The theoretical study of $D_s^+\to\pi^+\pi^0\pi^0$

TL;DR

This paper presents a theoretical model based on the chiral unitary approach to describe the decay process of $D_s^+$ into three pions, successfully fitting experimental invariant mass distributions by including multiple resonances.

Contribution

The study introduces a novel chiral unitary model for $D_s^+ o ext{3 pions}$ decay, incorporating several resonances to accurately reproduce experimental data.

Findings

Model fits well the invariant mass distributions of decay products.

Inclusion of multiple resonances improves the fit quality.

Dynamically generated $f_0(980)$ plays a key role in the decay process.

Abstract

Inspired by recent BESIII's amplitude analysis on $D_s^+\to\pi^+\pi^0\pi^0$, we develop a model based on the chiral unitary approach to discribe the $D_s^+\to\pi^+\pi^0\pi^0$ decay, where $D_s^+$ decays into a $\pi^+$ and a quark-antiquark pair through weak decay of charm quark. The interaction of pseudoscalar mesons produced by the hadronization of quark-antiquark pair will lead to dynamically generated $f_0(980)$. The dominant amplitudes from resonances $f_0(1370)$ and $f_2(1270)$ in BESIII fit are also included in our model. In addition to above contributions, to obtain a good fit we also add a amplitude from resonance $f_2(1430)$ to our model. Our model fits well $M_{\pi^0\pi^0}$ and $M_{\pi^+\pi^0}$ invariant mass distributions simultaneously.