First evidence for $\cos 2\beta >0$ and resolution of the CKM Unitarity Triangle ambiguity by a time-dependent Dalitz plot analysis of $B^0\to D^{(\ast )}{h}^0$ with $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decays

Abstract

We present first evidence that the cosine of the CP-violating weak phase $2\beta$ is positive, and hence exclude trigonometric multifold solutions of the CKM Unitarity Triangle using a time-dependent Dalitz plot analysis of $B^0\to D^{(\ast )}{h}^0$ with $D\to K_S^0{\pi }^{+}{\pi }^{-}$ decays, where $h^0\in \{{\pi }^0,\eta ,\omega \}$ denotes a light unflavored and neutral hadron. The measurement is performed combining the final data sets of the BaBar and Belle experiments collected at the ${\rm Y}(4S)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain $(471\pm 3)\times 10^{6}B\bar{B}$ pairs recorded by the BaBar detector and $(772\pm 11)\times 10^{6}B\bar{B}$ pairs recorded by the Belle detector. The results of the measurement are $\sin 2\beta =0.80\pm 0.14(stat.)\pm 0.06(syst.)\pm 0.03(\mathrm{model})$ 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 $\beta$ of the CKM Unitarity Triangle is $\beta ={\left(22.5\pm 4.4(stat.)\pm 1.2(syst.)\pm 0.6(\mathrm{model})\right)}^{\circ }$. The quoted model uncertainties are due to the composition of the $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics $e^{+}{e}^{-}\to c\bar{c}$ data sample. CP violation is observed in $B^0\to D^{(\ast )}{h}^0$ decays at the level of $5.1$ standard deviations. The significance for $\cos 2\beta >0$ is $3.7$ standard deviations. The trigonometric multifold solution $\pi /2-\beta =(68.1\pm 0.7{)}^{\circ }$ is excluded at the level of $7.3$ standard deviations. The measurement resolves an ambiguity in the determination of the apex of the CKM Unitarity Triangle.

To be submitted to Physical Review Letters

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