Asymptotic Padé predictions up to six loops in QCD and eight loops in λ ϕ 4

We assess the accuracy of our previous asymptotic Padé predictions of the five-loop QCD β -function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in powers of N F (the number of flavors) were correct to within 1%. Furthermore an examination of recent results in λ ϕ 4 theory indicates that the asymptotic Padé methods deliver predictions which increase in accuracy with loop order. Encouraged by this, we present six-loop asymptotic Padé predictions for the QCD β -function and quark mass anomalous dimension and also for the eight-loop β -function in O ( N ) λ ϕ 4 theory.