Implications of CP Asymmetries in $B \to \pi^+ \pi^-$

Abstract

CP asymmetries in $B^0(t)\to \pi^+ \pi^-$ are studied by relating this process in broken flavor SU(3) with $B^+\to K^0\pi^+$ and $B^0\to K^+\pi^-$. Using two different scenarios for SU(3) breaking, we show that the range of values of the weak phase $\alpha$ permitted by the measured asymmetries overlaps with that obtained from other CKM constraints, supporting the KM origin of the asymmetries. We evaluate the potential precision of this method to improve the determination of $\alpha$.