$a_0(1710)$-$f_0(1710)$ mixing effect in the $D_{s}^{+} \rightarrow K_S^{0} K_S^{0} π^{+}$ decay

Abstract: With the measurements of the decay $D^+_s \rightarrow K^0_S K^0_S \pi^+$ by the BESIII Collaboration, we investigate this three-body weak decay via the chiral unitary approach for the final state interaction, where the resonances $S(980)$ and $S(1710)$ are dynamically reproduced with the interaction of eleven coupled channels, and the $W$-external and -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 $K^0_S K^0_S$ and $K^0_S \pi^+$ invariant mass spectra measured by the BESIII Collaboration. The fitted results show that the enhancement around 1.7 GeV in $K^0_S K^0_S$ mass spectrum is overlapped with two visible peaks, indicating the mixing signal originated from the resonances $a_0(1710)$ and $f_0(1710)$ due to their different poles (masses). Thus, the decay $D^+_s \rightarrow K^0_S K^0_S \pi^+$ is helpful to reveal their molecular nature with the mixing signal, which can be more precisely measured in the future.