Asymptotic estimate of the n-loop QCD contribution to the total e+e- annihilation cross section

A technique for estimating the large-order QCD perturbative contributions to the total e+e- total cross section is presented which is based upon the renormalization group and momentum analyticity. Our estimate for the coefficient of (αs/π)3 has recently been confirmed by two exact calculations. We find that the effective expansion parameter is, in fact, not αs/π but rather 4π2eb1(αs/π), where b1 is the first coefficient in the expansion of the β function