A PREDICTION FOR THE 4-LOOP BETA-FUNCTION IN QCD

We predict that the four-loop contribution beta(3) to the QCD beta fun ction in the <(MS)over bar> prescription is given by beta(3) similar o r equal to 23600(900) - 6400(200)N-f + 350(70)N-f(2) + 1.5N(f)(3), whe re N-f is the number of flavours and the coefficient of N-f(3) is an e xact result from large-N-f expansion. In the phenomenologically-intere sting case N-f = 3, we estimate beta(3) = (7.6 +/- 0.1) x 10(3). We di scuss our estimate of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in lest applications to th e O(N) Phi(-1) theory, and on variations in the details of our estimat ion method, which goes beyond conventional Pade approximants by estima ting and correcting for subasymptotic deviations from exact results. ( C) 1997 Elsevier Science B.V.