Heavy Quark Expansion and Preasymptotic Corrections to Decay Widths in the 't Hooft Model

TL;DR

This paper investigates nonperturbative corrections to heavy hadron decay widths within the 't Hooft model, confirming the validity of the 1/m_Q expansion and exploring duality violations and hadronization effects.

Contribution

It analytically sums exclusive decay widths in the 't Hooft model and compares the results with OPE predictions, highlighting the role of spectator effects and duality violations.

Findings

1/m_Q expansion matches OPE predictions at computed orders

Identifies cases where duality is violated and saturated by a single final state

Provides detailed analysis of spectator-dependent effects and hadronization in the 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->oo), with the emphasis on the spectator-dependent effects 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 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.