Model-independent measurement of $D^0$-$\bar{D}{}^0$ mixing parameters in $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ decays at Belle and Belle II

We perform a model-independent measurement of the $D^0$-$\bar{D}{}^0$ mixing parameters using samples of $e^{+}{e}^{-}$-collision data collected by the Belle and Belle II experiments that have integrated luminosities of $951{\text{fb}}^{-1}$ and $408{\text{fb}}^{-1}$, respectively. Approximately $2.05\times {10}^6$ neutral $D$ mesons are reconstructed in the $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ channel, with the neutral $D$ flavor tagged by the charge of the pion in the $D^{\ast +}\to D^0{\pi }^{+}$ decay. Assuming charge-parity symmetry, the mixing parameters are measured to be $x=(4.0\pm 1.7\pm 0.4)\times {10}^{-3}$ and $y=(2.9\pm 1.4\pm 0.3)\times {10}^{-3}$, where the first uncertainties are statistical and the second systematic. The results are consistent with previous determinations.