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We compare the effects of different quark diagram topologies on the weakhadronic width of heavy-light mesons in the large N_c limit. We enumerate thevarious topologies and show that the only one dominant (or even comparable) inpowers of N_c to the noninteracting spectator "tree" diagram is the"annihilation" diagram, in which the valence quark-antiquark pair annihilateweakly. We compute the amplitude for this diagram in the 't Hooft model (QCD in1+1 spacetime dimensions with a large number of colors N_c) at the hadroniclevel and compare to the Born term partonic level. We find that quark-hadronduality is not well satisfied, even after the application of a smearingprocedure to the hadronic result. A number of interesting subtleties absentfrom the tree diagram case arise in the annihilation diagram case, and aredescribed in detail.Comment: 29 pages, 13 figs (of 18 eps files

Quark-hadron duality in the ’t Hooft model for meson weak decays: Different quark diagram topologies