$B_{s,d}-\bar B_{s,d}$ mixings and $b\to q (\ga, \ell \bar \ell)$ decays in private Higgs model

Abstract

We study the low energy phenomena induced by the lightest charged Higgs in the private Higgs (PH) model, in which each quark flavor is associated with a Higgs doublet. We show that the couplings of the charged Higgs scalars to fermions are fixed and the unknown parameters are only the masses and mixing elements of the charged Higgs scalars. As the charged Higgs masses satisfy with $M_b<M_{c}\ll M_{s} \ll M_{d,u}$, processes involving $B$-meson are expected to be the ideal places to test the PH model. In particular, we explore the constraints on the model from experimental data in $B$ physics, such as the branching ratio (BR) and CP asymmetry (CPA) of $B\to X_s \ga$, $B_{d,s}-\bar B_{d,s}$ mixings and the BR for $B\to K^* \ell^{+} \ell^{-}$. We illustrate that the sign of the Wilson coefficient for $B\to X_s \ga$ can be different from that in the standard model, while this flipped sign can be displayed by the forward-backward asymmetry of $B\to V \ell^{+} \ell^{-}$ with $V$ a vector meson. We also demonstrate that $B_{d,s}-\bar B_{d,s}$ mixings and their time-dependent CPAs are negligible small and the BR of $B\to K^* \ell^{+} \ell^{-}$ can have a more strict bound than that of $B\to X_s \ga$.