Charmed $\Lambda_c^+$ baryon decays into light scalar mesons in the topological $SU(3)_f$ framework

Abstract

Using the topological-diagram approach based on $SU(3)$ flavor symmetry, we investigate two-body $\Lambda_c^+\to {\bf B}S$ decays, where ${\bf B}$ denotes the final-state baryon and $S$ refers to a light scalar meson, such as $f_0/f_0(980)$, $a_0/a_0(980)$, $\sigma_0/f_0(500)$, or $\kappa/K_0^*(700)$. Our analysis indicates that interpreting the light scalar mesons as tetraquark states provides a more consistent description of the currently available experimental data. In particular, this framework naturally accommodates the experimentally observed branching fraction ${\cal B}(\Lambda_c^+ \to \Lambda a_0^+)$, which exceeds predictions based solely on long-distance effects by an order of magnitude. Within the tetraquark scenario, we predict ${\cal B}(\Lambda_c^+\to \Sigma^+ f_0)=(4.9\pm 1.9)\times 10^{-2}$ and ${\cal B}(\Lambda_c^+\to p f_0)=(3.6\pm 1.4)\times 10^{-3}$. Owing to $f_0-\sigma_0$ mixing, ${\cal B}(\Lambda_c^+\to \Sigma^+ \sigma_0)$ and ${\cal B}(\Lambda_c^+\to p\sigma_0)$ are suppressed to the levels of $1\times 10^{-3}$ and $5\times 10^{-5}$, respectively. These modes therefore provide sensitive probes of the internal structure of the light scalar mesons. More generally, the remaining branching ratios of $\Lambda_c^+ \to {\bf B} S$ are found to be comparable to those of $\Lambda_c^+ \to {\bf B}M$, where $M$ denotes a pseudoscalar meson. Their predicted sizes suggest that these decay modes should be accessible to ongoing and near-future experimental studies at BESIII, Belle II, and LHCb.