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

TL;DR

This paper presents a theoretical analysis of the $D_s^{+} o ext{pi}^+ ext{pi}^+ ext{pi}^- ext{eta}$ decay, modeling meson interactions and resonance generation to match experimental mass distributions.

Contribution

It introduces a novel theoretical framework combining quark-level decay, hadronization, and final state interactions to explain the decay process and resonance formation.

Findings

Successfully reproduces BESIII mass distributions

Identifies key resonances involved in decay

Demonstrates the role of G-parity filtering

Abstract

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.