The role of meson interactions in the $D_s^{+}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ decay

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 hadronize a pair or two pairs of $q\bar{q}$ 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 BESIII experiment.