Scalar resonances in the final state interactions of the decays $D^0\to {\pi }^0{\pi }^0{\pi }^0,{\pi }^0{\pi }^0\eta ,{\pi }^0\eta \eta$

Abstract

We investigate the scalar resonances in the processes of $D^0\to {\pi }^0{\pi }^0{\pi }^0,{\pi }^0{\pi }^0\eta ,{\pi }^0\eta \eta$ decays based on the chiral unitary approach for the final state interaction. We start from singly Cabibbo-suppressed production diagrams which provide a primary quark pair to hadronize two pseudoscalar mesons in $D^0$ decays. The resonances $f_0(500)$, $f_0(980)$ and $a_0(980)$ are dynamically produced from the final state interactions of the meson pairs. In our results, the experimental data for the ${\pi }^0\eta$ invariant mass spectrum of the $D^0\to {\pi }^0\eta \eta$ decay can be described well. We also make the predictions for the ${\pi }^0{\pi }^0$ invariant mass spectrum of the $D^0\to {\pi }^0{\pi }^0{\pi }^0$, where the $f_0(980)$ can be found, and for the ${\pi }^0{\pi }^0$, ${\pi }^0\eta$ invariant mass spectrum of the $D^0\to {\pi }^0{\pi }^0\eta$, where the $f_0(500)$, $f_0(980)$ and $a_0(980)$ appear. Furthermore, the branching ratios of each decay channel are predicted. We expect more accurate measurements of these decays to better understand the nature of the states $f_0(500)$, $f_0(980)$ and $a_0(980)$.