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Taking into account that the scalar $a_0(980)$ can be dynamically generatedfrom the pseudoscalar-pseudoscalar interaction within the chiral unitaryapproach, 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. Thepredicted Dalitz plots of $D^+\to \pi^+\pi^0\eta$ also manifest the significantsignals for $a_0(980)^+$ and $a_0(980)^0$ states. The uncertainties of theresults due to the free parameters are also discussed. Our study shows that theprocess $D^+\to \pi^+\pi^0\eta$ can be used to explore the nature of the scalar$a_0(980)$, thus we encourage the experimental physicists to measure thisreaction with more precision.

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