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Tests of quark–hadron duality in $τ$ -decays

Centre for Theoretical and Mathematical Physics, and Department of Physics, University of Cape Town, Rondebosch 7700, South Africa

National Insitute for Theoretical Physics, Private Bag X1, Matieland 07602, South Africa

E-mail Address: cesareo.dominguez@uct.ac.za

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L. A. Hernandez

Centre for Theoretical and Mathematical Physics, and Department of Physics, University of Cape Town, Rondebosch 7700, South Africa

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K. Schilcher

Centre for Theoretical and Mathematical Physics, and Department of Physics, University of Cape Town, Rondebosch 7700, South Africa

National Insitute for Theoretical Physics, Private Bag X1, Matieland 07602, South Africa

PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität, D-55099 Mainz, Germany

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H. Spiesberger

Centre for Theoretical and Mathematical Physics, and Department of Physics, University of Cape Town, Rondebosch 7700, South Africa

PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität, D-55099 Mainz, Germany

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https://doi.org/10.1142/S0217732316300366Cited by:4 (Source: Crossref)

Abstract

An exhaustive number of QCD finite energy sum rules for $τ$ -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 $τ$ -decay in the kinematic region above s $≃$ 2.2 GeV² for these kernels.

Keywords:

PACS: 12.38.Lg, 11.55.Hx, 13.35.Dx

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