In this paper, we calculate the next-to-leading order (NLO) new physics contributions to the mass splitting $\Delta M_{B_d}$ and the branching ratio $\mathcal{B}\left(\overrightarrow{B}{X}_s\gamma \right)$ 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 find that (a) an upper limit $|{\lambda }_{\mathrm{tt}}|<~1.7$ is obtained from the precision data of $\Delta M_{B_d}=0.502\mathrm{}\pm 0.007{\mathrm{ps}}^{-1},$ while $|{\lambda }_{\mathrm{tt}}|\approx 0.5$ is favored phenomenologicaly, (b) for $\overrightarrow{B}{X}_s\gamma$ 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 the NLO level by the measured branching ratio $\mathcal{B}\left(\overrightarrow{B}{X}_s\gamma \right),$ numerically, $188<~M_H<~215\mathrm{GeV}$ for $(|{\lambda }_{\mathrm{tt}}|,|{\lambda }_{\mathrm{bb}}|)=(0.5,18),$ (d) the NLO QCD contributions tend to cancel the LO contributions effectively, the lower limit on $M_H$ being consequently decreased by about 200 GeV, and (e) the allowed region of $M_H$ will be shifted toward the heavy mass end for a nonzero relative phase $\theta$ between the Yukawa couplings ${\lambda }_{\mathrm{tt}}$ and ${\lambda }_{\mathrm{bb}}.$ The numerical results for the conventional model II are also presented for the sake of comparison.

• Received 12 September 2003

DOI:https://doi.org/10.1103/PhysRevD.69.014002