Duality violations and spectral sum rules

Abstract

We study the issue of duality violations in the VV-AA vacuum polarization function in the chiral limit. This is done with the help of a model with an expansion in inverse powers of the number of colors, Nc, allowing us to consider resonances with a finite width. Due to these duality violations, the Operator Product Expansion (OPE) and the moments of the spectral function (e.g. the Weinberg sum rules) do not match at finite momentum, and we analyze this difference in detail. We also perform a comparative study of many of the different methods proposed in the literature for the extraction of the OPE parameters and find that, when applied to our model, they all fare quite similarly. In fact, the model strongly suggests that a significant improvement in precision can only be expected after duality violations are included. To this end, we propose a method to parameterize these duality violations. The method works quite well for the model, and we hope that it may also be useful in future determinations of OPE parameters in QCD.

29 pages, 9 figures, LateX file. Small changes to match journal version

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• Updated determination of chiral couplings and vacuum condensates from hadronic tau decay data
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• A New Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to $(g-2{)}_{\mu }$
• $D\to \rho {\ell }^{+}{\ell }^{-}$ Decays in the QCD Factorization Approach
• Low-energy constants and condensates from the tau hadronic spectral functions
• Low-energy constants and condensates from ALEPH hadronic $\tau$ decay data
• Conformal mapping of the Borel plane: going beyond perturbative QCD
• Determination of QCD condensates from tau-decay data
• Duality violations in tau hadronic spectral moments
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
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• The operator product expansion does not imply parity doubling of hadrons
• QCD Description of Hadronic Tau Decays
• Violations of Quark-Hadron Duality in Low-Energy Determinations of ${\alpha }_s$
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• What two models may teach us about duality violations in QCD
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• The origin of mass and the experiments on future high energy accelerators
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• Functional-analysis based tool for testing quark-hadron duality
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• Conformal mappings in perturbative QCD
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• Estimate of the systematic error in tau decay due to duality violations
• The linear radial spectrum of scalar mesons within the QCD sum rules in the planar limit
• Contribution from Duality Violations to the theoretical error on alpha_s
• Hadronic tau decays and the strong coupling
• Hadronic and radiative decays of the tau lepton
• Duality violation in QCD Sum Rules with the LR correlator
• Assuming Regge trajectories in holographic QCD: from OPE to Chiral Perturbation Theory
• ${\alpha }_s$ analyses from hadronic tau decays with OPAL and ALEPH data
• Confronting hadronic tau decays with non-leptonic kaon decays
• Correlators of hadron currents: the model and the ALEPH data on tau-decay
• ChPT parameters from tau-decay data
• Impact of Duality Violations on Spectral Sum Rule Analyses
• Migdal's model and holography
• alpha_s from tau decays revisited