April 1997 b → s l l process and multi - Higgs doublet model

Rare b decay processes are analyzed in the multi-Higgs doublet model. Taking account of the constraint from the b → s γ process, the branching ratio and the forward-backward asymmetry of the final leptons for the b → s ll process are calculated. It is shown that the branching ratio can be a few times larger than the standard model prediction and the asymmetry can be significantly different from that in the standard model. Combining these observable quantities it is possible to determine complex coupling constants associated with the charged Higgs mixing matrix. The CP violating charge asymmetry in the b → s ll process and the branching ratio of the b → s νν process are also calculated. In search for new physics beyond the Standard Model (SM), flavor changing neutral current (FCNC) processes can play an important role. Since the source of the flavor changing processes only lies in the Cabbibo-Kobayashi-Maskawa (CKM) matrix in the SM, it is possible to make precise predictions for various observable quantities in FCNC processes within the SM. An important example is the branching ratio of the b → s γ process, which was reported to be Br(b → s γ) = (2.32± 0.57± 0.35) × 10 from the CLEO experiment [1]. Using the observed top quark mass, the measured branching ratio is consistent with the SM prediction. Therefore this process becomes a very strong constraint on models beyond the SM such as two Higgs doublet model [2] and supersymmetric extensions of the SM [3]. In addition to the b → s γ process, the b → s ll and b → s νν processes can be important constraints on new physics. Current experimental bounds for these processes are only by one order of magnitudes above the SM predictions [4, 5]. In this letter we consider possible constraints on parameters in the multi-Higgs doublet model from these rare b decay processes. When the number of the Higgs doublets is more than three we can introduce complex phases in the charged Higgs mixing matrix. In this sense the multi-Higgs doublet model is a natural extension of the SM which involves a new source of the CP violation. Present phenomenological constraints on coupling constants in this model are considered, for example, in Ref.[6]. Remarkably it is pointed out in Ref.[7] that the strongest constraint on the imaginary part of coupling constant comes from the b → s γ process, not from the CP violating quantities such as neutron electric dipole moment. Here we study the b → s ll and b → s νν̄ processes in the same model. We found that within the present experimental constraints including the b → s γ process the branching ratio can be a few times larger than the SM predictions and the forward-backward asymmetry of the final leptons for b → s ll process can significantly differ from the SM. Combining information from the branching ratio and the forward-backward asymmetry, it is possible to determine the complex coupling constants in future experiments. We also calculate the CP violating charge asymmetry between the b → s ll and b → s ll decays, which turns out to be a few percent in the allowed region. We consider the multi-Higgs doublet model with the following Yukawa couplings,