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

The authors compare the effects of different quark diagram topologies on the weak hadronic width of heavy-light mesons in the large Nc limit. They enumerate the various topologies and show that the only one dominant (or even comparable) in powers of Nc to the noninteracting spectator ''tree'' diagram is the ''annihilation'' diagram, in which the valence quark-antiquark pair annihilate weakly. They compute the amplitude for this diagram in the 't Hooft model (QCD in 1+1 spacetime dimensions with a large number of colors Nc) at the hadronic level and compare to the Born term partonic level. They find that quark-hadron duality is not well satisfied, even after the application of a smearing procedure to the hadronic result. A number of interesting subtleties absent from the tree diagram case arise in the annihilation diagram case, and are described in detail