Theoretical interpretation of the $D^+_s \to \pi^+ \pi^0 \eta$ decay and the nature of $a_0(980)$

TL;DR

This paper offers a theoretical interpretation of certain $D_s^+$ decay processes, proposing that the $a_0(980)$ is a dynamically generated state, which explains experimental observations better than previous models.

Contribution

It introduces a molecular model for $a_0(980)$ and explains the decay patterns of $D_s^+$ through internal $W$ emission rather than $W$-annihilation, aligning with experimental data.

Findings

The $a_0(980)$ is likely a dynamically generated state from meson interactions.

Decay rates are better explained by internal $W$ emission than $W$-annihilation.

The model accounts for the negative interference observed between decay modes.

Abstract

In a recent paper \cite{Ablikim:2019pit}, the BESIII collaboration reported the so-called first observation of pure $W$-annihilation decays $D^+_s \to a^+_0(980) \pi^0$ and $D_s^+ \to a^0_0(980)\pi^+$. The measured absolute branching fractions are, however, puzzlingly larger than those of other measured pure $W$-annihilation decays by at least one order of magnitude. In addition, the relative phase between the two decay modes is found to be about 180 degrees. In this letter, we show that all these can be easily understood if the $a_0(980)$ is a dynamically generated state from $\bar{K} K$ and $\pi \eta$ interactions in coupled channels. In such a scenario, the $D^+_s$ decay proceeds via internal $W$ emission instead of $W$-annihilation, which has a larger decay rate than $W$-annihilation. The proposed decay mechanism and the molecular nature of the $a_0(980)$ also provide a natural explanation to the measured negative interference between the two decay modes.