Calculating Phases Between B => K* pi Amplitudes

A phase $ΔΦ$ between amplitudes for $B^0 \to K^{*0} π^0$ and $B^0 \to K^{*+} π^-$ 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 $B^0 \to K^{*+} π^-$ and $B^0 \to K^{*0} π^0$ forming together a smaller $I(K^* π) = 3/2$ amplitude. Applying flavor SU(3) and allowing for conservative theoretical uncertainties, we obtain lower limits on $|ΔΦ|$ and its charge-conjugate. Values of these two phases favored by the BaBar Collaboration are in good agreement with our bounds.

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