B^0-\bar{B}^0 mixing and B \to X_s \gamma decay in the third type 2HDM: effects of NLO QCD contributions

In this paper, we calculated the next-to-leading order (NLO) new physics contributions to the mass splitting $\text{dmd}$ and the branching ratio $\text{brbxsga}$ induced by the charged Higgs loop diagrams in the third type of two-Higgs-doublet models (model III) and draw the constraints on the free parameters of model III. For the model III under consideration, we found that (a) an upper limit $\mathrm{\mid }\text{ltt}\mathrm{\mid }\le 1.7$ is obtained from the precision data of $\text{dmd}=0.502\pm 0.007p{s}^{-1}$, while $\mathrm{\mid }\text{ltt}\mathrm{\mid }\approx 0.5$ is favored phenomenologicaly; (b) for $B\to X_s\gamma$ decay, the NLO QCD contributions tend to cancel the LO new physics contributions; © a light charged Higgs boson with a mass around or even less than 200 GeV is still allowed at NLO level by the measured branching ratio $\text{brbxsga}$: numerically, $188 \leq \mh \leq 215$GeVfor$(|\ltt|,|\lbb|)=(0.5,18)$; (d) the NLO QCD contributions tend to cancel the LO contributions effectively, the lower limit on $\text{mh}$ is consequently decreased by about 200 GeV; (e) the allowed region of $\text{mh}$ will be shifted toward heavy mass end for a non-zero relative phase $\theta$ between the Yukawa couplings $\text{ltt}$ and $\text{lbb}$. The numerical results for the conventional model II are also presented for the sake of a comparison.