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 quark diagram, which is the intermediate structure between topological diagram and triangle diagram, are expressed in the tensor form. The completeness of quark diagram is confirmed by the quark substructure of meson-meson scattering. The coefficient of each triangle diagram can be derived from the quark diagram and the total rescattering amplitudes are consistent with the ones derived from the chiral Lagrangian. If only the shortdistance 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 are only arisen from the SU (3) F breaking effects. Taking D → Kπ and D → ππ decays 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.

Direct CP violation in charmed meson decays within the standard model

“…In 2012 we have made the ansatz that ( + ) LD is of the same order of magnitude as and flavor independent. Very recently, this ansatz was shown to be justified in the diagrammatic approach under the SU(3) limit; that is, ( + ) LD = LD ≈ [9]. Then we have…”

From topological amplitude to rescattering dynamics in doubly charmed baryon decays

“…The minus sign before 1/2 arises from the cross in L(C ) 1 [u, d, s, u] because of the commutator in the effective chiral lagrangian of meson-meson scattering [19]. In T ⇒ T transition, the topological- s, u, d] vanishes due to the Pauli exclusion principle [19] and hence only…”

“…Inspired by the idea of topological diagram expressed in the invariant tensor [16][17][18], we proposed a theoretical framework to associate topological amplitude and rescattering dynamics in heavy meson decays in Ref. [19]. In this framework, both the triangle diagram and the topologicalscattering diagram are expressed in the tensor form.…”

“…The triangle diagrams derived from topological diagrams are the same with the ones derived from the chiral Lagrangian. In this work, we generalize the theoretical framework proposed in [19] to the doubly charmed baryon decays. It is found the twelve possible structures of meson-baryon scattering appear once each in the topological-scattering diagrams.…”

“…), the rescattering contributions in the T diagram are zero under the flavor SU (3) symmetry[19], L(T) 1 = L(T ) 2 = L(T ) 3 = L(T ) 4 = 0.Considering that there are two different configurations of triangle diagrams, the intermediate exchange particle served by meson or baryon, and all triangle diagrams are the same with same configuration under the flavor SU (3) symmetry, we get two proportional relations between the topological-scattering diagrams:L(C) 1 = L(C ) 1 = −L(E) = −L(P ), L(C) 2 = L(C ) 2 = −L(E ) = −L(P ). (33)Notice the sign arbitrariness of topological diagram does not affect the sign of triangle diagram because of Eq.…”