Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λϕ^4$
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| Format: | Preprint |
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2026
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| _version_ | 1866915925609938944 |
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| author | Gracey, J. A. Jack, I. Jones, D. R. T. |
| author_facet | Gracey, J. A. Jack, I. Jones, D. R. T. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_07596 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λϕ^4$ Gracey, J. A. Jack, I. Jones, D. R. T. High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λϕ^4$ |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.07596 |