B^0_{d,s} - \bar{B}^0_{d,s} mixing in the model III 2HDM

In the model III 2HDM there are new CP violating phases which would affect the $B_{d,s}^0 - \bar{B}_{d,s}^0$ mixing. In this paper, we calculate the new physics contributions to the neutral B meson mass splitting $\Delta M_{B_q}$ (q=d, s) at the next-to-leading order (NLO) level. Using the high accuracy data and other relevant data, we draw the constraints on the parameter space of the model III 2HDM. Moreover, we calculate the new physics corrections to the ratio $q/p$. It is found that the phase of $(q/p)_n$ for $B_d$ which is due to the new contributions is very small and consequently in agreement with the measurements of the time dependent CP asymmetry $S_{J/\psi K}$ in $B\to J/\psi K_S$. On the contrary, the phase of $(q/p)_n$ for $B_s$ is large enough to give significant effects on CP violation in the neutral $B_s$ system.