Fixed point structure of Pade-summation approximations to the QCD beta-function

V. Elias; F. Chishtie; T. G. Steele

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arXiv · hep-ph/9809471

Fixed point structure of Pade-summation approximations to the QCD beta-function

V. Elias·F. Chishtie·T. G. Steele

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Abstract

Padé-improvement of four-loop beta-functions in massive phi^4 scalar field theory is shown to predict the known five-loop contribution with astonishing (0.2%) accuracy, supporting the applicability of Pade-summations for approximating all-orders MS-bar QCD beta-functions, as suggested by Ellis, Karliner, and Samuel. Surprisingly, the most general set of [2|2] approximants consistent with known two-, three-, and four-loop contributions to the QCD beta-function with up to six flavours fail to exhibit any zeros that could be interpreted as positive infrared fixed points, regardless of the unknown five-loop term. When they occur, positive zeros of such [2|2] approximants are preceded by singularities, leading to a double-valued beta-function that is decoupled entirely from the infrared region, similar to the beta-function of SUSY gluodynamics.

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V. Elias, F. Chishtie, T. G. Steele. 1998-09-28. Fixed point structure of Pade-summation approximations to the QCD beta-function. https://arxiv.org/abs/hep-ph/9809471

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