Can the nature of $a_0(980)$ be tested in the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay?

Abstract

From the amplitude analysis of the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay, the BESIII Collaboration firstly observed the $D_s^{+}\to a_0(980{)}^{+}{\pi }^0$ and $D_s^{+}\to a_0(980{)}^0{\pi }^{+}$ decay modes, which are expected to occur through the pure $W$-annihilation processes. The measured branching fraction $\mathcal{B}[D_s^{+}\to a_0(980{)}^{+(0)}{\pi }^{0(+)},a_0(980{)}^{+(0)}\to {\pi }^{+(0)}\eta ]$ is, however, found to be larger than those of known $W$-annihilation decays by one order of magnitude. This apparent contradiction can be reconciled if the two decays are induced by internal $W$-conversion or external $W$-emission mechanisms instead of $W$-annihilation mechanism. In this work, we propose that the $D_s^{+}$ decay proceeds via both the external and internal $W$-emission instead of $W$-annihilation mechanisms. In such a scenario, we perform a study of the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay by taking into account the contributions from the tree diagram $D_s^{+}\to {\rho }^{+}\eta \to {\pi }^{+}{\pi }^0\eta$ and the intermediate ${\rho }^{+}\eta$ and $K^{\ast }\bar{K}/K{\bar{K}}^{\ast }$ triangle diagrams. The intermediate $a_0(980)$ state can be dynamically generated from the final state interactions of coupled $K\bar{K}$ and $\pi \eta$ channels, and it is shown that the experimental data can be described fairly well, which supports the interpretation of $a_0(980)$ as a molecular state.

arXiv comment14 pages, 8 figures

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Cited by in corpus (11)

• Theoretical study of the process $D_s^{+}\to {\pi }^{+}{K}_S^0{K}_S^0$ and the isovector partner of $f_0(1710)$
• Production of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ in $B$ decays as $D^{(\ast )}K$ and $D_s^{(\ast )}\eta$ molecules
• Hadronic three-body D decays mediated by scalar resonances
• Unveiling the $a_0(1710)$ nature in the process $J/\psi \to {\bar{K}}^0{K}^{+}{\rho }^{-}$
• The $\pi f_0(500)$ decay of the $a_1(1260)$
• Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• The role of meson interactions in the $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ decay
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Contributions of $\rho (770,1450)\to \omega \pi$ for the Cabibbo-favored $D\to h\omega \pi$ decays
• Rescattering-induced $D\to SS$ weak decays