Measurement of $CP$ asymmetries in $B^0\to K_S^0{\pi }^0\gamma$ decays at Belle II

We report measurements of time-dependent $CP$ asymmetries in $B^0\to K_S^0{\pi }^0\gamma$ decays based on a data sample of $(388\pm 6)\times {10}^6$ $B\bar{B}$ events collected at the $\mathrm{{\rm Y}}(4S)$ resonance with the Belle II detector. The Belle II experiment operates at the SuperKEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We measure decay-time distributions to determine $CP$-violating parameters $S$ and $C$. We determine these parameters for two ranges of $K_S^0{\pi }^0$ invariant mass: $m(K_S^0{\pi }^0)\in (0.8,1.0)$ $GeV\mathrm{/}{c}^2$, which is dominated by $B^0\to K^{\ast 0}(\to K_S^0{\pi }^0)\gamma$ decays, and a complementary region $m(K_S^0{\pi }^0)\in (0.6,0.8)\cup (1.0,1.8)$ $GeV\mathrm{/}{c}^2$. Our results have improved precision as compared to previous measurements and are consistent with theory predictions.