Amplitude analysis and branching fraction measurement of the decay $D^{+} \to K_S^0π^+π^0π^0$
Using 2.93 $\rm{fb}^{-1}$ of $e^+e^-$ collision data collected with the BESIII detector at the center-of-mass energy 3.773\,GeV, we perform the first amplitude analysis of the decay $D^+\to K_S^0π^+π^0π^0$ and determine the relative magnitudes and phases of different intermediate processes. The absolute branching fraction of $D^+\to K_S^0π^+π^0π^0$ is measured to be $(2.888\pm0.058_{\rm stat.}\pm0.069_{\rm syst.})\%$. The dominant intermediate processes are $D^+\to K_S^0a_1(1260)^+(\to ρ^+π^0)$ and $D^+\to \bar{K}^{*0}ρ^+$, with branching fractions of $(8.66\pm1.04_{\rm stat.}\pm1.39_{\rm syst.})\!\times \!10^{-3}$ and $(9.70\pm0.81_{\rm stat.}\pm0.53_{\rm syst.})\!\times \!10^{-3}$, respectively.