Measurement of $\cos 2\beta$ in $B^0\to D^{(\ast )}{h}^0$ with $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decays by a combined time-dependent Dalitz plot analysis of BaBar and Belle data

Abstract

We report measurements of $\sin 2\beta$ and $\cos 2\beta$ from a time-dependent Dalitz plot analysis of $B^0\to D^{(\ast )}{h}^0$ with $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decays, where the light unflavored and neutral hadron $h^0$ is a ${\pi }^0$, $\eta$, or $\omega$ meson. The analysis is performed with a combination of the final data sets of the \babar\ and Belle experiments containing $471\times 10^6$ and $772\times 10^6$ $B\bar{B}$ pairs collected at the ${\rm Y}\left(4S\right)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. We measure $\sin 2\beta =0.80\pm 0.14(stat.)\pm 0.06(syst.)\pm 0.03(\mathrm{model})$ and $\cos 2\beta =0.91\pm 0.22(stat.)\pm 0.09(syst.)\pm 0.07(\mathrm{model})$. The result for the direct measurement of the angle is $\beta ={\left(22.5\pm 4.4(stat.)\pm 1.2(syst.)\pm 0.6(\mathrm{model})\right)}^{\circ }$. The last quoted uncertainties are due to the composition of the $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ decay amplitude model, which is newly established by a Dalitz plot amplitude analysis of a high-statistics $e^{+}{e}^{-}\to c\bar{c}$ data sample as part of this analysis. We find the first evidence for $\cos 2\beta >0$ at the level of $3.7$ standard deviations. The measurement excludes the trigonometric multifold solution $\pi /2-\beta =(68.1\pm 0.7{)}^{\circ }$ at the level of $7.3$ standard deviations and therefore resolves an ambiguity in the determination of the apex of the CKM Unitarity Triangle. The hypothesis of $\beta =0^{\circ }$ is ruled out at the level of $5.1$ standard deviations, and thus CP violation is observed in $B^0\to D^{(\ast )}{h}^0$ decays.

arXiv commentTo be submitted to Physical Review D

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