Roles of $a_0(980)$ and $a_0(1710)$ in Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$

Abstract

Motivated by the BESIII amplitude analysis of the single Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$, we investigate this reaction by taking into account the contributions from the $a_0(980)$, $\rho$, and $a_0(1710)$, where the scalar meson $a_0(980)$ could be dynamically generated from the $S$-wave pseudoscalar meson-pseudoscalar meson interaction within the chiral unitary approach. Our theoretical predictions for the ${\pi }^0\eta$, ${\pi }^{+}\eta$, and ${\pi }^{+}{\pi }^0$ invariant mass distributions are in agreement with the BESIII measurements, especially the clear peaks around 1~GeV in the ${\pi }^0\eta$ and ${\pi }^{+}\eta$ invariant mass distributions could be associated with the dynamically generated state $a_0(980)$. Furthermore, we demonstrate that the intermediate $a_0(1710)$ is also necessary to describe the enhancement structure around $1.6\sim 1.7$~GeV in the ${\pi }^{0/+}\eta$ invariant mass distribution. More precise experimental measurements of this process could provide deeper insights into the nature of the scalar mesons $a_0(980)$ and $a_0(1710)$.

8 pages, 5 figures

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