From topological amplitude to rescattering dynamics

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