Measurement of $\cos{2\beta}$ 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 2 beta and cos 2 beta using a time-dependent Dalitz plot analysis of B-0 -> D((*))h(0) with D -> 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 uses a combination of the final data sets of the BABAR and Belle experiments containing 471 x 10(6) and 772 x 10(6) B (B) over bar pairs collected at the gamma(4S) resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. We measure sin 2 beta = 0.80 +/- 0.14(stat) +/- 0.06(syst) +/- 0.03(model) and cos 2 beta = 0.91 +/- 0.22(stat) +/- 0.09(syst) +/- 0.07(model). The result for the direct measurement of the angle is beta = (22.5 +/- 4.4(stat) +/- 1.2(syst) +/- 0.6(model))degrees. The last quoted uncertainties are due to the composition of the D-0 -> K-S(0)pi(+)pi(-) decay amplitude model, which is newly established by a Dalitz plot amplitude analysis of a high-statistics e(+) e(-) -> c (c) over bar 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 +/- 0.7)degrees 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 degrees is ruled out at the level of 5.1 standard deviations, and thus CP violation is observed in B-0 -> D-(*) h(0) decays. The measurement assumes no direct CP violation in B-0 -> D-(*) h(0) decays.