The exclusive $B->(K,K^{\ast }){\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ decays in a CP softly broken two Higgs doublet model

We study the differential branching ratio, forward-backward asymmetry, CP-violating asymmetry, CP-violating asymmetry in the forward-backward asymmetry and polarization asymmetries in the $B->K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ and $B -> K^* \ell^+ \ell^-$ decays in the context of a CP softly broken two Higgs doublet model. We analyze the dependencies of these observables on the model parameters by paying a special attention to the effects of neutral Higgs boson (NHB) exchanges and possible CP violating effects. We find that NHB effects are quite significant for both decays. A combined analysis of above-mentioned observables seems to be very promising as a testing ground for new physics beyond the SM, especially for the existence of the CP-violating phase in the theory.