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We present first evidence that the cosine of the CP-violating weak phase$2\beta$ is positive, and hence exclude trigonometric multifold solutions ofthe CKM Unitarity Triangle using a time-dependent Dalitz plot analysis of$B^{0} \to D^{(*)} h^{0}$ with $D \to K_{S}^{0} \pi^{+} \pi^{-}$ decays, where$h^{0} \in \{\pi^{0}, \eta, \omega \}$ denotes a light unflavored and neutralhadron. The measurement is performed combining the final data sets of the BaBarand Belle experiments collected at the $\Upsilon(4S)$ resonance at theasymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. Thedata samples contain $( 471 \pm 3 )\times 10^6\, B\bar{B}$ pairs recorded bythe BaBar detector and $( 772 \pm 11 )\times 10^6\, B\bar{B}$ pairs recorded bythe Belle detector. The results of the measurement are $\sin{2\beta} = 0.80 \pm0.14 \,(\rm{stat.}) \pm 0.06 \,(\rm{syst.}) \pm 0.03 \,(\rm{model})$ and$\cos{2\beta} = 0.91 \pm 0.22 \,(\rm{stat.}) \pm 0.09 \,(\rm{syst.}) \pm 0.07\,(\rm{model})$. The result for the direct measurement of the angle $\beta$ ofthe CKM Unitarity Triangle is $\beta = \left( 22.5 \pm 4.4 \,(\rm{stat.}) \pm1.2 \,(\rm{syst.}) \pm 0.6 \,(\rm{model}) \right)^{\circ}$. The quoted modeluncertainties are due to the composition of the $D^{0} \to K_{S}^{0} \pi^{+}\pi^{-}$ decay amplitude model, which is newly established by performing aDalitz plot amplitude analysis using a high-statistics $e^{+}e^{-} \toc\bar{c}$ data sample. CP violation is observed in $B^{0} \to D^{(*)} h^{0}$decays at the level of $5.1$ standard deviations. The significance for$\cos{2\beta}>0$ is $3.7$ standard deviations. The trigonometric multifoldsolution $\pi/2 - \beta = (68.1 \pm 0.7)^{\circ}$ is excluded at the level of$7.3$ standard deviations. The measurement resolves an ambiguity in thedetermination of the apex of the CKM Unitarity Triangle.

physical review letters

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