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

We present first evidence that the cosine of the CP-violating weak phase $2beta$ is positive, and hence exclude trigonometric multifold solutions of the CKM Unitarity Triangle using a time-dependent Dalitz plot analysis of $B^{0} D^{(*)} h^{0}$ with $D K_{S}^{0} pi^{+} pi^{-}$ decays, where $h^{0} {pi^{0}, eta, omega }$ 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 $Upsilon(4S)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain $( 471 pm 3 )times 10^6, Bbar{B}$ pairs recorded by the BaBar detector and $( 772 pm 11 )times 10^6, Bbar{B}$ pairs recorded by the Belle detector. The results of the measurement are $sin{2beta} = 0.80 pm 0.14 ,(rm{stat.}) pm 0.06 ,(rm{syst.}) pm 0.03 ,(rm{model})$ and $cos{2beta} = 0.91 pm 0.22 ,(rm{stat.}) pm 0.09 ,(rm{syst.}) pm 0.07 ,(rm{model})$. The result for the direct measurement of the angle $beta$ of the CKM Unitarity Triangle is $beta = left( 22.5 pm 4.4 ,(rm{stat.}) pm 1.2 ,(rm{syst.}) pm 0.6 ,(rm{model}) right)^{circ}$. The quoted model uncertainties are due to the composition of the $D^{0} K_{S}^{0} pi^{+} pi^{-}$ decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics $e^{+}e^{-} cbar{c}$ data sample. CP violation is observed in $B^{0} D^{(*)} h^{0}$ decays at the level of $5.1$ standard deviations. The significance for $cos{2beta}u003e0$ 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.