B. Grinstein et Rf. Lebed, EXPLICIT QUARK-HADRON DUALITY IN HEAVY-LIGHT MESON WEAK DECAYS IN THET-HOOFT MODEL, Physical review. D. Particles and fields, 57(3), 1998, pp. 1366-1378
We compute the nonleptonic weak decay width of a heavy-light meson in
1 + 1 spacetime dimensions with a large number of QCD colors (the 't H
ooft model) as a function of the heavy quark mass. In this limit, QCD
is exactly soluble, and decay modes an dominated by two-particle final
states. We compare the results to the tree-level partonic decay width
of the heavy quark in order to test quark-hadron duality in this univ
erse. We find that this duality is surprisingly well satisfied in the
heavy quark limit, in that the difference between the sum of exclusive
partial widths and the tree-level partonic width approaches a constan
t as M --> infinity, and the deviation is well-fit by a small 1/M corr
ection. We comment on the meaning of this conclusion and its implicati
ons for the use of quark-hadron duality in hadronic physics.