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

May, 1998
29 pages
Published in:
  • Phys.Rev.D 59 (1999) 054022
e-Print:
Report number:
  • UCSD-PTH-98-14,
  • JLAB-THY-98-18

Citations per year

19982005201220192024012345
Abstract: (arXiv)
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.
Note:
  • 29 pages, 13 figs (of 18 eps files)
  • B: hadronic decay
  • B: width
  • anti-B: width
  • quantum chromodynamics
  • dimension: 2
  • expansion 1/N: color
  • Feynman graph
  • tree approximation
  • quark antiquark: annihilation
  • model: parton