TheRratio in e+e-, the determination of α (MZ2) and a possible non-perturbative gluonic contribution

Abstract
We review the determination of the QED coupling at the Z pole, which is a crucial parameter for electroweak theory. We include recent e+e-→ hadron data from Novosibirsk and Beijing to re-evaluate α(MZ2). We find α(MZ2)-1 = 128.973±0.035 or 128.934±0.040 according, respectively, to whether inclusive or exclusive e+e-→ hadron data are used respectively in the interval 1.4(s)1/22.1 GeV. The error is mainly due to uncertainties in the data in the low-energy region, (s)1/22.5 GeV. We find that no advantage is obtained by analytic continuation of the dispersion relation into the complex s plane. We show that the hints of structure for (s)1/2~2.5 GeV may be evidence of a non-perturbative gluonic contribution to R(s).