Rare radiativeBdecays to orbitally excitedKmesons

The exclusive rare radiative B meson decays to orbitally excited axial-vector mesons $K_1^{*}\mathrm{}\left(1270\right),\hspace{0.5em}{K}_1\mathrm{}\left(1400\right),$ and to the tensor meson $K_2^{*}\mathrm{}\left(1430\right)\mathrm{}$ are investigated in the framework of the relativistic quark model based on the quasipotential approach in quantum field theory. These decays are considered without employing the heavy quark expansion for the s quark. Instead the s quark is treated to be light and the expansion in inverse powers of the large recoil momentum of the final $K^{**}$ meson is used to simplify calculations. It is found that the ratio of the branching fractions of rare radiative B decays to axial vector $K_1^{*}\mathrm{}\left(1270\right)\mathrm{}$ and $K_1\mathrm{}\left(1400\right)\mathrm{}$ mesons is significantly influenced by relativistic effects. The obtained results for B decays to the tensor meson $K_2^{*}\mathrm{}\left(1430\right)\mathrm{}$ agree with recent experimental data from CLEO and Belle.