We perform a theoretical study of the $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ decay. We look first at the basic $D_s^{+}$ decay at the quark level from external and internal emission. Then we hadronize a pair or two pairs of $q\overline{q}$ states to have mesons at the end. Posteriorly the pairs of mesons are allowed to undergo final state interaction, by means of which the $a_0(980)$, $f_0(980)$, $a_1(1260)$, and $b_1(1235)$ resonances are dynamically generated. The $G$ parity is used as a filter of the possible channels, and from those with negative $G$ parity only the ones that can lead to ${\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ at the final state are kept. Using transition amplitudes from the chiral unitary approach that generates these resonances and a few free parameters, we obtain a fair reproduction of the six mass distributions reported in the BESIII experiment.

• Received 20 May 2022
• Accepted 4 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.074027

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Published by the American Physical Society