Amplitude Analysis and Branching Fraction Measurement of $D^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$

We present the first amplitude analysis of the hadronic decay $D^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$, using $e^{+}{e}^{-}$ collision data collected with the BESIII detector at a center-of-mass energy of 3.773~GeV, corresponding to an integrated luminosity of 20.3~fb${}^{-1}$. The fit fractions of the intermediate processes are measured, in which the $D^{+}\to \rho (770{)}^{+}{\pi }^0$ component is found to be dominant with a branching fraction of $(3.08\pm {0.10}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.05}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\times {10}^{-3}$. Based on the amplitude analysis, the branching fraction of $D^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$ is measured to be $(4.84\pm {0.05}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.05}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\times {10}^{-3}$. In addition, the CP asymmetries, both for specific amplitudes and integrated over the entire phase space, are measured.