Measurement of time-dependent $CP$ violation in $B^0\to K_S^0{\pi }^0{\pi }^0$ decays

We report a measurement of time-dependent $CP$ violation in $B^0 \to K^0_S \pi^0 \pi^0$decaysusingadatasampleof$772 \times 10^6$ $B\bar{B}$ pairs collected by the Belle experiment runnin g at the $\mathrm{{\rm Y}}(4S)$ resonance at the KEKB $e^{+}{e}^{-}$ collider. This decay proceeds mainly via a $b\to sd\bar{d}$ “penguin” amplitude. The results are $\sin 2\phi^{\rm eff}1 = 0.92^{+0.27}{-0.31}~$(stat\mathrm{.})$\pm 0.11$(syst\mathrm{.})and$$\mathcal{A}$ = 0.28 \pm 0.21$(stat\mathrm{.})$\pm 0.04$(syst\mathrm{.}),whicharethemostprecisemeasurementsof$CP$violationinthisdecaymodetodate\mathrm{.}Thevalueforthe$CP$-violating parameter $\sin 2{\varphi }_1^{\mathrm{e}\mathrm{f}\mathrm{f}}$ is consistent with that obtained using decay modes proceeding via a $b\to c\bar{c}s$ “tree” amplitude.