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.

12 pages, 6 figures; slight revisions and clarifications

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• Improved method for CKM constraints in charmless three-body B and B_s decays
• Measurement of CP Asymmetry in a Time-Dependent Dalitz Analysis of B^0 \to (ρπ)^0 and a Constraint on the Quark Mixing Matrix Angle ϕ_2
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• Relative phases in Dalitz plot amplitudes for $D^0\to K_S{\pi }^{+}{\pi }^{-}$ and $D^0\to {\pi }^0{K}^{+}{K}^{-}$
• Relative helicity phases in planar Dirac scattering
• Determination of Weak Amplitudes using Bose Symmetry and Dalitz Plots