Heavy flavor decays and OPE 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 testground for calculations of nonleptonic and semileptonic inclusive widths of heavy flavors based on the operator product expansion (OPE). The OPE-based predictions up to terms ${\cal O}(1/m_Q^4)$, inclusively, are confronted with the "phenomenological" results, obtained by summation of all open exclusive decay channels, one by one, a perfect match is found. The issue of duality violations is discussed, the amplitude of oscillating terms is estimated. The method is applied to the realistic case of hadronic $τ$ decays.