What two models may teach us about duality violations in QCD

TL;DR

This paper investigates duality violations in QCD using two models, showing how resonance properties affect these violations and proposing methods to mitigate their impact in sum rule analyses.

Contribution

It introduces a comparative analysis of duality violations using the Coulomb system and a light-quark correlator model, and suggests suppression techniques in sum rules.

Findings

Duality violations are maximal for zero-width bound states.

Broader resonances exhibit weaker duality violations.

Appropriate weight functions can suppress duality violations.

Abstract

Though the operator product expansion is applicable in the calculation of current correlation functions in the Euclidean region, when approaching the Minkowskian domain, violations of quark-hadron duality are expected to occur, due to the presence of bound-state or resonance poles. In QCD finite-energy sum rules, contour integrals in the complex energy plane down to the Minkowskian axis have to be performed, and thus the question arises what the impact of duality violations may be. The structure and possible relevance of duality violations is investigated on the basis of two models: the Coulomb system and a model for light-quark correlators which has already been studied previously. As might yet be naively expected, duality violations are in some sense "maximal" for zero-width bound states and they become weaker for broader resonances whose poles lie further away from the physical axis. Furthermore, to a certain extent, they can be suppressed by choosing appropriate weight functions in the finite-energy sum rules. A simplified Ansatz for including effects of duality violations in phenomenological QCD sum rule analyses is discussed as well.