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

26 December 2018

Abstract: We report measurements of $\mathrm{sin}2\beta$ and $\mathrm{cos}2\beta$ using a time-dependent Dalitz plot analysis of ${B}^{0}\to {D}^{\left(*\right)}{h}^{0}$ 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 uses a combination of the final data sets of the BaBar and Belle experiments containing $471×{10}^{6}$ and $772×{10}^{6}\text{}\text{}B\overline{B}$ pairs collected at the $\Upsilon \left(4S\right)$ resonance at the asymmetric-energy $B$ factories PEP-II at SLAC and KEKB at KEK, respectively. We measure $\mathrm{sin}2\beta =0.80±0.14\left(\mathrm{stat}\right)±0.06\left(\mathrm{syst}\right)±0.03\left(\text{model}\right)$ and $\mathrm{cos}2\beta =0.91±0.22\left(\mathrm{stat}\right)±0.09\left(\mathrm{syst}\right)±0.07\left(\text{model}\right)$. The result for the direct measurement of the angle is $\beta =\left(22.5±4.4\left(\mathrm{stat}\right)±1.2\left(\mathrm{syst}\right)±0.6\left(\text{model}\right)\right)°$. 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 ${e}^{+}{e}^{-}\to c\overline{c}$ data sample as part of this analysis. We find the first evidence for $\mathrm{cos}2\beta >0$ at the level of 3.7 standard deviations. The measurement excludes the trigonometric multifold solution $\pi /2-\beta =\left(68.1±0.7\right)°$ 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 $\beta =0°$ is ruled out at the level of 5.1 standard deviations, and thus $CP$ violation is observed in ${B}^{0}\to {D}^{\left(*\right)}{h}^{0}$ decays. The measurement assumes no direct $CP$ violation in ${B}^{0}\to {D}^{\left(*\right)}{h}^{0}$ decays.

Published in: Physical Review D 98 (2018)