LANDAU POLES, ULTRAVIOLET FIXED POINTS, AND “TRIVIALITY” IN THE PERTURBATIVE EXPANSION OF (λΦ4)4

The “triviality” of (λΦ4)4 means that the continuum theory has a vanishing renormalized coupling λR. This result inherently conflicts with the standard perturbative approach, which begins by postulating a nonzero, cutoff-independent λR, and which suffers from pathologies — either Landau poles (in odd orders) or spurious ultraviolet fixed points (in even orders). We show how the known structure of perturbation theory can be rearranged, to arbitrarily high orders, to fulfil the condition λR=0. The corresponding renormalization group flow of the bare coupling coincides with that needed to renormalize the effective potential, as calculated in any “triviality”-compatible approximation. Although λR vanishes, the physical mass is finite; there is no proportionality between the two. That implies that the Higgs mass does not represent a measure of the observable interaction strength in the scalar sector of the standard model.