Parton-Hadron duality in QCD sum rules: quantum mechanical examples

Abstract

Motivated by recent work on three-point QCD sum rules in heavy quark physics, we use the simple quantum mechanical models to study the basic issue of duality in three-point sum rules. We show that while in all of these models the duality in two-point sum rules works fine, the duality in three-point sum rules may be 100%- violated, leading to completely unreliable predictions for the matrix elements in question. The implications for three-point QCD sum rules are discussed. A new estimate for the parameter ${\lambda }_1$ of HQET is given.

Comments: 31 pages, 19 figures. Several references are added. Several typos and minor numerical mistakes are corrected. None of new changes alters any result of the paper