From topological amplitude to rescattering dynamics in doubly charmed baryon decays

The doubly charmed baryon Xi(++)(cc) cc was observed by LHCb Collaboration in 2017. The branching fractions of two-body doubly charmed baryon decays were predicted in the framework of a rescattering mechanism, and some SU(3)(F) relations were investigated in the topological amplitudes. In this work, we study the correlation between a topological diagram at quark level and a rescattering triangle diagram at hadron level in the doubly charmed baryon decay. The completeness of our framework is confirmed from the fact that all 12 possible structures of meson-baryon scattering appear once each in the intermediate form between the topological diagram and the triangle diagram, topological-scattering diagram. It is found that the triangle diagrams derived from the topological diagrams are consistent with the ones derived directly from the chiral Lagrangian. The relative magnitudes of rescattering contributions in the C, C', E, E', P, and P' diagrams extracted from SU(3)(F) symmetry are consistent with the numerical analysis in literature. Taking Xi(++)(cc) -> Xi(+)(c)pi(+), Xi(+)(cc) -> Xi(0)(c)pi(+), and Xi(+)(cc) Xi(+)(c)pi(0) modes as examples, we show the isospin relation is satisfied in terms of triangle diagrams.

Automated summary

In this study, we investigated the correlation between topological diagrams and triangle diagrams in the decay of doubly charmed baryons. We confirmed the completeness of our framework and found the consistency between triangle diagrams derived from topological diagrams and those derived directly from the chiral Lagrangian. Furthermore, the relative magnitudes of rescattering contributions extracted from SU(3)(F) symmetry were consistent with numerical analysis.