Amplitude analysis and branching-fraction measurement of $D_{s}^{+} \to π^{+}π^{0}η^{\prime}$

Using data collected with the BESIII detector in $e^+e^-$ collisions at center-of-mass energies between 4.178 and 4.226 GeV and corresponding to 6.32~fb$^{-1}$ of integrated luminosity, we report the amplitude analysis and branching-fraction measurement of the $D^+_s \to π^+ π^0 η^{\prime}$ decay. We find that the dominant intermediate process is $D^+_s \toρ^+ η^{\prime}$ and the significances of other resonant and nonresonant processes are all less than $3σ$. The upper limits on the branching fractions of $S$-wave and $P$-wave nonresonant components are set to $0.10\%$ and $0.74\%$ at the $90\%$ confidence level, respectively. In addition, the branching fraction of the $D^+_s \to π^+ π^0 η^{\prime}$ decay is measured to be $(6.15\pm0.25(\rm stat.)\pm0.18(\rm syst.))\%$, which receives significant contribution only from $D_s^+\to ρ^+η^{\prime}$ according to the amplitude analysis.