  In this paper, we compute the forward-backward asymmetry and the isospin
asymmetry of the $B \to K^* \mu^+ \mu^-$ decay. The $B \to K^*$ transition form
factors (TFFs) are key components of the decay. To achieve a more accurate QCD
prediction, we adopt a chiral correlator for calculating the QCD light-cone sum
rules for those TFFs with the purpose of suppressing the uncertain high-twist
distribution amplitudes. Our predictions show that the asymmetries under the
Standard Model and the Minimal Supersymmetric Standard Model with minimal
flavor violation are close in shape for $q^2 \ge 6~{\rm GeV}^2$ and are
consistent with the Belle, LHCb and CDF data within errors. When $q^2 < 2~{\rm
GeV}^2$, their predictions behave quite differently. Thus a careful study on
the $B \to K^* \mu^+ \mu^-$ decay within small $q^2$-region could be helpful
for searching new physics beyond the Standard Model. As a further application,
we also apply the $B \to K^*$ TFFs to the branching ratio and longitudinal
polarization fraction of the $B\to K^*\nu\bar\nu$ decay within different
models.
