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 (alpha-s/pi)3 has recently been confirmed by two exact calculations. We find that the effective expansion parameter is, in fact, not alpha-s/pi but rather 4-pi-2eb1(alpha-s/pi), where b1 is the first coefficient in the expansion of the beta-function.