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

The exclusive semileptonic $B\to π(ρ) eν$ 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 $π(ρ)$ 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 $Γ(B\to πeν)=(3.1\pm 0.6)\times \vert V_{ub}\vert ^2\times 10^{12}$s${}^{-1}$ and $Γ(B\to ρeν)=(5.7\pm 1.2)\times \vert V_{ub}\vert ^2\times 10^{12}$s${}^{-1}$. The relation between semileptonic and rare radiative $B$-decays is discussed.