Role of the scalar $f_0(980)$ in the process $D_s^+ \to \pi^{+} \pi^{0} \pi^{0}$

TL;DR

This paper investigates the role of the $f_0(980)$ scalar meson in the decay process $D_s^+ o ho^+ o ho^0 o ext{pions}$, using a chiral unitary approach to analyze BESIII data and the contributions of intermediate resonances.

Contribution

It introduces a model that dynamically generates the $f_0(980)$ from $S$-wave pseudoscalar interactions and includes intermediate resonances, providing a better understanding of the decay process.

Findings

The $f_0(980)$ plays a significant role in the decay process.

Intermediate resonances $f_0(1370)$ and $f_2(1270)$ are necessary for accurate description.

The model reproduces experimental data reasonably well.

Abstract

Based on the BESIII measurements on the reaction of $D_s^+\to \pi^+\pi^0\pi^0$, we investigate this process by considering the $S$-wave pseudoscalar-pseudoscalar interaction within the unitary chiral approach, and the contributions from the intermediate resonances $f_0(1370)$ and $f_2(1270)$. Our calculation could reasonably reproduce the experimental data, and our results imply that the $f_0(980)$, dynamically generated from the $S$-wave pseudoscalar-pseudoscalar interaction, plays an important role in this process, and the contributions from the intermediate resonances $f_0(1370)$ and $f_2(1270)$ are also necessary. The more precise measurements of this process in future could shed light on the nature of the $f_0(1370)$ and $f_2(1270)$.