Quark-Hadron Duality in the 't Hooft Model for Meson Weak Decays: Different Quark Diagram Topologies

Abstract

We compare the effects of different quark diagram topologies on the weak hadronic width of heavy-light mesons in the large N_c limit. We enumerate the various topologies and show that the only one dominant (or even comparable) in powers of N_c to the noninteracting spectator "tree" diagram is the "annihilation" diagram, in which the valence quark-antiquark pair annihilate weakly. We compute the amplitude for this diagram in the 't Hooft model (QCD in 1+1 spacetime dimensions with a large number of colors N_c) at the hadronic level and compare to the Born term partonic level. We 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.

29 pages, 13 figs (of 18 eps files)

References in corpus (4)

• An Illustrative Example of How Quark-Hadron Duality Might Work
• Heavy flavor decays, OPE and duality in two-Dimensional 't Hooft model
• Explicit Quark-hadron Duality in Heavy-light Meson Weak Decays in the 't Hooft Model
• How quark hadron duality in QCD may work

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