The B ---> π K puzzle and the Bulk Randall-Sundurm model

Abstract: The recent measurements of the direct CP asymmetries ($A_{CP}$) in the penguin-dominated $B\to K \pi$ decays show some discrepancy from the standard model (SM) prediction. While $A_{CP}$ of $B^+ \to \pi^0 K^+$ and that of $B^0 \to \pi^- K^+$ in the naive estimate of the SM are expected to have very similar values, their experimental data are of the opposite sign and different magnitudes. We study the effects of the custodial bulk Randall-Sundrum model on this $A_{CP}$. In this model, the misalignment of the five-dimensional (5D) Yukawa interactions to the 5D bulk gauge interactions in flavor space leads to tree-level flavor-changing neutral current by the Kaluza-Klein gauge bosons. In a large portion of the parameter space of this model, the observed nonzero $A_{CP}(B^+ \to \pi^0 K^+) - A_{CP}(B^0 \to \pi^- K^+)$ can be explained only with low Kaluza-Klein mass scale $M_{KK}$ around 1 TeV. Rather extreme parameters is required to explain it with $M_{KK}\simeq 3\tev$. The new contributions to well-measured branching ratios of $B \to K \pi$ decays are also shown to be suppressed.