Scalar interactions and the polarizations of $B\to \varphi K^{\ast }$

We try to understand the polarization puzzle in $B\to \varphi K^{\ast }$ decays with a simple Higgs model associated with flavor changing neutral current at tree level. The new interactions can effectively reduce the longitudinal polarization $\mathrm{\mid }{A}_0{\mathrm{\mid }}^2$. In particular, we find that if the couplings of $b$-quark in different chiralities to Higgs are the same, the transverse polarization $\mathrm{\mid }{A}_{\perp }{\mathrm{\mid }}^2$ 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 $\mathrm{\mid }{A}_{\parallel }{\mathrm{\mid }}^2$ is enhanced.