Topological diagram analysis of $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ decays in the $SU(3)_F$ limit and beyond

Charm baryon decay plays an important role in studying non-perturbative baryonic transitions. Compared to other hadron multiplets, the flavor symmetry of baryon decuplet is more simple and attractive. In this work, we study the topological amplitudes of charmed baryon decays into decuplet baryon in the flavor symmetry and the linear $SU(3)_F$ breaking. It is found most of topological diagrams are suppressed by the K\"orner-Pati-Woo theorem in the $SU(3)_F$ limit. Only two independent amplitudes contributing to the $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ decays, with one dominating the branching fractions. The Lee-Yang parameters of all $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ modes are the same in the $SU(3)_F$ limit, and there are only four possible values for the CP asymmetries. After including the first-order $SU(3)_F$ breaking effects, the $\Xi^+_c\to \Sigma^{* +}\overline K^0$ and $\Xi^+_c\to \Xi^{* 0}\pi^+$ decays have non-zero branching fractions. The number of free parameter contributing to the $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ decays in the linear $SU(3)_F$ breaking is smaller than the available data. The $SU(3)_F$ breaking part of the quark loop diagram can be extracted by global fitting of branching fractions, which could help us understand the CP violation in charm sector. Additionally, some new isospin equations are proposed to test the K\"orner-Pati-Woo theorem.