Roles of $a_0(980)^+ f_0(500,980)$ and $a_1(1260)^+η$ production mechanisms in decay $D_s^+ \to π^+ π^0 π^0 η$

Abstract

In this work, we theoretically investigate the decay mechanism of $D_s^+ \to π^+ π^0 π^0 η$ based on BESIII data, considering two mechanisms: the production of two dynamically generated resonances, $D_s^+ \to a_0(980)^+ f_0(500,980)$, and a process with one dynamically generated resonance, $D_s^+ \to a_1(1260)^+η$. In the first mechanism, the interactions $π^+η$ and $K^+\bar{K}^0$ are included to generate the $a_0(980)^+$, while coupled-channel interactions involving $π^+π^-$, $π^0π^0$, $K^+K^-$, $K^0\bar{K}^0$, $ηη$, and $π^0η$ are adopted to generate the $f_0(500)$ as well as the $f_0(980)$. For the second mechanism, the $πρ$ and $\bar{K}^*{K} - K^*\bar{K}$ channels are included to generate the $a_1(1260)$. With these interactions, the amplitudes are calculated in the chiral unitary approach and used to compute the invariant mass spectra of $D_s^+ \to π^+ π^0 π^0 η$. The results suggest that the peak near 1000~\text{MeV} in the $π^+η$ invariant mass spectrum can be well interpreted as the $a_0(980)^+$ arising from a cusp effect. The $f_0(980)$, generated together with the $f_0(500)$, is responsible for the small structure near 1000 MeV in the $π^0π^0$ spectrum. The $a_1(1260)^+$ and its decay to $ρ^+π^0$ followed by the subsequent $ρ^+$ decay provide a good description of the $π^+π^0π^0$ and $π^+π^0$ mass spectra. The inclusion of an additional resonance near 800 MeV in the $π^+η$ spectrum leads to only a marginal improvement of the fit.