Radiative B decays to the axial K mesons at next-to-leading order

We calculate the branching ratios of $B\to K_1\gamma$ at next-to-leading order (NLO) of $\alpha_s$ where $K_1$ is the orbitally excited axial vector meson. The NLO decay amplitude is divided into the vertex correction and the hard spectator interaction part. The one is proportional to the weak form factor of $B\to K_1$ transition while the other is a convolution between light-cone distribution amplitudes and hard scattering kernel. Using the light-cone sum rule results for the form factor, we have $\calB(B^0\to K_1^0(1270)\gamma)=(0.828\pm0.335)\times 10^{-5}$ and $\calB(B^0\to K_1^0(1400)\gamma)=(0.393\pm0.151)\times 10^{-5}$.