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

TL;DR

This paper analyzes the $D^+ o \pi^0\pi^+\eta$ decay process, highlighting the roles of scalar mesons $a_0(980)$ and $a_0(1710)$, and successfully matches experimental data with theoretical models.

Contribution

It introduces a comprehensive theoretical model including $a_0(980)$, $ ho$, and $a_0(1710)$ contributions, clarifying their roles in the decay process and matching experimental invariant mass distributions.

Findings

The $a_0(980)$ can be dynamically generated from pseudoscalar interactions.

The $a_0(1710)$ is essential for explaining the structure around 1.6-1.7 GeV.

The model agrees well with BESIII measurements.

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 $a_0(1710)$.