First measurement ofϕ3with a model-independent Dalitz plot analysis ofB±→DK±,D→KS0π+π−decay

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Abstract

We present the first measurement of the angle ${\ensuremath{\phi}}_{3}$ of the unitarity triangle using a model-independent Dalitz plot analysis of ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}D{K}^{\ifmmode\pm\else\textpm\fi{}}$, $D\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays. The method uses, as input, measurements of the strong phase of the $D\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ amplitude from the CLEO Collaboration. The result is based on the full data set of $772\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected by the Belle experiment at the $\ensuremath{\Upsilon}(4S)$ resonance. We obtain ${\ensuremath{\phi}}_{3}=({77.3}_{\ensuremath{-}14.9}^{+15.1}\ifmmode\pm\else\textpm\fi{}4.1\ifmmode\pm\else\textpm\fi{}4.3)\ifmmode^\circ\else\textdegree\fi{}$ and the suppressed amplitude ratio ${r}_{B}=0.145\ifmmode\pm\else\textpm\fi{}0.030\ifmmode\pm\else\textpm\fi{}0.010\ifmmode\pm\else\textpm\fi{}0.011$. Here the first error is statistical, the second is the experimental systematic uncertainty, and the third is the error due to the precision of the strong-phase parameters obtained by CLEO.

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