Study of the six-loop beta function of the λ φ44 theory

We investigate whether the six-loop beta function of the λφ44 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 λ where the perturbative calculation of the six-loop beta function is reliable, the theory does not exhibit robust evidence for an ultraviolet zero.