Theoretical study of $f_0(980)$, $a_0(980)$ and $Ξ(1/2^-)$ in the process $Ξ_c^+ \to Σ^+K^+K^-$

TL;DR

This work leverages the chiral unitary approach to study the nonleptonic weak decay $\Xi_c^+ \to \Sigma^+K^+K^-$. The $\Xi(1/2^-)$ resonance is generated dynamically through $S$-wave meson–baryon interactions in a six-channel coupled-system, while the light scalar mesons $f_0(980)$ and $a_0(980)$ emerge from $S$-wave meson–meson interactions; the total decay amplitude combines a tree term with MB and MM rescattering encoded in Bethe–Salpeter dynamics $T=[1-VG]^{-1}V$. Numerically, a pronounced peak around $M(K^-\Sigma^+)\approx 1690$ MeV signals the $\Xi(1/2^-)$, and a cusp near $M(K^+K^-)\approx 980$ MeV reflects $f_0(980)$/ $a_0(980)$ effects, with robustness against variations in the color factor and interference phase. The results offer clear experimental signatures to validate the dynamical nature of these resonances and motivate precise measurements of the $\Xi_c^+$ decay in future experiments.

Abstract

We employed the chiral unitarity approach to investigate the decay process $Ξ_c^+ \to Σ^+K^+K^-$. by considering that the low lying nucleon resonance $Ξ(1/2^-)$ and the low lying scalar meson $f_0(980)$ and $a_0(980)$ that could be dynamically generated through $S$-wave pseudoscalar meson-octet baryon and the $S$-wave pseudoscalar meson-pseudoscalar meson interactions, respectively. In the invariant mass distributions of $Σ^+K^-$ and $K^+K^-$, we observe a distinct peak structure associated with the resonant state $Ξ(1/2^-)$ and a bit enhancement near the $K^+K^-$ threshold that is corresponding to the mesons $f_0(980)$ and $a_0(980)$, respectively. Consequently, we recommend more precise experimental measurements of this process in the future.

Figures (9)

• Figure 1: Quark level diagram for the process $\Xi_c^+ \to K^+ s \left(\bar{u}u+\bar{d}d+\bar{s}s\right)us$ via the $W^+$ external emission.
• Figure 2: The mechanisms of the decay $\Xi_c^+ \to \Sigma^+K^+K^-$, (a) tree diagram, (b) the $S$-wave final state interactions.
• Figure 3: Quark level diagram. (a) The process $\Xi_c^+\to \Sigma^+$$s \left(\bar{u}u+\bar{d}d+\bar{s}s\right)\bar{s}$ via the $W^+$ internal emission. (b) Th -e process $\Xi_c^+ \to \Sigma^+ d \left(\bar{u}u+\bar{d}d+\bar{s}s\right)\bar{d}$ via the $W^+$ inter -nal emission.
• Figure 4: The mechanisms of the decay $\Xi_c^+ \to \Sigma^+K^+K^-$, (a) tree diagram, (b) the $S$-wave final state interactions.
• Figure 5: The $K^-\Sigma^+$ invariant mass distribution of the process $\Xi_c^+ \to \Sigma^+K^+K^-$ decay.