Notes on $B\to K^* γ$

Abstract

We analyzed two form factors $T_1(q^2)$ and $T_2(q^2)$ which enter the $B\to K^* \ell^+ \ell^-$ decay rate and are accessible in the lattice calculations for $B \to K^* γ$. The extrapolation to $q^2=0$, necessary for $B\to K^* γ$ is examined. The flat behavior of $T_2(q^2)$ is shown to be disfavored. From the double constrained unitarity bounds by the lattice result at small recoil and the light cone sum rule one at large recoil, the pole/double pole fit is preferred with the `pole' masses as free parameters. We also show a consistency of two approaches in the heavy quark limit. Besides several byproducts of this analysis, our final (conservative) result for the form factor that determines $B\to K^* γ$ rate is $T(0)=0.15\pm 0.04$.