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

The direct CP-violating asymmetries for the penguin-dominated b → sg, b → sγ, and b → sl⁺l^- decays are reexamined using the generalized 4x 4 Kobayashi-Maskawa matrix proposed by Bjorken. We find that the fourth generation effect on these asymmetries are significantly constrained by the sign of sin Ф₃/ sin Ф₁, the imaginary part of the loop integral function for c-quark Im(I_c) , and the mass of t'-quark. Most of the previous predictions for this effect are too optimistic.