Relativistic description of the exclusive rare radiative decays of B mesons

The exclusive rare radiative B 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 vector meson allows for the expansion of the decay form factor in inverse powers of the b-quark mass. This considerably simplifies the analysis of these decays. The 1/${\mathit{m}}_{\mathit{b}}$ expansion is carried out up to second order. The form factor of B→${\mathit{K}}^{\mathrm{*}}$γ decay is found to be ${\mathit{F}}_1^{\mathit{B}\to \mathit{K}\mathrm{*}}$γ(0)=0.32±0.03 and it leads to scrB(B→${\mathit{K}}^{\mathrm{*}}$γ)=(4.5±1.5)×${10}^{\mathrm{-}5}$, which is in agreement with the recent CLEO data. The form factors of the decays B→ργ, ${\mathit{B}}_{\mathit{s}}$→φγ, and ${\mathit{B}}_{\mathit{s}}$→${\mathit{K}}^{\mathrm{*}}$γ are also considered. The relation berween rare radiative and semileptonic B decays into light vector mesons is discussed.