# First Evidence for $\mathrm{cos}2\beta >0$ and Resolution of the Cabibbo-Kobayashi-Maskawa Quark-Mixing Unitarity Triangle Ambiguity

26 December 2018

Abstract: We present first evidence that the cosine of the $CP$-violating weak phase $2\beta$ is positive, and hence exclude trigonometric multifold solutions of the Cabibbo-Kobayashi-Maskawa (CKM) Unitarity Triangle 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 ${h}^{0}\in \left\{{\pi }^{0},\eta ,\omega \right\}$ 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 $\Upsilon \left(4S\right)$ resonance at the asymmetric-energy $B$ factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain $\left(471±3\right)×{10}^{6}B\overline{B}$ pairs recorded by the BABAR detector and $\left(772±11\right)×{10}^{6}B\overline{B}$ pairs recorded by the Belle detector. The results of the measurement are $\mathrm{sin}2\beta =0.80±0.14\left(\mathrm{stat}\right)±0.06\left(\mathrm{syst}\right)±0.03\left(\text{model}\right)$ and $\mathrm{cos}2\beta =0.91±\phantom{\rule{0ex}{0ex}}0.22\left(\mathrm{stat}\right)±0.09\left(\mathrm{syst}\right)±0.07\left(\text{model}\right)$. The result for the direct measurement of the angle $\beta$ of the CKM Unitarity Triangle 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 measurement assumes no direct $CP$ violation in ${B}^{0}\to {D}^{\left(*\right)}{h}^{0}$ decays. The quoted model uncertainties are due to the composition of the ${D}^{0}\to {K}_{S}^{0}{\pi }^{+}{\pi }^{-}$ decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics ${e}^{+}{e}^{-}\to c\overline{c}$ data sample. $CP$ violation is observed in ${B}^{0}\to {D}^{\left(*\right)}{h}^{0}$ decays at the level of 5.1 standard deviations. The significance for $\mathrm{cos}2\beta >0$ is 3.7 standard deviations. The trigonometric multifold solution $\pi /2-\beta =\left(68.1±0.7\right)°$ 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.

Published in: Physical Review Letters 121 (2018)