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In a recent paper \cite{Ablikim:2019pit}, the BESIII collaboration reportedthe so-called first observation of pure $W$-annihilation decays $D^+_s \toa^+_0(980) \pi^0$ and $D_s^+ \to a^0_0(980)\pi^+$. The measured absolutebranching fractions are, however, puzzlingly larger than those of othermeasured pure $W$-annihilation decays by at least one order of magnitude. Inaddition, the relative phase between the two decay modes is found to be about180 degrees. In this letter, we show that all these can be easily understood ifthe $a_0(980)$ is a dynamically generated state from $\bar{K} K$ and $\pi \eta$interactions in coupled channels. In such a scenario, the $D^+_s$ decayproceeds via internal $W$ emission instead of $W$-annihilation, which has alarger decay rate than $W$-annihilation. The proposed decay mechanism and themolecular nature of the $a_0(980)$ also provide a natural explanation to themeasured negative interference between the two decay modes.

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