Calculating Phases Between B => K* pi Amplitudes

TL;DR

This paper derives bounds on the phase difference between specific B meson decay amplitudes, using flavor symmetry and experimental data, to aid in constraining CKM parameters.

Contribution

It introduces a general argument for destructive interference in B meson decay amplitudes and provides bounds on phase differences considering theoretical uncertainties.

Findings

Lower limits on phase differences are established.

Experimental phase values align with derived bounds.

Destructive interference reduces certain decay amplitude contributions.

Abstract

A phase $\Delta \Phi$ between amplitudes for $B^0 \to K^{*0} \pi^0$ and $B^0 \to K^{*+} \pi^-$ 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 $B^0 \to K^{*+} \pi^-$ and $B^0 \to K^{*0} \pi^0$ forming together a smaller $I(K^* \pi) = 3/2$ 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.