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 $B^0\to\omega K^0_S$ to be $A_{\omega K^0_S} =-0.36\pm 0.19(stat)\pm 0.05(syst)$ 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 $B^+\to\omega K^+$ to be $A_{CP} (B^+ \to \omega K^+)=-0.03\pm 0.04 \pm 0.01$, 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 $B^0\to\eta'K^0$ decay we obtain $S_{\eta'K^0} = 0.68 \pm 0.07\pm 0.03$ 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 $S_{\pi^+\pi^-} = -0.64\pm 0.08\pm 0.03$. This result is used in an isospin analysis to constrain the $\phi_2$ angle of the unitarity triangle, with which we rule out the region $23.8^\circ < \phi_2 < 66.8^\circ$ at the $1\sigma$ 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 $f_L = 0.21^{+0.18}_{-0.22}\pm 0.13$. We obtain also the first evidence of the $B^0\to f_0\rho^0$ decay, by measuring $B(B^0\to f_0 \rho^0)\times B(f_0\to \pi^+\pi^-) = (0.86\pm 0.27 \pm 0.14)\times 10^{-6}$.