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We address numerical aspects of local quark-hadron duality using the exampleof the exactly solvable 't Hooft model, two-dimensional QCD with N_c -->infinity. The primary focus of these studies is total semileptonic decay widthsrelevant for extracting |V_{cb}| and |V_{ub}|. We compare the exactchannel-by-channel sum of exclusive modes to the corresponding rates obtainedin the standard 1/m_Q expansion arising from the Operator Product Expansion. Animpressive agreement sets in unexpectedly early, immediately after thethreshold for the first hadronic excitation in the final state. Yet even athigher energy release it is possible to discern the seeds of duality-violatingoscillations. We find the ``Small Velocity'' sum rules to be exceptionally wellsaturated already by the first excited state. We also obtain a convincingdegree of duality in the differential distributions and in an analogue ofR_{e^+e^-}(s). Finally, we discuss possible lessons for semileptonic decays ofactual heavy quarks in QCD.Comment: 45 pages, 16 eps figures include

Precision studies of duality in the ’t Hooft model