Abstract :
We re-examine the estimate of αs and of the QCD condensates from e+e− → I = 1 hadrons data. We conclude that e+e− at low energies gives a value of Λ compatible with the one from LEP and from tau inclusive decay. Using a τ-like inclusive process and QCD spectral sum rules, we estimate the size of the D = 4 to 9 condensates by a fitting procedure without invoking stability criteria. We find 〈αsG2〉 = (7.1 ± 0.7)10−2 GeV4, ϱαs〈uu〉2 = (5.8 ± 0.9)10−4 GeV6, which confirm previous sum rules estimate based on stability criteria. The corrections due to the D = 8 condensates and to instantons on the vector component of τ-decay are respectively δ1(8) = −(1.5 ± 0.6)10−2(1.78Mτ)8 and δ1(9) = −(7.0 ± 26.5)10−4(1.78Mτ)9, which indicate that δ1(8) is one order magnitude higher than the vacuum saturation value, while the D ≥ 9 instanton-like contribution to the the vector component of the τ-decay width is a negligible correction. We also show that, due to the correlation between the D = 4 and1Mτ2 contributions in the ratio of the Laplace sum rules, the present value of the gluon condensate already excludes the recent estimate of the 1Mτ2-term from FESR in the axial-vector channel. Combining our non-perturbative results with the resummed perturbative corrections to the τ-width Rτ, we deduce from the present data αs(Mτ) = 0.33 ± 0.03.
