Heavy quark expansion and preasymptotic corrections to decay widths in the ’t Hooft model

Abstract

We address nonperturbative power corrections to inclusive decay widths of heavy flavor hadrons in the context of the 't Hooft model (two-dimensional QCD at ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}),$ with the emphasis on the ``spectator-dependent'' effects, i.e., those sensitive to the flavor of the spectator. The summation of exclusive widths is performed analytically using the 't Hooft equation. We show that the ${1/m}_{Q}$ expansion of both the weak annihilation and Pauli interference widths coincides with the OPE predictions to the computed orders. Violation of local duality in the inclusive widths is quantified, and the new example is identified where the OPE prediction and the actual effect are completely saturated by a single final state. The qualitative aspects of quark hadronization emerging from the analysis in the 't Hooft model are discussed. Certain aspects of the summation of spectator-independent hadronic weak decay widths are given in more detail, which were not spelled out previously. We also give some useful details of the ${1/m}_{Q}$ expansion in the 't Hooft model.