Quark-hadron duality: pinched kernel approch

TL;DR

This paper uses pinched kernel finite energy sum rules with ALEPH data to investigate quark-hadron duality violations, extending the spectral function analysis up to 10 GeV^2 in a model-independent way.

Contribution

It introduces a model-independent method using pinched kernel FESR to study quark-hadron duality violations with experimental spectral data.

Findings

Good saturation of the FESR without explicit DV models

Spectral functions consistent with perturbative QCD up to 10 GeV^2

Supports minimal duality violations in the studied channels

Abstract

Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark-hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to $s = 10\; {\mbox{GeV}^2}$ by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using $e^+ e^-$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.