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

Understand

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.