Scalar interactions and the polarizations of $B\to \phi K^*$

We try to understand the polarization puzzle in $B\to \phi K^*$ decays with a simple Higgs model associated with flavor changing neutral current at tree level. The new interactions can effectively reduce the longitudinal polarization $|A_0|^2$. In particular, we find that if the couplings of $b$-quark in different chiralities to Higgs are the same, the transverse polarization $|A_\perp|^2$ can receive the largest contribution and its value can be as large as 30%. On the other hand, with opposite sign in the couplings, the other transverse polarization $|A_{\parallel}|^2$ is enhanced.