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.

中文翻译：

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SU（3）Flimit 中魅力重子衰变的拓扑振幅


受魅重子衰变在研究弱相互作用和强相互作用中起着重要作用。拓扑图是分析重强子衰变动力学的直观工具。在这项工作中，我们研究了迷人的重子反三重子 （Bc ̄3） 衰变成轻重子八位字节 （B8） 和轻介子 （M） 的拓扑图。建立了拓扑图和不变张量之间的一对一映射。首次提出了 Bc ̄3→BS8M 模式的拓扑图（其中 BS8 和 BA8 是 q1↔q2 对称和反对称八位字节）和带有夸克环的图。拓扑的完整性通过排列来确认。拓扑的线性关系是通过推导出由三阶和二阶八位张量构建的拓扑振幅之间的关系来获得的。研究发现，导致 Bc ̄3→BS8M 模式的拓扑结构可以由导致 Bc ̄3→BA8M 模式的拓扑结构决定，反之亦然。由拓扑分解的 SU（3） 不可约振幅方程是通过两个不同的中间振幅推导出来的。但是，由于拓扑的数量超过了 SU（3） 不可约幅度的数量，因此不存在逆解。将这个框架应用于标准模型，发现有 13 个独立的 SU（3） 不可约幅度导致 Bc ̄3→B8M 衰减。 其中，与 3D 算子相关的 4 个振幅对 CP 不对称性很重要。考虑到小 Cabibbo-Kobayashi-Maskawa 矩阵元素和 Körner-Pati-Woo 定理引起的抑制，魅力重子衰变的分支分数由 SU（3）F 极限中的五个 SU（3） 不可约振幅主导。夸克环图可以增强 U 形自旋破坏效应并增加两个衰减通道的分支分数差。系统测量单个 Cabibbo 抑制模式的分支分数有助于确定在魅力重子扇区中寻找 CP 不对称性的有前途的通道。