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

Abstract

We investigate whether the seven-loop beta function of the $\lambda {\varphi }_4^4$ 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 $\lambda$ where the perturbative calculation of the seven-loop beta function is reliable, the theory does not exhibit evidence for an ultraviolet zero.

Comments: 6 pages, latex, 2 figures. arXiv admin note: substantial text overlap with arXiv:1610.03733