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Based on our previous work about the role of $a_0(1710)$ in the$D_s^+\to\pi^+K_S^0K_S^0$ decay [Phy. Rev. D 105, 116010 (2022)], we perform afurther theoretical study of $a_0(1710)^+$ in the process $D^+_s \to \pi^0a_0(1710)^+ \to \pi^0 K^+ K^0_S$. In addition to $a_0(1710)$, the contributionsof $K^*$ and $a_0(980)$ are also taken into account. Firstly, we consider thecontributions from the tree diagrams of $K^{*+} \to K^+\pi^0$ and $\bar{K}^{*0}\to \pi^0 \bar{K}^0$. Secondly, we describe the final state interaction of$K\bar{K}$ in the chiral unitary approach to study the contribution of$a_0(980)$, while the $a_0(1710)$ state is dynamically generated from the$K^*\bar{K}^*$ interaction, and then decays into $K^+\bar{K}^0$. Since thefinal $K^+ K_S^0$ state is in pure isospin $I=1$, the $D_s^+\to\pi^0K^+K_s^0$decay is an ideal process to study the $a_0(1710)^+$ and $a_0(980)^+$resonances. Based on our theoretical calculations, it is found that the recentexperimental measurements on the $K^+K^0_S$, $\pi^0K^+$, and $\pi^0 K_S^0$invariant mass distributions can be well reproduced, which supports themolecular $K^*\bar{K}^*$ nature of the scalar $a_0(1710)$ resonance.

Further understanding the nature of $a_0(1710)$ in the $D^+_s \to \pi^0 K^+ K^0_S$ decay