Calculating Phases Between B => K* pi Amplitudes

Abstract

A phase $\Delta \Phi$ between amplitudes for $B^0\to K^{\ast 0}{\pi }^0$ and $B^0\to K^{\ast +}{\pi }^{-}$ plays a crucial role in a method for constraining Cabibbo-Kobayashi-Maskawa (CKM) parameters. We present a general argument for destructive interference between amplitudes for $B^0\to K^{\ast +}{\pi }^{-}$ and $B^0\to K^{\ast 0}{\pi }^0$ forming together a smaller $I(K^{\ast }\pi )=3/2$ amplitude. Applying flavor SU(3) and allowing for conservative theoretical uncertainties, we obtain lower limits on $|\Delta \Phi |$ and its charge-conjugate. Values of these two phases favored by the BaBar Collaboration are in good agreement with our bounds.

Comments: 12 pages, 6 figures; slight revisions and clarifications