Measurement of time-dependent $CP$ violation in $B^0 to K^0_S pi^0 pi^0$ decays

We report a measurement of time-dependent $CP$ violation in $B^0 to K^0_S pi^0 pi^0$ decays using a data sample of $772 times 10^6$ $Bbar{B}$ pairs collected by the Belle experiment runnin g at the $Upsilon (4S)$ resonance at the KEKB $e^+ e^-$ collider. This decay proceeds mainly via a $bto sdbar{d}$ penguin amplitude. The results are $sin 2phi^{rm eff}_1 = 0.92^{+0.27}_{-0.31}~$ (stat.) $pm 0.11$ (syst.) and $mathcal{A} = 0.28 pm 0.21$ (stat.) $pm 0.04$ (syst.), which are the most precise measurements of $CP$ violati on in this decay mode to date. The value for the $CP$-violating parameter $sin 2phi^{rm eff}_1$ is consistent with that obtained using decay modes proceeding via a $bto cbar{c}s$ tree amplitude.