Difference inB+andB0DirectCPAsymmetry as an Effect of a Fourth Generation

Direct $CP$ violation in $B^0\to K^{+}{\pi }^{-}$ decay has emerged at the $-10\%$ level, but the asymmetry in $B^{+}\to K^{+}{\pi }^0$ mode is consistent with zero. This difference points towards possible new physics in the electroweak penguin operator. We point out that a sequential fourth generation, with sizable $V_{t^{\prime }s}^{*}{V}_{t^{\prime }b}$ and near maximal phase, could be a natural cause. We use the perturbative QCD factorization approach for $B\to K\pi$ amplitudes. While the $B^0\to K^{+}{\pi }^{-}$ mode is insensitive to $t^{\prime }$, we critically compare $t^{\prime }$ effects on direct $CP$ violation in $B^{+}\to K^{+}{\pi }^0$ with $b\to s{\ell }^{+}{\ell }^{-}$ and $B_s$ mixing. If the $K^{+}{\pi }^0-K^{+}{\pi }^{-}$ asymmetry difference persists, we predict $\sin 2{\Phi }_{B_s}$ to be negative.