Theoretical interpretation of the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay and the nature of $a_0(980)$

Abstract

In a recent paper \cite{Ablikim:2019pit}, the BESIII collaboration reported the so-called first observation of pure $W$-annihilation decays $D_s^{+}\to a_0^{+}(980){\pi }^0$ and $D_s^{+}\to a_0^0(980){\pi }^{+}$. The measured absolute branching fractions are, however, puzzlingly larger than those of other measured pure $W$-annihilation decays by at least one order of magnitude. In addition, the relative phase between the two decay modes is found to be about 180 degrees. In this letter, we show that all these can be easily understood if the $a_0(980)$ is a dynamically generated state from $\bar{K}K$ and $\pi \eta$ interactions in coupled channels. In such a scenario, the $D_s^{+}$ decay proceeds via internal $W$ emission instead of $W$-annihilation, which has a larger decay rate than $W$-annihilation. The proposed decay mechanism and the molecular nature of the $a_0(980)$ also provide a natural explanation to the measured negative interference between the two decay modes.

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• Production of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ in $B$ decays as $D^{(\ast )}K$ and $D_s^{(\ast )}\eta$ molecules
• Productions of $X(3872)$, $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B_{(s)}$ decays offer strong clues on their molecular nature
• Theoretical study of the $D^0\to K^{-}{\pi }^{+}\eta$ reaction
• Scalar resonances in the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay
• The $a_0(980)$ in the single Cabibbo-suppressed process ${\Lambda }_c\to {\pi }^0\eta p$
• Combined theoretical study of the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ reactions
• Study of the Decay $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ and Observation of the W-annihilation Decay $D_s^{+}\to a_0(980{)}^{+}{\rho }^0$
• Observation of ${\Lambda }_c^{+}\to \Lambda a_0(980{)}^{+}$ and Evidence for $\Sigma (1380{)}^{+}$ in ${\Lambda }_c^{+}\to \Lambda {\pi }^{+}\eta$
• Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$
• Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$
• 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
• Theoretical study in the ${\bar{B}}^0\to J/\psi {\bar{K}}^{\ast 0}{K}^0$ and ${\bar{B}}^0\to J/\psi f_1(1285)$ decays
• The theoretical study of $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$
• Contributions of $\rho (770,1450)\to \omega \pi$ for the Cabibbo-favored $D\to h\omega \pi$ decays
• Roles of $a_0(980)$ and $a_0(1710)$ in Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$