First model-independent determination of the relative strong phase between ${D}^{0}$ and ${\overline{D}}^{0}\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and its impact on the CKM angle $\ensuremath{\gamma}/{\ensuremath{\phi}}_{3}$ measurement

First model-independent determination of the relative strong phase between $D^{0}$ and ${\bar{D}}^{0} \to K_{S}^{0} π^{+} π^{-}$ and its impact on the CKM angle $γ / ϕ_{3}$ measurement

R. A. Briere et al. (CLEO Collaboration)

Phys. Rev. D 80, 032002 – Published 12 August 2009

Abstract

We exploit the quantum coherence between pair-produced $D^{0}$ and ${\bar{D}}^{0}$ in $ψ (3770)$ decays to make a first determination of the relative strong phase differences between $D^{0} \to K_{S}^{0} π^{+} π^{-}$ and ${\bar{D}}^{0} \to K_{S}^{0} π^{+} π^{-}$ , which are of great importance in determining the Cabibbo-Kobayashi-Maskawa angle $γ / ϕ_{3}$ in $B^{-} \to D^{0} ({\bar{D}}^{0}) K^{-}$ decays. Using $818 {pb}^{- 1}$ of $e^{+} e^{-}$ collision data collected with the CLEO-c detector at $E_{cm} = 3.77 GeV$ , we employ a binned Dalitz-plot analysis of $K_{S}^{0} π^{+} π^{-}$ and $K_{L}^{0} π^{+} π^{-}$ decays recoiling against flavor-tagged, $C P$ -tagged, and $K_{S}^{0} π^{+} π^{-}$ -tagged events to determine these strong phase differences.