Scalar resonances in the final state interactions of the decays $D^{0} \rightarrow \pi^{0}\pi^{0}\pi^{0}, \pi^{0}\pi^{0}\eta,\pi^{0}\eta\eta$

TL;DR

This paper studies scalar resonances in specific $D^{0}$ decays using a chiral unitary approach, successfully describing experimental data and predicting invariant mass spectra and branching ratios to better understand these resonances.

Contribution

It introduces a novel application of the chiral unitary approach to analyze scalar resonances in $D^{0}$ decays, providing new predictions for invariant mass spectra and decay branching ratios.

Findings

Successfully describes the $ ext{π}^0 ext{η}$ invariant mass spectrum in $D^{0} ightarrow ext{π}^0 ext{η} ext{η}$ decay.

Predicts the presence of $f_{0}(980)$ in the $ ext{π}^0 ext{π}^0$ spectrum of $D^{0} ightarrow ext{π}^0 ext{π}^0 ext{π}^0$.

Provides branching ratio predictions for various decay channels.

Abstract

We investigate the scalar resonances in the processes of $D^{0} \rightarrow \pi^{0}\pi^{0}\pi^{0}, \pi^{0}\pi^{0}\eta, \pi^{0}\eta\eta$ decays based on the chiral unitary approach for the final state interaction. We start from singly Cabibbo-suppressed production diagrams which provide a primary quark pair to hadronize two pseudoscalar mesons in $D^{0}$ decays. The resonances $f_{0}(500)$, $f_{0}(980)$ and $a_{0}(980)$ are dynamically produced from the final state interactions of the meson pairs. In our results, the experimental data for the $\pi^{0}\eta$ invariant mass spectrum of the $D^{0} \rightarrow \pi^{0}\eta\eta$ decay can be described well. We also make the predictions for the $\pi^{0}\pi^{0}$ invariant mass spectrum of the $D^{0} \rightarrow \pi^{0}\pi^{0}\pi^{0}$, where the $f_{0}(980)$ can be found, and for the $\pi^{0}\pi^{0}$, $\pi^{0}\eta$ invariant mass spectrum of the $D^{0} \rightarrow \pi^{0}\pi^{0}\eta$, where the $f_{0}(500)$, $f_{0}(980)$ and $a_{0}(980)$ appear. Furthermore, the branching ratios of each decay channel are predicted. We expect more accurate measurements of these decays to better understand the nature of the states $f_{0}(500)$, $f_{0}(980)$ and $a_{0}(980)$.