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Testing the Concept of Quark–Hadron Duality with the ALEPH τ Decay Data

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An Erratum to this article was published on 06 June 2012

Abstract

We propose a modified procedure for extracting the numerical value for the strong coupling constant α s from the τ lepton hadronic decay rate into non-strange particles in the vector channel. We employ the concept of the quark–hadron duality specifically, introducing a boundary energy squared s p > 0, the onset of the perturbative QCD continuum in Minkowski space (Bertlmann et al. in Nucl Phys B 250:61, 1985; de Rafael in An introduction to sum rules in QCD. In: Lectures at the Les Houches Summer School. arXiv: 9802448 [hep-ph], 1997; Peris et al. in JHEP 9805:011, 1998). To approximate the hadronic spectral function in the region s > s p, we use analytic perturbation theory (APT) up to the fifth order. A new feature of our procedure is that it enables us to extract from the data simultaneously the QCD scale parameter \({\Lambda_{\overline{\rm MS}}}\) and the boundary energy squared s p. We carefully determine the experimental errors on these parameters which come from the errors on the invariant mass squared distribution. For the \({\overline{\rm MS}}\) scheme coupling constant, we obtain \({\alpha_s(m^{2}_{\tau})=0.3204\pm 0.0159_{exp.}}\). We show that our numerical analysis is much more stable against higher-order corrections than the standard one. Additionally, we recalculate the “experimental” Adler function in the infrared region using final ALEPH results. The uncertainty on this function is also determined.

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  1. Andrea Razmadze Mathematical Institute, M. Aleksidze St. 1, 0193, Tbilisi, Georgia

    B. A. Magradze

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An erratum to this article can be found at http://dx.doi.org/10.1007/s00601-012-0449-4

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Magradze, B.A. Testing the Concept of Quark–Hadron Duality with the ALEPH τ Decay Data. Few-Body Syst 48, 143–169 (2010). https://doi.org/10.1007/s00601-010-0113-9

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