Exclusive semileptonic decays of B mesons into light mesons in the relativistic quark model

The exclusive semileptonic $B\to \pi(\rho) e\nu$ decays are studied in the framework of the relativistic quark model based on the quasipotential approach in quantum field theory. The large recoil momentum of the final $\pi(\rho)$ meson allows for the expansion of the decay form factors at $q^2=0$ in the inverse powers of $b$-quark mass. This considerably simplifies the analysis of these decays. The $1/m_b$ expansion is carried out up to the first order. It is found that the $q^2$-dependence of the axial form factor $A_1$ is different from the $q^2$-behaviour of other form factors. We find $\Gamma(B\to \pi e\nu)=(3.1\pm 0.6)\times \vert V_{ub}\vert ^2\times 10^{12}$s${}^{-1}$ and $\Gamma(B\to \rho e\nu)=(5.7\pm 1.2)\times \vert V_{ub}\vert ^2\times 10^{12}$s${}^{-1}$. The relation between semileptonic and rare radiative $B$-decays is discussed.Comment: 11 pages, Latex, 3 figure

Termination of Original F5

The original F5 algorithm introduced by Faug\`ere is formulated for any homogeneous polynomial set input. The correctness of output is shown for any input that terminates the algorithm, but the termination itself is proved only for the case of input being regular polynomial sequence. This article shows that algorithm correctly terminates for any homogeneous input without any reference to regularity. The scheme contains two steps: first it is shown that if the algorithm does not terminate it eventually generates two polynomials where first is a reductor for the second. But first step does not show that this reduction is permitted by criteria introduced in F5. The second step shows that if such pair exists then there exists another pair for which the reduction is permitted by all criteria. Existence of such pair leads to contradiction. Version v3 fixes the bibliography

Rare radiative B decay to the orbitally excited K_2^*(1430) meson

The exclusive rare radiative B meson decay to the orbitally excited tensor K_2^*(1430) meson is investigated in the framework of the relativistic quark model based on the quasipotential approach in quantum field theory. The calculated branching ratio BR(B --> K_2^*(1430)\gamma)=(1.7\pm 0.6)\times 10^{-5} as well as the ratio BR(B --> K_2^*(1430)\gamma)/BR(B --> K^*(892)\gamma)=0.38\pm 0.08 is found in a good agreement with recent experimental data from CLEO.Comment: 10 pages, RevTe

New analysis of semileptonic B decays in the relativistic quark model

We present the new analysis of the semileptonic B decays in the framework of the relativistic quark model based on the quasipotential approach. Decays both to heavy D^{(*)} and light \pi(\rho) mesons are considered. All relativistic effects are systematically taken into account including contributions of the negative-energy states and the wave function transformation from the rest to moving reference frame. For heavy-to-heavy transitions the heavy quark expansion is applied. Leading and subleading Isgur-Wise functions are determined as the overlap integrals of initial and final meson wave functions. For heavy-to-light transitions the explicit relativistic expressions are used to determine the dependence of the form factors on the momentum transfer squared. Such treatment significantly reduces theoretical uncertainties and increases reliability of obtained predictions. All results for form factors, partial and total decay rates agree well with recent experimental data and unquenched lattice calculations. From this comparison we find the following values of the Cabibbo-Kobayashi-Maskawa matrix elements: |V_{cb}|=(3.85\pm0.15\pm 0.20)*10^{-2} and |V_{ub}|=(3.82\pm0.20\pm0.20)*10^{-3}, where the first error is experimental and the second one is theoretical.Comment: 25 pages, 11 figure