Theoretical study of Ds+→π+π0π0

Abstract

Inspired by the BESIII Collaboration's recent amplitude analysis on ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, we develop a model based on the chiral unitary approach to describe the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ decay, where ${D}_{s}^{+}$ decays into ${\ensuremath{\pi}}^{+}$ and a quark-antiquark pair through weak decay of a charm quark. The interaction of pseudoscalar mesons produced by the hadronization of a quark-antiquark pair will lead to dynamically generated ${f}_{0}(980)$. The dominant amplitudes from resonances ${f}_{0}(1370)$ and ${f}_{2}(1270)$ in the BESIII fit are also included in our model. In addition to the above contributions, to obtain a good fit, we also add an amplitude from the resonance ${f}_{2}(1430)$ to our model. Our model provides a good fit for the ${M}_{{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}}$ and ${M}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}}$ invariant mass distributions simultaneously.