Asymptotic Padé approximants validated on five-loop QCD data now yield six-loop QCD beta-function and quark-mass anomalous-dimension predictions plus eight-loop results in scalar theory.
RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function
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abstract
The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the \bar{MS} series momentum-space for the QCD static potential are calculated and compared to values obtained via asymptotic Pad\'e-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Pad\'e-predictions. The predicted value for the third RG-accessible coefficient is found to be within 7% relative |error| of its true value for n_f leq 6, and is shown to be in exact agreement with its true value in the n_f \to \infty limit. Asymptotic Pad\'e estimates are also obtained for the remaining (RG-inaccessible) three-loop coefficient. Comparison is also made with recent estimates of the three-loop contribution to the configuration-space static-potential function.
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2026 1verdicts
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Asymptotic Pad\'e Predictions up to Six Loops in QCD and Eight Loops in $\lambda\phi^4$
Asymptotic Padé approximants validated on five-loop QCD data now yield six-loop QCD beta-function and quark-mass anomalous-dimension predictions plus eight-loop results in scalar theory.