Heavy flavor decays, OPE and duality in two-Dimensional 't Hooft model

Abstract

The 't Hooft model (two-dimensional QCD in the limit of large number of colors) is used as a laboratory for exploring various aspects of the heavy quark expansions in the nonleptonic and semileptonic decays of heavy flavors. We perform a complete operator analysis and construct the operator product expansion (OPE) up to terms O(1/m_Q^4), inclusively. The OPE-based predictions for the inclusive widths are then confronted with the "phenomenological" results, obtained by summation of all open exclusive decay channels, one by one. The summation is carried out analytically, by virtue of the 't Hooft equation. The two alternative expressions for the total widths match. We comment on the recent claim in the literature of a 1/m_Q correction to the total width which would be in clear conflict with the OPE result. The issue of duality violations both in the simplified setting of the 't Hooft model and in actual QCD is discussed. The amplitude of oscillating terms is estimated.

RevTex, 39 pages, 8 figures. Presentation is made more detailed, particular in the part regarding duality violations. Numerical estimates for tau decays are changed, an additional plot is provided

References in corpus (2)

• An Illustrative Example of How Quark-Hadron Duality Might Work
• Explicit Quark-hadron Duality in Heavy-light Meson Weak Decays in the 't Hooft Model

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