HQET and Form Factor Effects in $B\to K^{(*)}\ell^+\ell^-$

Abstract

We examine the rates for the exclusive decays $B\to K^{(*)}\ell^+\ell^-$. We use the scaling predictions of the heavy quark effective theory to extract the necessary form factors from fits to various combinations of data. These data include the $D\to K^{(*)}\ell\nu$ semileptonic decays, as well as the nonleptonic decays $B\to K^{(*)}\psi^{(\prime)}$ and the rare decay $B\to K^*\gamma$. We use different parametrizations of form factors, and find that integrated decay rates are not very sensitive to the forms chosen. However, the decay spectra and the forward-backward asymmetry in $B\to K^*\ell^+\ell^-$ are sensitive to the forms chosen for the form factors, while the lepton polarization asymmetry in $\bar B^0\to \bar K^0\mu^+\mu^-$ is largely independent of the choice of form factors. Contributions from charmonium resonances dominate the spectra and integrated rates. In our `best' scenario, we find $Br(\bar B^0\to \bar K^0\mu^+\mu^-)=2.0\pm 0.3\times 10^{-6}$ and $Br(\bar B^0\to \bar K^{*0}\mu^+\mu^-)=8.1\pm 2.0\times 10^{-6}$. We also make predictions for other polarization observables in these decays.