Topological amplitudes of charmed baryon decays in the𝑆⁢𝑈⁢(3)𝐹limit

Abstract

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 (ℬ𝑐⁢¯3) decays into a light baryon octet (ℬ8) and a light meson (𝑀). A one-to-one mapping between the topological diagram and the invariant tensor is established. The topological diagrams of the ℬ𝑐⁢¯3→ℬ𝑆8⁢𝑀 modes (where ℬ𝑆8 and ℬ𝐴8 are the 𝑞1↔𝑞2 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. It is found the topologies contributing to the ℬ𝑐⁢¯3→ℬ𝑆8⁢𝑀 modes can be determined by the topologies contributing to the ℬ𝑐⁢¯3→ℬ𝐴8⁢𝑀 modes, and vice versa. The equations of 𝑆⁢𝑈⁡(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 𝑆⁢𝑈⁡(3) irreducible amplitudes. Applying this framework to the Standard Model, it is found there are thirteen independent 𝑆⁢𝑈⁡(3) irreducible amplitudes contributing to the ℬ𝑐⁢¯3→ℬ8⁢𝑀 decays. Among these, four amplitudes associated with three-dimensional operators are significant for 𝐶⁢𝑃 asymmetries. Considering the suppressions due to small Cabibbo-Kobayashi-Maskawa matrix elements and the Körner-Pati-Woo theorem, the branching fractions of charmed baryon decays are dominated by five 𝑆⁢𝑈⁡(3) irreducible amplitudes in the 𝑆⁢𝑈⁢(3)𝐹 limit. Quark-loop diagrams could enhance the 𝑈-spin breaking effects and increase the branching fraction difference of two decay channels. Systematic measurements of branching fractions of the singly Cabibbo-suppressed modes could help identify promising channels for searching for 𝐶⁢𝑃 asymmetries in the charmed baryon sector.