Roles of $a_0(980{)}^{+}{f}_0(500,980)$ and $a_1(1260{)}^{+}\eta$ production mechanisms in decay $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0\eta$

Abstract

In this work, we theoretically investigate the decay mechanism of $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0\eta$ 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, $D_s^{+}\to a_1(1260{)}^{+}\eta$. In the first mechanism, the interactions ${\pi }^{+}\eta$ and $K^{+}{\bar{K}}^0$ are included to generate the $a_0(980{)}^{+}$, while coupled-channel interactions involving ${\pi }^{+}{\pi }^{-}$, ${\pi }^0{\pi }^0$, $K^{+}{K}^{-}$, $K^0{\bar{K}}^0$, $\eta \eta$, and ${\pi }^0\eta$ are adopted to generate the $f_0(500)$ as well as the $f_0(980)$. For the second mechanism, the $\pi \rho$ and ${\bar{K}}^{\ast }K-K^{\ast }\bar{K}$ 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 $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0\eta$. The results suggest that the peak near 1000~\text{MeV} in the ${\pi }^{+}\eta$ 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 ${\pi }^0{\pi }^0$ spectrum. The $a_1(1260{)}^{+}$ and its decay to ${\rho }^{+}{\pi }^0$ followed by the subsequent ${\rho }^{+}$ decay provide a good description of the ${\pi }^{+}{\pi }^0{\pi }^0$ and ${\pi }^{+}{\pi }^0$ mass spectra. The inclusion of an additional resonance near 800 MeV in the ${\pi }^{+}\eta$ spectrum leads to only a marginal improvement of the fit.

Comments: 10 pages, 6 figures