Search for $CP$ Violation and Measurement of the Branching Fraction in the Decay $D^0\to K_S^0{K}_S^0$

We report a study of the decay $D^0\to K_S^0{K}_S^0$ using 921~fb${}^{-1}$ of data collected at or near the $\mathrm{{\rm Y}}(4S)$ and $\mathrm{{\rm Y}}(5S)$ resonances with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. The measured time-integrated $CP$ asymmetry is $ A_{CP}(D^0 \to K^0_S K^0_S) = (-0.02 \pm 1.53 \pm 0.02 \pm 0.17) %$,andthebranchingfractionis$$\mathcal{B}$ (D^{0}\rightarrow K_{S}^{0}K_{S}^{0})$=(1.321$\pm$0.023$\pm$0.036$\pm$0.044)$\times$10$^{-4}$, where the first uncertainty is statistical, the second is systematic, and the third is due to the normalization mode ($D^0\to K_S^0{\pi }^0$). These results are significantly more precise than previous measurements available for this mode. The $A_{CP}$ measurement is consistent with the standard model expectation.