Time-dependent CP violation in $B$ decays at Belle

Using the full data sample collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider, we present three recent measurements of time-dependent CP violation in $B$ decays, and a measurement of branching fraction of the $B^0\to {\rho }^0{\rho }^0$ decay. We studied $B\to \omega K$ decays and measured the values of CP violation parameters in $B^0\to \omega K_S^0$ to be $A_{\omega K_S^0}=-0.36\pm 0.19(stat)\pm 0.05(syst)$ and $S_{\omega K^0_S}= +0.91\pm 0.32 \pm 0.05 $, which gives the first evidence of CP violation in this decay. In addition, we measured the direct CP violation in $B^+\to\omega K^+$tobe$A_{CP} (B^+ \to \omega K^+)=-0.03\pm 0.04 \pm 0.01$, and two branching fractions $B(B^0\to \omega K^0)=(4.5\pm 0.4\pm 0.3)\times {10}^{-6}$ and $B(B^{+}\to \omega K^{+})=(6.8\pm 0.4\pm 0.4)\times {10}^{-6}$ (preliminary). From the measurement of CP violation parameters in the $B^0\to {\eta }^{\mathrm{\prime }}{K}^0$ decay we obtain $S_{{\eta }^{\mathrm{\prime }}{K}^0}=0.68\pm 0.07\pm 0.03$ and $A_{\eta’K^0} = +0.03 \pm 0.05\pm 0.04$ (preliminary), which are the world’s most precise values to date. Measuring CP violating parameters in the $B^0\to {\pi }^{+}{\pi }^{-}$ decay gives $A_{{\pi }^{+}{\pi }^{-}}=+0.33\pm 0.06\pm 0.03$ and $S_{\pi^+\pi^-} = -0.64\pm 0.08\pm 0.03$\mathrm{.}Thisresultisusedinanisospinanalysistoconstrainthe$\phi_2$angleoftheunitaritytriangle,withwhichweruleouttheregion$23.8^\circ < \phi_2 < 66.8^\circ$atthe$1\sigma$ confidence level. The measured branching fraction of the $B^0\to {\rho }^0{\rho }^0$ decay is $B(B^0\to\rho^0\rho^0) = (1.02\pm 0.30\pm 0.15)\times 10^{-6}$, with the fraction of longitudinally polarized ${\rho }^0$ mesons being $f_L=0.21_{-0.22}^{+0.18}\pm 0.13$. We obtain also the first evidence of the $B^0\to f_0{\rho }^0$ decay, by measuring $B(B^0\to f_0 \rho^0)\times B(f_0\to \pi^+\pi^-) = (0.86\pm 0.27 \pm 0.14)\times 10^{-6}$.