Evidence for $a_0(980)$ as tetraquark from the triangle rescattering $D_s^+\to π^+π^0η$ decay

Y. K. Hsiao, Yao Yu, Bai-Cian Ke

Published 2019-09-16Version 1

We study the $D_s^+\to \pi^+(a_0(980)^0\to)\pi^0\eta$, $\pi^0(a_0(980)^+\to)\pi^+\eta$ decays, which have been recently measured by the BESIII collaboration. We propose that $D_s^+\to \pi^{+(0)}(a_0(980)^{0(+)}\to)\pi^{0(+)}\eta$ receives the main contribution from the triangle rescattering process, where $\eta$ and $\rho^+$ in $D_s^+\to \eta \rho^+$, by exchanging $\pi^{0(+)}$, are formed as $a_0(980)^{0(+)}$ and $\pi^{+(0)}$, respectively. Particularly, we calculate that ${\cal B}(D_s^+\to a_0(980)^{0(+)}\pi^{+(0)})= (1.7\pm 0.4)\times 10^{-2}$ and ${\cal B}(D_s^+\to \pi^{+(0)}(a_0(980)^{0(+)}\to)\pi^{0(+)}\eta) =(1.5\pm 0.3)\times 10^{-2}$, in consistent with the data. The $a_0(980)^{0(+)}$ production is by receiving $s\bar s$ from $\eta$ and $u\bar u-d\bar d$ $(u\bar d)$ from $\pi^{0(+)}$, which indicates that $a_0(980)^{0(+)}$ is a tetraquark state.