Charmed baryon decays: $SU(3)_F$ breaking and CP violation

Abstract

We present a comprehensive study of anti-triplet charmed baryon decays into octet baryons and pseudoscalar mesons using the $SU(3)_F$ flavor symmetry framework. By decomposing the flavor structure, all decay amplitudes are parametrized with a minimal set of irreducible amplitudes, and the K\"{o}rner-Pati-Woo theorem further reduces the number of independent parameters from the original 35 to 19 under exact symmetry when small terms proportional to $\lambda_b = V_{cb}^*V_{ub}$ are neglected. The independent number becomes 27 with leading $SU(3)_F$ breaking effects. A global fit to 51 experimental measurements yields a $\chi^2$/d.o.f. of 2.36 and provides precise values for the decay amplitudes. Notable discrepancies are observed in the fitted branching fractions of $\Xi_c^0 \to \Xi^- \pi^+$ and $\Xi_c^+ \to \Xi^- \pi^+ \pi^+$, which exceed current measurements by more than $2\sigma$. Incorporating final-state rescattering effects to recover the main effects of terms proportional to $\lambda_b$, we predict enhanced CP violation, with $A_{CP}$ reaching up to $10^{-3}$ in golden channels such as $\Xi_c^0 \to p K^-$ and $\Xi_c^0 \to \Sigma^+ \pi^-$. Our analysis also finds that the branching ratio for $\Xi_c^+ \to \Lambda \pi^+$ is enhanced to $(9.7 \pm 1.2) \times 10^{-4}$ due to significant cancellations.