Tests of quark-hadron duality in tau-decays

TL;DR

This paper uses QCD sum rules and updated experimental data to test the validity of quark-hadron duality in tau decays, finding no significant violations above 2.2 GeV².

Contribution

It introduces pinched integration kernels in sum rules to effectively suppress duality violations and experimental errors in tau decay analyses.

Findings

No compelling evidence of duality violations above 2.2 GeV²

Consistent gluon condensate values from vector and axial vector spectral functions

Validation of chiral sum rules and low-energy parameters

Abstract

An exhaustive number of QCD finite energy sum rules for $\tau$-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension $d=2$ condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions $d=6$ and $d=8$, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic $\tau$-decay in the kinematic region above $s\simeq2.2$ GeV$^{2}$ for these kernels.