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arXiv · 2301.01830

Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda \phi^4_4$ Theory

Robert Shrock
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Abstract

We investigate whether the seven-loop beta function of the $\lambda \phi^4_4$ theory exhibits evidence for an ultraviolet zero. In addition to a direct analysis of the beta function, we calculate and study Pad\'e approximants and discuss effects of scheme transformations on the results. Confirming and extending our earlier studies of the five-loop and six-loop beta functions, we find that in the range of $\lambda$ where the perturbative calculation of the seven-loop beta function is reliable, the theory does not exhibit evidence for an ultraviolet zero.

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Robert Shrock. 2023-01-04. Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda \phi^4_4$ Theory. https://doi.org/10.1103/physrevd.107.056018

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