A prediction for the 4-loop β function in QCD

We predict that the four-loop contribution β3 to the QCD β function in the MS prescription is given by β3 ⋍ 23600(900) − 6400(200)Nf + 350(70)Nf2 + 1.5Nf3, where Nf is the number of flavours and the coefficient of Nf3 is an exact result from large-Nf expansion. In the phenomenologically-interesting case Nf = 3, we estimate β3 = (7.6±0.1) × 103. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) Φ4 theory, and on variations in the details of our estimation method, which goes beyond conventional Padé approximants by estimating and correcting for subasymptotic deviations from exact results.