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

We report a study of the decay $D^0 to K^0_S K^0_S$ using 921~fb$^{-1}$ of data collected at or near the $Upsilon(4S)$ and $Upsilon(5S)$ 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) %$, and the branching fraction is $mathcal{B} (D^{0}rightarrow K_{S}^{0}K_{S}^{0})$ = (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.