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

TL;DR

This paper uses tau-lepton decay data and QCD sum rules to determine vacuum condensates, test sum rule validity, and evaluate chiral parameters, finding no significant duality violations above 2.2 GeV².

Contribution

It introduces pinched integration kernels in sum rules to suppress duality violations and accurately determine various vacuum and chiral condensates from experimental data.

Findings

Vacuum condensates of dimensions 2 and 4 are determined.

Validity of Weinberg sum rules is confirmed.

No significant duality violations observed above 2.2 GeV².

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 ${\cal{O}}(p^4)$ 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.