From topological amplitude to rescattering dynamics in doubly charmed baryon decays

The doubly charmed baryon $\Xi^{++}_{cc}$ was observed by LHCb cooperation in 2017. The branching fractions of two-body doubly charmed baryon decays were predicted in the framework of rescattering mechanism, and some $SU(3)_F$ relations were investigated in the topological amplitudes. In this work, we study the correlation between topological diagram at quark level and rescattering triangle diagram at hadron level in the doubly charmed baryon decay. The completeness of our framework is confirmed from the fact that all the twelve possible structures of meson-baryon scattering appear once each in the the intermediate form between topological diagram and triangle diagram, topological-scattering diagram. It is found 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 $C$, $C^\prime$, $E$, $E^\prime$, $P$ and $P^\prime$ diagrams extracted from $SU(3)_F$ symmetry are consistent with the numerical analysis in literature. Taking $\Xi^{++}_{cc}\to \Xi^+_c\pi^+$, $\Xi^{+}_{cc}\to \Xi^0_c\pi^+$ and $\Xi^{+}_{cc}\to \Xi^+_c\pi^0$ modes as examples, we show the isospin relation is satisfied in terms of triangle diagrams.