Analysis of Hadronic Weak Decays of Charmed Baryons in the Topological Diagrammatic Approach

We perform a global fit to the experimental data of two-body charmed baryon decays based on the topological diagrammatic approach (TDA) and take into account the phase shifts between $S$- and $P$-wave amplitudes as inspired by the recent BESIII measurement of the decay asymmetry in the decay $\Lambda_c^+\to \Xi^0K^+$. The TDA has the advantage that it is more intuitive, graphic and easier to implement model calculations. The measured branching fractions and decay asymmetries are well accommodated in the TDA except for a few modes, in particular, the predicted ${\cal B}(\Xi_c^0\to \Xi^-\pi^+)=(2.83\pm0.10)\%$ is larger than its current value. The equivalence of the TDA and the irreducible SU(3) approach (IRA) is established. We show that the number of the minimum set of tensor invariants in the IRA and the topological amplitudes in the TDA is the same and present their relations. The predicted magnitudes of $S$- and $P$-wave amplitudes and their phase shifts are presented for measured and yet-to-be-measured modes in both the TDA and IRA which can be tested in the near future. Besides the decay $\Lambda_c^+\to \Xi^0 K^+$, there exist several modes which proceed only through $W$-exchange. In particular, the observed channel $\Xi_c^0\to \Sigma^+ K^-$ should have phase shifts similar to that in $\Lambda_c^+\to \Xi^0 K^+$ and its decay asymmetry is predicted to be $-0.21\pm0.17$ which can be used to test our theoretical framework. In contrast, the TDA leads to a large $\alpha$ of order $-0.93$ for the decay $\Xi_c^+\to \Xi^0\pi^+$ even after the phase-shift effect is incorporated in the fit.