From topological amplitude to rescattering dynamics

We proposed a theoretical framework to correlate the topological diagram at quark level and rescattering dynamics at hadron level. In the framework, both the hadronic triangle diagram, and the topological-scattering diagram, which is the intermediate structure between topological diagram and triangle diagram, are expressed in the tensor form. The completeness of topological-scattering diagram is confirmed by the quark substructure of meson-meson scattering. The coefficient of each triangle diagram can be derived from the topological-scattering diagram and the total rescattering amplitudes are consistent with the ones derived from the chiral Lagrangian. If only the short-distance T diagram is considered as the weak vertex in triangle diagram, the rescattering contributions in the C, E and P diagrams have definite proportional relation of L(C) : L(E) : L(P) = -2 : 1 : 1 under the SU(3)(F) symmetry, and the rescattering contributions in the T and A diagrams only arise from the SU(3)(F) breaking effects. Taking D -> K pi and D -> pi pi modes as examples, we present our framework in detail. We find the Isospin relations in these decays are still valid in terms of triangle diagrams. Besides, the conclusions in the D meson decays under the SU(3)(F) symmetry can be generalized to the B meson decays under the SU(4)(F) symmetry.

Automated summary

This study proposes a theoretical framework to correlate the topological diagram at quark level and rescattering dynamics at hadron level. By analyzing the triangle diagrams, the researchers find the relation between the rescattering contributions in different diagrams and derive the total rescattering amplitudes. The framework is further applied to the decays of D and B mesons and demonstrates the validity of isospin relations.