Study of the six-loop beta function of the λφ44 theory

We investigate whether the six-loop beta function of the lambda phi(4)(4) theory exhibits evidence for an ultraviolet zero. As part of our analysis, we calculate and analyze Pade 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.