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

Abstract

The doubly charmed baryon was first observed by LHCb via the non-leptonic decay $\Xi_{cc}^{++}\to \Lambda^+_cK^-\pi^+\pi^+$ in 2017. Subsequently, ongoing efforts have been made to identify other doubly charmed baryons. However, there is no systematic analysis of the topological decomposition for non-leptonic decays of doubly charmed baryons. In this work, we study the topological amplitudes of doubly charmed baryon decays in the $SU(3)_F$ limit. Tree- and penguin-induced topological diagrams for the $\mathcal{B}_{cc}\to \mathcal{B}_c M$ and $\mathcal{B}_{cc}\to \mathcal{B} D$ decays are presented. The linear relations between the topological amplitudes and the $SU(3)$ irreducible amplitudes are derived through tensor contraction and $SU(3)$ decomposition. The magnitude pattern of the topological diagrams is analyzed in the rescattering dynamics and the large $N_c$ expansion. In addition, some amplitude relations are derived to test the K\"orner-Pati-Woo theorem in the isospin limit.