Study of the Six-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory

Abstract

We investigate whether the six-loop beta function of the $\lambda {\varphi }_4^4$ theory exhibits evidence for an ultraviolet zero. As part of our analysis, we calculate and analyze Padé approximants to this beta function. Extending our earlier results at the five-loop level, we find that in the range of $\lambda$ where the perturbative calculation of the six-loop beta function is reliable, the theory does not exhibit robust evidence for an ultraviolet zero.

arXiv comment7 pages latex, 2 figures

References in corpus (4)

• The Multiple Zeta Value Data Mine
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• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Renormalization group functions of ${\varphi }^4$ theory in the MS-scheme to six loops

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