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

Abstract

We measure the branching fraction for the Cabibbo-suppressed decay $D^0\rightarrow K^0_S\,K^0_S\,\pi^+\pi^-$ and search for $CP$ violation via a measurement of the $CP$ asymmetry $A_{\rm CP}$ as well as the $T$-odd triple-product asymmetry $a^T_{\rm CP}$. 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 $D^0\rightarrow K^0_S\,\pi^+\pi^-$; the result is $\mathcal{B}(D^0\rightarrow K^0_S\,K^0_S\,\pi^+\pi^-) = [4.79 \pm 0.08\,({\rm stat}) \pm 0.10\,({\rm syst}) \pm 0.31\,({\rm norm})]\times 10^{-4}$, where the first uncertainty is statistical, the second is systematic, and the third is from uncertainty in the normalization channel. We also measure $A_{\rm CP} = [-2.51\,\pm 1.44\,({\rm stat})\,^{+0.11}_{-0.10}\,({\rm syst})]\%$, and $a^T_{\rm CP} = [-1.95\,\pm 1.42\,({\rm stat})\,^{+0.14}_{-0.12}\,({\rm syst})]\%$. These results show no evidence of CP violation.