Topological amplitudes of charmed baryon decays in the $SU(3)_F$ limit

Charmed baryon decay plays an important role in studying the weak and strong interactions. Topological diagram is an intuitive tool for analyzing the dynamics of heavy hadron decays. In this work, we investigate the topological diagrams of charmed baryon antitriplet ($\mathcal{B}_{c\overline 3}$) decays into a light baryon octet ($\mathcal{B}_8$) and a light meson ($M$). The topological diagrams of the $\mathcal{B}_{c\overline 3}\to \mathcal{B}_8^S M$ modes (where $\mathcal{B}_8^S$ and $\mathcal{B}_8^A$ are the $q_1\leftrightarrow q_2$ symmetric and antisymmetric octets) and the diagrams with a quark loop are presented for the first time. The completeness of topologies is confirmed by permutation. The linear relations of topologies are obtained by deriving the relation between the topological amplitudes constructed by the third- and second-rank octet tensors. The equations of $SU(3)$ irreducible amplitudes decomposed by topologies are derived through two different intermediate amplitudes. However, the inverse solution does not exist since the number of topologies exceeds number of $SU(3)$ irreducible amplitudes. Applying this framework to the Standard Model, it is found there are thirteen independent $SU(3)$ irreducible amplitudes contributing to the $\mathcal{B}_{c\overline 3}\to \mathcal{B}_8 M$ decays. Among these, four amplitudes associated with three-dimensional operators are significant for $CP$ asymmetries. Considering the suppressions due to small Cabibbo-Kobayashi-Maskawa matrix elements $V_{cb}^*V_{ub}$ and the K\"orner-Pati-Woo theorem, the branching fractions of charmed baryon decays are dominated by five $SU(3)$ irreducible amplitudes in the $SU(3)_F$ limit.