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 $1\mathrm{/}{m}_b$ 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${}^{-1}$\mathrm{.}Therelationbetweensemileptonicandrareradiative$B$-decays is discussed.