Constraints on the Fourth Generation Effect on CF Violation in Penguin-Dominated b→s Decays

The direct CP-violating asymmetries for the penguin・dominated b sg,b→sg,and b→sγ,and b→sl+l^(-) decays are reexamined using the generalized 4×4 Kobayasbi-Maskawa matrix proposed by Bjorken.We find that the fourth generation effect on these asymmetries are significantly constrained by the sign of sin Φ3/sin Φ1,the imaginary part of the loop integral function for c-quark Im(Ic),and the mass of quark.Most of the previous predictions for this effect are too optimistic.