Amplitude analysis and branching fraction measurement of the decay $D^{+}\to K_S^0{\pi }^{+}{\pi }^0{\pi }^0$

Using 2.93 ${\mathrm{f}\mathrm{b}}^{-1}$ 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 $D^{+}\to K_S^0{\pi }^{+}{\pi }^0{\pi }^0$ and determine the relative magnitudes and phases of different intermediate processes. The absolute branching fraction of $D^{+}\to K_S^0{\pi }^{+}{\pi }^0{\pi }^0$ is measured to be $(2.888\pm {0.058}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.069}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\mathrm{\%}$. The dominant intermediate processes are $D^{+}\to K_S^0{a}_1(1260{)}^{+}(\to {\rho }^{+}{\pi }^0)$ and $D^{+}\to {\bar{K}}^{\ast 0}{\rho }^{+}$, with branching fractions of $(8.66\pm {1.04}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {1.39}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\text{\hspace{0.17em}⁣}\times \text{\hspace{0.17em}⁣}{10}^{-3}$ and $(9.70\pm {0.81}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.53}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\text{\hspace{0.17em}⁣}\times \text{\hspace{0.17em}⁣}{10}^{-3}$, respectively.