The Radiative rare decays $B\to K^{\ast \ast }\gamma$ in the light-cone QCD sum rule approach

We predict contributions of higher $K$-resonances to the radiative rare decays $b\to s\gamma$, in the framework of the QCD sum rules on the light cone, which combines the traditional QCD sum rule method with the description of final state mesons in terms of the light-cone wave functions of increasing twist. Our calculations are restricted to the leading twist-two operators for $K^{\ast }(892)$ and to the asymptotic wave function for the other $K^{\ast \ast }$-mesons. Using experimental data on the semileptonic $\tau \to K^{\ast \ast }{\nu }_{\tau }$ decays, we extract the corresponding decay constants for vector and axial-vector $K^{\ast \ast }$-mesons. Based on our estimate of the transition form factor $F_1^{K^{\ast }(892)}(0)=0.32\pm 0.06$ and the $K_2^{\ast }(1430)$ decay constant $f_{K_2^{\ast }(1430)}=(160\pm 20)MeV$, we find good agreement with experimental results. The two largest fractions of the inclusive $b\to s\gamma$ branching ratio are found to be $(10.0\pm 4.0)$ for $B\to K^{\ast }(892)\gamma$ and $(5.0\pm 2.0)%$for$B\to K_2^*(1430)\gamma$ decays. We also compare our results with the existing theoretical predictions.