PERTURBATIVE QUANTUM CHROMODYNAMICS - EVIDENCE THAT ALPHA-S RUNS

We consider the theoretical predictions of perturbative quantum chromo dynamics (QCD) for the quantities Re+e-, R(tau) and GAMMA(hadronic)Z0. Using alpha(s)(M(tau)) = = 0.34(-0.05)+0.04), we find that alpha(s)(3 4 GeV) = 0.140(-0.008)+0.006 in agreement with the value extracted fro m experiment, alpha(s)(34 GeV) = 0.148(22), and alpha(s)(M(Z)) = 0.119 (5), in excellent agreement with the experimental value from LEP, alph a(s)(M(Z)) = 0.120(7). We show that using only the above value for alp ha(s) (M-) as input and no free parameters we can predict alpha(s) (mu ) for M(tau) less-than-or-equal-to mu less-than-or-equal-to 200 GeV. O ur result is in agreement with all known experimental values. Thus it can be seen that alpha(s) truly runs, in agreement with perturbative Q CD.