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 sin2β and cos2β using a time-dependent Dalitz plot analysis of B0→D(*)h0 with D→KS0π+π- decays, where the light unflavored and neutral hadron h0 is a π0, η, or ω meson. The analysis uses a combination of the final data sets of the BaBar and Belle experiments containing 471×106 and 772×106 BB¯ pairs collected at the ϒ(4S) resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. We measure sin2β=0.80±0.14(stat)±0.06(syst)±0.03(model) and cos2β=0.91±0.22(stat)±0.09(syst)±0.07(model). The result for the direct measurement of the angle is β=(22.5±4.4(stat)±1.2(syst)±0.6(model))°. The last quoted uncertainties are due to the composition of the D0→KS0π+π- decay amplitude model, which is newly established by a Dalitz plot amplitude analysis of a high-statistics e+e-→cc¯ data sample as part of this analysis. We find the first evidence for cos2β>0 at the level of 3.7 standard deviations. The measurement excludes the trigonometric multifold solution π/2-β=(68.1±0.7)° 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 β=0° is ruled out at the level of 5.1 standard deviations, and thus CP violation is observed in B0→D(*)h0 decays. The measurement assumes no direct CP violation in B0→D(*)h0 decays.