Search for an ultraviolet zero in the seven-loop beta function of the λ φ44 theory

Robert Shrock

doi:10.1103/PhysRevD.107.056018

Search for an ultraviolet zero in the seven-loop beta function of the λ φ44 theory

Robert Shrock

Institute for Theoretical Physics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We investigate whether the seven-loop beta function of the λφ44 theory exhibits evidence for an ultraviolet zero. In addition to a direct analysis of the beta function, we calculate and study Padé 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 λ where the perturbative calculation of the seven-loop beta function is reliable, the theory does not exhibit evidence for an ultraviolet zero.

Original language	English
Article number	056018
Journal	Physical Review D
Volume	107
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevD.107.056018
State	Published - Mar 15 2023

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10.1103/PhysRevD.107.056018

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abstract = "We investigate whether the seven-loop beta function of the λφ44 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 λ 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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N2 - We investigate whether the seven-loop beta function of the λφ44 theory exhibits evidence for an ultraviolet zero. In addition to a direct analysis of the beta function, we calculate and study Padé 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 λ 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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Search for an ultraviolet zero in the seven-loop beta function of the λ φ44 theory

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