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

TL;DR

This work develops a comprehensive $SU(3)_F$-based topological-amplitude framework for two-body non-leptonic decays of doubly charmed baryons, detailing tree- and penguin-induced diagrams for channels like $\mathcal{B}_{cc}\to \mathcal{B}_{c\overline 3}M$, $\mathcal{B}_{cc}\to \mathcal{B}_{c6}M$, $\mathcal{B}_{cc}\to \mathcal{B}_{8}D$, and $\mathcal{B}_{cc}\to \mathcal{B}_{10}D$. It derives linear relations between topological amplitudes and $SU(3)$ irreducible amplitudes via tensor contraction, and analyzes magnitude patterns through rescattering dynamics and the large $N_c$ expansion. The paper also tests the Körner-Pati-Woo theorem in the isospin limit, deriving testable relations and highlighting potential violations due to long-distance rescattering. By connecting symmetry-based flavor sum rules with explicit topological decompositions, it provides a framework to predict relations among branching fractions and CP asymmetries, guiding both experimental measurements and future theory in this sector.

Abstract

The doubly charmed baryon was first observed by LHCb via the non-leptonic decay $Ξ_{cc}^{++}\to Λ^+_cK^-π^+π^+$ 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.

Figures (10)

• Figure 1: Topological diagrams of the $\Xi_{cc}$ and $\Omega_{cc}$ decays into a charmed baryon and a light meson.
• Figure 2: Topological diagrams in doubly charmed baryon decays into a charmed meson and a light octet baryon $\mathcal{B}_8^S$, in which "$)$" indicates that the two light quarks in final-state baryon are symmetric in flavor.
• Figure 3: Topological diagrams in $\Xi_{cc}$ and $\Omega_{cc}$ decays into a charmed meson and a light decuplet baryon.
• Figure 4: Long-distance rescattering contributions in diagram $C_1$.
• Figure 5: Long-distance rescattering contributions in diagram $C_2$.