From topological amplitude to rescattering dynamics

Abstract

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 → Kπ and D → ππ 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.