Radiative dileptonic decays of B-meson in the general two Higgs doublet model

We investigate the exclusive $B\to \gamma \ell^+ \ell^- $ decay in the general two Higgs doublet model (model III) including the neutral Higgs boson effects with an emphasis on possible CP-violating effects. For this decay, we analyse the dependencies of the forward-backward asymmetry of the lepton pair, $A_{FB}$, CP-violating asymmetry, $A_{CP}$, and the CP-violating asymmetry in forward-backward asymmetry, $A_{CP}(A_{FB})$, on the model parameters and also on the neutral Higgs boson effects. We have found that $A_{FB}\sim 10^{-1}, 10^{-2}$, $A_{CP}\sim 10^{-2}, 10^{-1}$ and $A_{CP}(A_{FB}) \sim 10^{-2}, 10^{-1}$ depending on the relative magnitude of the Yukawa couplings $\bar{\xi}_{N,tt}^{U}$ and $\bar{\xi}_{N,bb}^{D}$ in the model III. We also observe that these physical quantities are sensitive to the model parameters and neutral Higgs boson effects are quite sizable for some values of the coupling $\bar{\xi}_{N,\tau \tau}^{D}$.