Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λϕ^4$

J. A. Gracey; I. Jack; D. R. T. Jones

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arXiv · 2601.07596

Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λϕ^4$

J. A. Gracey·I. Jack·D. R. T. Jones

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Abstract

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 flavours) were correct to within $1\%$. Furthermore an examination of recent results in $λϕ^4$ 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 $O(N)$ $λϕ^4$ theory.

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J. A. Gracey, I. Jack, D. R. T. Jones. 2026-04-09. Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λϕ^4$. https://arxiv.org/abs/2601.07596

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