Roles of $f_0(980)$ and $a_0(980)$ in the process $Λ_c^+ \to pK_S^0K_S^0$: a clean probe of the $K\bar K$ final-state interaction

Abstract

Based on the Belle measurement of $Λ_c^+ \to pK_S^0K_S^0$, we study the contributions of the light scalar mesons $f_0(980)$ and $a_0(980)$, dynamically generated from the $S$-wave pseudoscalar meson--pseudoscalar meson interaction within the chiral unitary approach, to the threshold enhancement in the $K_S^0K_S^0$ invariant mass squared distribution, and examine the possible contribution of the intermediate $Σ(1620)$ resonance in the $pK_S^0$ subsystem. We first argue that the $Λ_c^+ \to pK_S^0K_S^0$ channel is a cleaner probe of the $K\bar K$ final-state interaction than the charged channel $Λ_c^+ \to pK^+K^-$, since the $ϕ$ and $Λ^*$ contributions are forbidden and the $Σ(1620)$ and $Σ(1660)$ couple weakly to the $\bar{K}N$ channel. The threshold enhancement in the $K_S^0K_S^0$ invariant mass squared distribution is well described by the $S$-wave $K^0\bar K^0$ final-state interaction alone, with the $f_0(980)$ contribution dominating while that of $a_0(980)$ is small, supporting the interpretation of $f_0(980)$ as a $K\bar K$ hadronic molecular state. Future high-precision measurements by Belle~II and the proposed Super Tau-Charm Facility will help test the roles of the $f_0(980)$ and $a_0(980)$ and of the possible $Σ(1620)$ contribution in this process.