Unification of Flavor SU(3) Analyses of Heavy Hadron Weak Decays

Analyses of heavy mesons and baryons hadronic charmless decays using the flavor SU(3) symemtry can be formulated in two different forms. One is to construct the SU(3) irreducible representation amplitude (IRA) by decomposing effective Hamiltonian, and the other is to draw the topological diagrams (TDA). In the flavor SU(3) limit, we study various $B/Dto PP,VP,VV$, $B_cto DP/DV$ decays, and two-body nonleptonic decays of beauty/charm baryons, and demonstrate that when all terms are included these two ways of analyzing the decay amplitudes are completely equivalent. Furthermore we clarify some confusions in drawing topological diagrams using different ways of describing beauty/charm baryons.