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

Abstract

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.

7 pages, 6 figures, comments are welcome

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