$D^0$-$\bar{D}^0$ mixing and CP violation results from Belle

We report the results on $D^0$-$\bar{D}^0$ mixing in the decays of $D^0\to K^+\pi^-$ and $D^0\to K_S^0\pi^+\pi^-$, and CP violation in $D^0\to\pi^0\pi^0$ using a data sample with an integrated luminosity of about 1~ab$^{-1}$ recorded with the Belle detector, at different center of mass energies. The mixing is observed in $D^0\to K^+\pi^-$ with the mixing parameters $x'^2=(0.09\pm 0.22)\times 10^{-3}$, $y'=(4.6\pm 3.4)\times 10^{-3}$ and the ratio of doubly Cabibbo-suppressed to Cabibbo-favored decay rates $R_{D}=(3.53\pm0.13)\times 10^{-3}$, where the quoted uncertainties combine both statistical and systematic contributions. For the $D^0\to K_S^0\pi^+\pi^-$ decay, assuming CP conservation we measure mixing parameters $x=(0.56\pm 0.19^{+0.03+0.06}_{-0.09-0.09})\%$ and $y=(0.30\pm 0.15^{+0.04+0.03}_{-0.05-0.06})\%$, where the uncertainties are statistical, experimental systematics, and that due to amplitude model. We measure the mixing parameters allowing CP violation for this decay mode, and obtain $|q/p|=0.90^{+0.16+0.05+0.06}_{-0.15-0.04-0.05}$ and arg($q/p$)=$(-6\pm 11 \pm3^{+3}_{-4})^{\circ}$ that are consistent with no CP violation. The time-integrated CP asymmetry in the decay $D^0\to\pi^0\pi^0$ is measured to be, $[-0.03\pm 0.64(stat) \pm 0.10(syst)]\%$, consistent with CP conservation. We also present an updated measurement of CP asymmetry in $D^0\to K_S^0\pi^0$.