Application of HQET to $B\to K^{(*)}$ Transitions

We examine the measured rates for the decays $D\to K^{(*)}\ell\nu$, $B\to K^{(*)}\psi^{(\prime)}$ and $B\to K^*\gamma$ in a number of scenarios, in the framework of the heavy quark effective theory. We attempt to find a scenario in which all of these decays are described by a single set of form factors. Once such a scenario is found, we make predictions for the rare decays $B\to K^{(*)}\ell^+\ell^-$. While we find that many scenarios can provide adequate descriptions of all the data, somewhat surprisingly, we observe that two popular choices of form factors, namely monopolar forms and exponential forms, exhibit some shortcomings, especially when confronted with polarization observables. We predict $Br(\bar B^0\to \bar K^0\mu^+\mu^-)= 6.4\pm 1.0\times 10^{-7}$ and $Br(\bar B^0\to \bar K^{*0}\mu^+\mu^-)= 3.8\pm 1.3\times 10^{-6}$. We also make predictions for polarization observables in these decays.