Measurement of the time-integrated $CP$ asymmetry in $D^0\to {\pi }^0{\pi }^0$ decays at Belle II

We measure the time-integrated $CP$ asymmetry, $A_{CP}$, in $D^0\to {\pi }^0{\pi }^0$ decays reconstructed in $e^{+}{e}^{-}\to c\bar{c}$ events collected by Belle II during 2019–2022. The data corresponds to an integrated luminosity of 428${\mathrm{f}\mathrm{b}}^{-1}$. The $D^0$ decays are required to originate from the flavor-conserving $D^{\ast +}\to D^0{\pi }^{+}$ decay to determine the charm flavor at production time. Control samples of $D^0\to K^{-}{\pi }^{+}$ decays, with or without an associated pion from a $D^{\ast +}$ decay, are used to correct for detection asymmetries. The result, $A_{CP}(D^0\to {\pi }^0{\pi }^0)=(0.30\pm 0.72\pm 0.20)\mathrm{\%}$, where the first uncertainty is statistical and the second systematic, is consistent with $CP$ symmetry.