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 $\dmd$ and the branching ratio $\brbxsga$ 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 $|\ltt|\leq 1.7$ is obtained from the precision data of $\dmd=0.502 \pm 0.007 ps^{-1}$, while $|\ltt| \approx 0.5$ is favored phenomenologicaly; (b) for $B \to X_s \gamma$ decay, the NLO QCD contributions tend to cancel the LO new physics contributions; (c) 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 $\brbxsga$: numerically, $188 \leq \mh \leq 215$ GeV for $(|\ltt|,|\lbb|)=(0.5,18)$; (d) the NLO QCD contributions tend to cancel the LO contributions effectively, the lower limit on $\mh$ is consequently decreased by about 200 GeV; (e) the allowed region of $\mh$ will be shifted toward heavy mass end for a non-zero relative phase $\theta$ between the Yukawa couplings $\ltt$ and $\lbb$. The numerical results for the conventional model II are also presented for the sake of a comparison.