Enhanced KL to pi0 nu nubar from Direct CP Violation in B to K pi with Four Generations

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Recent CP violation results in B decays suggest that Z penguins may have large weak phase. This can be realized by the four generation (standard) model. Concurrently, B to Xs l+ l- and Bs mixing allow for sizable Vt's* Vt'b only if it is nearly imaginary. Such large effects in b to s transitions would affect s to d transitions, as kaon constraints would demand Vt'd different from zero. Using Gamma(Z to b bbar) to bound |Vt'b|, we infer sizable |Vt's| < |Vt'b| < |Vus|. Imposing epsilonₖ, K+ to pi+ nu nubar and epsilon'/epsilon constraints, we find Vt'd* Vt's = few x 10(-4) with large phase, enhancing KL to pi0 nu nubar to 5x10(-10) or even higher. Interestingly, DeltaₘBd and sin(2PhiBd) are not much affected, as |Vt'd* Vt'b| << |Vtd* Vtb| = 0.01.