A prediction for the 4-loop beta function in QCD

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