Amplitude analysis and branching fraction measurement of the decay D+ → ${K}_{S}^{0}$ π + π 0 π 0

Using 2.93 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 + → ${K}_{S}^{0}$ π + π 0 π 0 and determine the relative magnitudes and phases of different intermediate processes. The absolute branching fraction of D + → ${K}_{S}^{0}$ π + π 0 π 0 is measured to be (2.888 ± 0.058stat. ± 0.069syst. )%. The dominant intermediate processes are D + → ${K}_{S}^{0}$ a 1(1260)+(→ ρ + π 0) and D + → $\overline{K}$ *0 ρ +, with branching fractions of (8.66 ± 1.04stat. ± 1.39syst. ) × 10 −3 and (9.70 ± 0.81stat. ± 0.53syst. ) × 10 −3, respectively.