A novel method for searching the $\Xi_c^{0/+}$-$\Xi_c^{\prime 0/+}$ mixing effect in the angular distribution analysis of a four-body $\Xi_c^{0/+}$ decay

In this work, we raised a novel method for searching the $\Xi^{0+}_c$-$\Xi_c^{0+\prime}$ mixing effect in an angular distribution analysis of the $\Xi_c\to\Xi^{(\prime)}(\Lambda \pi)\ell^+\nu$ decay, where the mixing effect can be observed by the appearance of the $\Xi^{\prime}$ resonant. Armed with this angular distribution, the decay branching fraction and the forward-backward asymmetry are predicted. We pointed out that the forward-backward asymmetry, as a function of the invariant mass square of $\Xi^{(\prime)}$ and the $\Xi^{0+}_c$-$\Xi_c^{0+\prime}$ mixing angle $\theta_c$, can be used to distinguish the two resonants $\Xi^{(\prime)}$ and even provide a possibility to determine the exact mixing angle.