Theoretical study on $Λ_c^+ \to ΛK^+\bar{K}^0$ decay and $Ξ^*(1690)$ resonance

Abstract

We present a theoretical study of $Ξ^*(1690)$ resonance in the $Λ_c^+ \to ΛK^+ \bar{K}^0$ decay, where the weak interaction part proceeds through the Cabibbo-favored process $c \to s + u\bar{d}$. Next, the intermediate two mesons and one baryon state can be constructed with a pair of $q\bar{q}$ with the vacuum quantum numbers. Finally, the $Ξ^*(1690)$ is mainly produced from the final state interactions of $\bar{K}Λ$ in coupled channels, and it is shown in the $\bar{K}Λ$ invariant mass distribution. Besides, the scalar meson $a_0(980)$ and nucleon excited state $N^*(1535)$ are also taken into account in the decaying channels $K^+\bar{K}^0$ and $K^+Λ$, respectively. Within model parameters, the $K^+ \bar{K}^0$, $\bar{K}^0 Λ$ and $K^+ Λ$ invariant mass distributions are calculated, and it is found that our theoretical results can reproduce well the experimental measurements, especially for the clear peak around $1690$ MeV in the $\bar{K}Λ$ spectrum. The proposed weak decay process $Λ_c^+ \to ΛK^+ \bar{K}^0$ and the interaction mechanism can provide valuable information on the nature of the $Ξ^*(1690)$ resonance.