Searching for charged Higgs boson in polarized top quark

The charged Higgs boson is quite common in many new physics models. In this study we examine the potential of observing a heavy charged Higgs boson in its decay mode of top quark and bottom quark in the type-II two-Higgs-doublet model. In this model, the chirality structure of the coupling of a charged Higgs boson to the top and bottom quark is very sensitive to the value of $\mathrm{tan}\ensuremath{\beta}$. As the polarization of the top quark can be measured experimentally from the top-quark decay products, one could make use of the top-quark polarization to determine the value of $\mathrm{tan}\ensuremath{\beta}$. We perform a detailed analysis of measuring top-quark polarization in the production channels $gb\ensuremath{\rightarrow}t{H}^{\ensuremath{-}}$ and $g\overline{b}\ensuremath{\rightarrow}\overline{t}{H}^{+}$. We calculate the helicity amplitudes of the charged Higgs boson production and decay. Our calculation shows that the top quark from the charged Higgs boson decay provides a good probe for measuring $\mathrm{tan}\ensuremath{\beta}$, especially for the intermediate $\mathrm{tan}\ensuremath{\beta}$ region. On the contrary, the top quark produced in association with the charged Higgs boson cannot be used to measure $\mathrm{tan}\ensuremath{\beta}$ because its polarization is highly contaminated by the $t$-channel kinematics.