$a_0\left(1710\right)\text{−}{f}_0\left(1710\right)$ mixing effect in the $D_s^{+}\to K_S^0{K}_S^0{\pi }^{+}$ decay

With the measurements of the decay $D_s^{+}\to K_S^0{K}_S^0{\pi }^{+}$ by the BESIII collaboration, we investigate this three-body weak decay via the chiral unitary approach for the final state interaction, where the resonances $S\left(980\right)$ and $S\left(1710\right)$ are dynamically reproduced with the interaction of eleven coupled channels, and the $W$-external and $W$-internal emission mechanisms are considered at the quark level. Besides, we also take into account the contribution from the $P$-wave resonance $K^{*}(892{)}^{+}$ and make a combined fit of the $K_S^0{K}_S^0$ and $K_S^0{\pi }^{+}$ invariant mass spectra measured by the BESIII collaboration. The fitted results show that the enhancement around 1.7 GeV in $K_S^0{K}_S^0$ mass spectrum is overlapped with two visible peaks, indicating the mixing signal originated from the resonances $a_0\left(1710\right)$ and $f_0\left(1710\right)$ due to their different poles (masses). Thus, the decay $D_s^{+}\to K_S^0{K}_S^0{\pi }^{+}$ is helpful to reveal their molecular nature with the mixing signal, which can be more precisely measured in the future.