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 ${\Xi }_{cc}^{++}\to {\Lambda }_c^{+}{K}^{-}{\pi }^{+}{\pi }^{+}$ 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 Körner-Pati-Woo theorem in the isospin limit.

Comments: 24 pages, published version