CP violation in $B_{d,s}\to l^{+}{l}^{-}$ in the model III 2HDM

We have calculated the Wilson coefficients $C_{10},C_{Q_i}$ (i=1,2) in the $\overline{MS}$ renormalization scheme in the model III 2HDM. Using the obtained Wilson coefficients, we have analyzed the CP violation in decays $B^0_q\to l^+l^-$(q=d,s)inthemodel\mathrm{.}TheCPasymmetry,$A_{CP}$, depends on the parameters of models and $A_{CP}$ in $B_d\to l^{+}{l}^{-}$ can be as large as 40% and 35% for $l=\tau$ and $l=\mu$ respectively. It can reach 4% for $B_s^0$ decays. Because in SM CP violation is smaller than or equal to O(${10}^{-3}$) which is unobservably small, an observation of CP asymmetry in the decays $B^0_q \to l^+l^- (q=d,s)$ would unambiguously signal the existence of new physics.