A Prediction for the 4-Loop β Function
Abstract
We predict that the four-loop contribution β3 to the QCD β function in the MS-bar prescription is given by β3 23,600(900) - 6,400(200) Nf + 350(70) Nf2 + 1.5 Nf3, 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) x 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) 4 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.
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