Chiral sum rules and vacuum condensates from tau-lepton decay data

Abstract

QCD finite energy sum rules, together with the latest updated ALEPH data on hadronic decays of the tau-lepton are used in order to determine the vacuum condensates of dimension $d=2$ and $d=4$. These data are also used to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension $d=6$ and $d=8$, as well as the chiral correlator at zero momentum, proportional to the counter term of the $\mathcal{O}(p^4)$ Lagrangian of chiral perturbation theory, ${\bar{L}}_{10}$. Suitable (pinched) integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations. We find no compelling indications of duality violations in the kinematic region above $s\simeq 2.2$ GeV${}^2$ after using pinched integration kernels.

Revised version with additional discussions/comments

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• Hadronic Z- and tau-Decays in Order alpha_s^4
• S-parameter and pseudo-Nambu-Goldstone boson mass from lattice QCD
• Determination of QCD condensates from tau-decay data
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Cited by in corpus (6)

• Precision physics with inclusive QCD processes
• Charm Quark Mass with Calibrated Uncertainty
• Anomalous magnetic moment of the muon, a hybrid approach
• Tests of quark-hadron duality in tau-decays
• Charm quark mass determined from a pair of sum rules
• Quark-hadron duality: pinched kernel approch