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.

7 pages latex, 2 figures

References in corpus (2)

• 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

Cited by in corpus (4)

• A new method to sum divergent power series: educated match
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model
• Study of the Question of an Ultraviolet Zero in the Six-Loop Beta Function of the O($N$) $\lambda |\vec{\varphi }{|}^4$ Theory