Role of scalar $a_0(980)$ in the single Cabibbo Suppressed process $D^+ \to \pi^{+} \pi^{0} \eta$

Taking into account that the scalar $a_0(980)$ can be dynamically generated from the pseudoscalar-pseudoscalar interaction within the chiral unitary approach, we have studied the single Cabibbo-suppressed process $D^+\to \pi^+\pi^0\eta$. We find clear peaks of $a_0(980)^+$ and $a_0(980)^0$ in the $\pi^+\eta$ and $\pi^0\eta$ invariant mass distributions, respectively. The predicted Dalitz plots of $D^+\to \pi^+\pi^0\eta$ also manifest the significant signals for $a_0(980)^+$ and $a_0(980)^0$ states. The uncertainties of the results due to the free parameters are also discussed. Our study shows that the process $D^+\to \pi^+\pi^0\eta$ can be used to explore the nature of the scalar $a_0(980)$, thus we encourage the experimental physicists to measure this reaction with more precision.