Exclusive $B\to K^{**} \gamma$ Decays in the QCD LCSR 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 (LCSR). Our calculations are restricted to the leading twist-two operators for $K^*(892)$ and to the asymptotic wave function for the other $K^{**}$-mesons. Using experimental data on the semileptonic $\tau\to K^{**}\nu_{\tau}$ decays, we extract the corresponding decay constants for vector and axial-vector $K^{**}$-mesons. We present results for the corresponding branching ratios and compare them with the existing theoretical predictions.