Measurement of the branching fraction and search for CP violation in $D^0\to K_S^0{K}_S^0{\pi }^{+}{\pi }^{-}$ decays at Belle

We measure the branching fraction for the Cabibbo-suppressed decay $D^0\to K_S^0{K}_S^0{\pi }^{+}{\pi }^{-}$ and search for $CP$ violation via a measurement of the $CP$ asymmetry $A_{\mathrm{C}\mathrm{P}}$ as well as the $T$-odd triple-product asymmetry $a_{\mathrm{C}\mathrm{P}}^T$. We use 922 fb${}^{-1}$ of data recorded by the Belle experiment, which ran at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The branching fraction is measured relative to the Cabibbo-favored normalization channel $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$; the result is $\mathcal{B}(D^0\to K_S^0{K}_S^0{\pi }^{+}{\pi }^{-})=[4.79\pm 0.08(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.10(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\pm 0.31(\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m})]\times {10}^{-4}$, where the first uncertainty is statistical, the second is systematic, and the third is from uncertainty in the normalization channel. We also measure $A_{\mathrm{C}\mathrm{P}}=[-2.51\pm 1.44(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}){}_{-0.10}^{+0.11}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\mathrm{\%}$, and $a_{\mathrm{C}\mathrm{P}}^T=[-1.95\pm 1.42(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}){}_{-0.12}^{+0.14}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\mathrm{\%}$. These results show no evidence of CP violation.