to be only asymptotic (except in the case of Maxwell molecules). The velocity distribution function is also studied. At any value of $a^*$, it exhibits an algebraic high-velocity tail that is responsible for the divergence of velocity moments. For sufficiently negative $a^*$, moments of degree four and higher may diverge, while for positive $a^*$ the divergence occurs in moments of degree equal to or larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat flux plus other minor changes added. Revised version accepted for publication in PR

Magnetic vortex as a ground state for micron-scale antiferromagnetic samples

Here we consider micron-sized samples with any axisymmetric body shape and made with a canted antiferromagnet, like hematite or iron borate. We find that its ground state can be a magnetic vortex with a topologically non-trivial distribution of the sublattice magnetization $\vec{l}$ and planar coreless vortex-like structure for the net magnetization $\vec{M}$. For antiferromagnetic samples in the vortex state, in addition to low-frequency modes, we find high-frequency modes with frequencies over the range of hundreds of gigahertz, including a mode localized in a region of radius $\sim$ 30--40 nm near the vortex core.Comment: 20 pages, 1 figur