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

We report measurements of $sin{2beta}$ and $cos{2beta}$ from a time-dependent Dalitz plot analysis of $B^{0} to D^{(*)} h^{0}$ 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 $772 times 10^{6}$ $Bbar{B}$ pairs collected at the $Upsilonleft(4Sright)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. We measure $sin{2beta} = 0.80 pm 0.14 ,(rm{stat.}) pm 0.06 ,(rm{syst.}) pm 0.03 ,(rm{model})$ 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 is $beta = left( 22.5 pm 4.4 ,(rm{stat.}) pm 1.2 ,(rm{syst.}) pm 0.6 ,(rm{model}) right)^{circ}$. 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 $e^{+}e^{-} to cbar{c}$ data sample as part of this analysis. We find the first evidence for $cos2beta>0$ 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 $B^{0} to D^{(*)} h^{0}$ decays.