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 charged Higgs boson to the top- and bottom-quark is very sensitive to the value of $tanbeta$. 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 $tanbeta$. We preform a detailed analysis of measuring top-quark polarization in the production channels $gbto tH^-$ and $gbar{b}to bar{t}H^+$. 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 $tanbeta$, especially for the intermediate $tanbeta$ region. On the contrary, the top-quark produced in association with the charged Higgs boson cannot be used to measure $tanbeta$ because its polarization is highly contaminated by the $t$-channel kinematics.
From the current ATLAS and CMS results on Higgs boson mass and decay rates, the NMSSM is obviously better than the MSSM. To explain the fine-tuning problems such as gauge hiearchy problem and strong CP problem in the SM, we point out that supersymmet
ry does not need to provide a dark matter candidate, i.e., R-parity can be violated. Thus, we consider three kinds of the NMSSM scenarios: in Scenarios I and II R-parity is conserved and the lightest neutralino relic density is respectively around and smaller than the observed value, while in Scenario III R-parity is violated. To fit all the experimental data, we consider the chi^2 analyses, and find that the Higgs boson mass and decay rates can be explained very well in these Scenarios. Considering the small chi^2 values and fine-tuning around 2-3.7% (or 1-2%), we obtain the viable parameter space with light (or relatively heavy) supersymmetric particle spectra only in Scenario III (or in Scenarios I and II). Because the singlino, Higgsinos, and light stop are relatively light in general, we can relax the LHC supersymmetry search constraints but the XENON100 experiment gives a strong constraint in Scenarios I and II. In all the viable parameter space, the anomalous magnetic moment of the muon (g_{mu} - 2)/2 are generically small. With R-parity violation, we can increase (g_{mu} - 2)/2, and avoid the contraints from the LHC supersymmetry searches and XENON100 experiment. Therefore, Scenario III with R-parity violation is more natural and realistic than Scenarios I and II.
Varying the Standard Model (SM) fermion Yukawa couplings universally by a generic positive scale factor ($F_{Yu}$), we study the phenomenological fit to the current available experimental results for the Higgs boson search at hadron colliders. We poi
nt out that the Higgs production cross section and its decay branching ratio to $gammagamma$ can be varied oppositely by $F_{Yu}$ to make their product almost invariant. Thus, our scenario and the SM Higgs are indistinguishable in the inclusive $Hto gammagamma$ channel. The current measurements on direct Yukawa coupling strength in the $Hto bbar{b}/tautau$ channel are not precise enough to fix the scale factor $F_{Yu}$. The most promising is the vector-boson-fusion channel in which the CMS has already observed possible suppression effect on the Yukawa couplings. Further more, the global $chi^2$ fit of the experimental data can get the optimal value by introducing a suppression factor $F_{Yu}sim1/2$ on the SM Yukawa couplings.
