Study of $\bar{K}^*(892)^0 η$ and $K_S^0 a_0(980)^0$ in the $D^{0} \to K_{S}^{0}π^0η$ decay

We perform an amplitude analysis of the decay $D^0 \to K_S^0 π^0 η$ and measure its absolute branching fraction to be $(1.016 \pm 0.013_{\text {stat.}} \pm 0.014_{\text {syst.}})\%$. The analysis utilizes $20.3~\mathrm{fb}^{-1}$ of $e^{+}e^{-}$ collision data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector. The branching fraction of the intermediate process $D^0 \rightarrow \bar{K}^*(892)^0 η$ is determined to be $(0.73 \pm 0.05_{\text {stat.}} \pm 0.03_{\text {syst.}}) \%$, which is $5 σ$ smaller than the result measured in $D^0 \to K^- π^+ η$ by the Belle experiment. As a result, the magnitudes of the $W$-exchange and QCD-penguin exchange amplitudes are found to be less than half of their current estimations. Furthermore, we determine $\mathcal{B}(D^0\to K_S^0a_0(980)^0, a_0(980)^0\to π^0η) = (9.88\pm 0.37_{\rm stat.}\pm 0.42_{\rm syst.})\times10^{-3}$, with a precision improved by a factor of 4.5 compared to the world average.