Revisiting quark-hadron duality for heavy meson non-leptonic decays in two-dimensional QCD

TL;DR

This paper examines quark-hadron duality in heavy meson decays using a solvable two-dimensional QCD model, comparing theoretical predictions with hadronic decay data to assess the accuracy of heavy quark expansion methods.

Contribution

It provides a numerical analysis of quark-hadron duality in a two-dimensional QCD model, highlighting the conditions under which inclusive and exclusive decay rates agree or differ.

Findings

Inclusive and exclusive decay rates differ by up to current experimental errors.

Excellent agreement observed for the ratio of D meson lifetimes.

Discrepancies are comparable to theoretical uncertainties in four-dimensional QCD.

Abstract

We study lifetimes of heavy mesons in the 't Hooft model, a large-$N_c$ theory of strong interaction in two-dimensional spacetime. Since this model is solvable, one can evaluate the total decay widths through hadronic amplitudes that are determined unambiguously within the formalism. We investigate quark-hadron duality by numerically comparing the exclusive result and one from the heavy quark expansion, with the contribution of Pauli interference being consistently incorporated. Within certain numerical accuracy, we find that the maximal difference between inclusive and exclusive rates for $\tau[D^+_s]/\tau[D^0]$ $(\tau[B^+]/\tau[B^0])$ is as large as the current experimental (theoretical) error in four-dimensions, except for $\tau[D^+]/\tau[D^0]$, where an excellent agreement between the rates is seen.