We exploit the fact that within massless perturbative QCD the same Green's
function determines the hadronic contribution to the τ decay width and the
moments of the e+e− cross section. This allows one to obtain relations
between physical observables in the two processes up to an unprecedented high
order of perturbative QCD. A precision measurement of the τ decay width
allows one then to predict the first few moments of the spectral density in
e+e− annihilations integrated up to s∼mτ2 with high accuracy.
The proposed tests are in reach of present experimental capabilities.Comment: 7 pages, Latex, no figure