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.

Comments: Revised version with additional discussions/comments