Possibility of Large Final State Interaction Phases in Light of B \to K\pi and \pi\pi Data

Abstract

The newly observed ${\bar{B}}^0\to {\bar{K}}^0{\pi }^0$ mode is quite sizable while ${\pi }^{-}{\pi }^{+}$ is rather small. Data also hint at ${\pi }^{-}{\pi }^0\gtrsim {\pi }^{-}{\pi }^{+}$. Though consistent with zero, central values of CP violating asymmetries in $K^{-}{\pi }^{+,0}$ and ${\bar{K}}^0{\pi }^{-}$ show an interesting pattern. Taking cue from these, we suggest that, besides $\gamma \equiv \arg (V_{ub}^{\ast })$ being large, the rescattering phase $\delta$ in $K\pi$ and $\pi \pi$ modes may be greater than $90^{\circ }$. If this is true, not only the above trends can be accounted for, one would also find ${\pi }^0{\pi }^0\sim {\pi }^{-}{\pi }^{+,0}$, and the CP asymmetry in ${\bar{B}}^0$ vs. $B^0\to {\pi }^{-}{\pi }^{+}$ could be as large as -60%. These results can be tested in a couple of years.

Comments: 4 pages, revtex, 3 eps figures, an error on SU(3) corrected. Version to be published in Phys. Rev. Lett