Study of the question of an ultraviolet zero in the six-loop beta function of the O(N) λ|(φ)over-right-arrow|4 theory

We study the possibility of an ultraviolet (UV) zero in the six-loop beta function of an O(N) lambda vertical bar(phi) over right arrow vertical bar(4) theory field theory in d = 4 spacetime dimensions. For general N, in the range of values of. where a perturbative calculation is reliable, we find evidence against such a UV zero in this six-loop beta function.