Precision studies of duality in the 't Hooft model - art. no. 094011

We address the numerical aspects of local quark-hadron duality using the ex ample of the exactly solvable 't Hooft model, two-dimensional QCD with N-c- ->infinity. The primary focus of these studies is the total semileptonic de cay widths relevant for extracting \V-cb\ and \V-ub\. We compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtain ed in the standard 1/m(Q) expansion arising from the operator product expan sion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet ev en at higher energy release it is possible to discern the seeds of duality- violating oscillations. We find the "small velocity" sum rules to be except ionally well saturated already by the first excited state. We also obtain a convincing degree of duality in the differential distributions and in an a nalogue of Re+e-(s). Finally, we discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.