Topological Diagram Analysis of Charmed Baryon Decays with Vector Mesons

In this work, we further develop the application of the topological diagram approach (TDA) to charmed baryon weak decays $\mathcal{B}_c \to \mathcal{B} V$ with a vector meson in the final state. By incorporating the Korner-Pati-Woo theorem, we show that only five independent sets of TDA parameters are required. Relations among different decay channels arising from isospin, U-spin, and V-spin symmetries are explicitly derived within the TDA framework. Partial wave contributions and form factors associated with different topological diagrams are extracted from global fits to the experimental data. It is found that the form factors $A_2$ and $B_2$ induced from the tensor interaction of the vector mreson with octet baryons are comparable in magnitude to $A_1$ and $B_1$, implying the importance of the tensor coupling in $\mathcal{B}_c \to \mathcal{B} V$ decays. Branching fractions for all $\mathcal{B}_c\to \mathcal{B} V$ channels are predicted, and most measured modes are found to be in good agreement with current data. More physical observables, including up-down asymmetries, longitudinal polarizations as well as observables in the subsequent decays are also predicted. Our results provide a systematic framework for understanding charmed baryon weak decays with vector mesons and can be further tested with future experiments.