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The BESIII collaboration has recently reported the first time measurement ofthe decay asymmetry $\alpha(\Lambda_c^+ \to \Xi^0 K^+) = 0.01 \pm 0.16(stat.)\pm 0.03(syst.)$ and also a sizable phase shift of $\delta_P-\delta_S = -1.55\pm 0.25$ or $1.59\pm 0.25$ between S- and P-wave amplitudes. This impliessignificant strong phase shifts in the decay amplitudes. The strong phasesindicate the existence of rescattering or loop effects, which are challengingto calculate due to non-perturbative effects. By employing the flavor $SU(3)_F$symmetry and applying the K\"orner-Pati-Woo theorem to reduce the number ofparameters, we find that the current data already allow us to obtain, for thefirst time, model-independent decay amplitudes and their strong phases. Theestablishment of the existence of sizable strong phases opens a window forfuture investigations into CP violation. In our fit, a notable discrepancyemerges in the branching ratio of $\Xi_c^0 \to \Xi^- \pi^+$. The directrelationship between $\Gamma (\Lambda_c^+ \to \Lambda e^+\nu_e)$ and $\Gamma(\Xi_c^0 \to \Xi^- e^+\nu_e)$, along with newly discovered $SU(3)_F$ relations,collectively suggests an underestimation of $\mathcal{B}(\Xi_c^0 \to \Xi^-\pi^+)$ in experimental findings.

Complete determination of $SU(3)_F$ amplitudes and strong phase in $\Lambda_c^+ \to \Xi^0 K^+$