Charmed $Λ_c^+$ 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 $\Lambda_c^+$ is a member of the anti-triplet charmed baryons (${\bf B}_c$), ${\bf B}$ denotes a 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 demonstrates that short-distance contributions, represented by the topological amplitudes, play a dominant role in these decays. In particular, this framework naturally accounts for the experimentally observed branching ratio ${\cal B}(\Lambda_c^+ \to \Lambda a_0^+)$, which exceeds predictions based solely on long-distance effects by an order of magnitude. Considering the light scalar mesons as tentraquark states, we predict ${\cal B}(\Lambda_c^+\to p f_0,p\sigma_0) =(1.7\pm 0.6,0.02\pm0.01)\times 10^{-3}$ and ${\cal B}(\Lambda_c^+\to \Sigma^{+} f_0,\Sigma^{+} \sigma_0) =(0.7\pm 0.5, 1.5\pm 0.7)\times 10^{-2}$. In addition, the decay $\Lambda_c^+ \to \Xi^0 \kappa^+$, which proceeds via a single $W$-exchange diagram, is found to have a branching fraction of $(4.9 \pm 0.9) \times 10^{-2}$. These results suggest that the branching ratios of ${\bf B}_c \to {\bf B} S$ are generally comparable to those of ${\bf B}_c \to {\bf B}M$, where $M$ denotes a pseudoscalar meson. The predicted rates are sufficiently large to be probed in current experiments at BESIII, Belle II, and LHCb, offering promising opportunities to explore the internal structure of light scalar mesons.