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

• Received 20 January 2003

DOI:https://doi.org/10.1103/PhysRevD.67.096007