Diminished Upper Bounds on the Unification Mass Scales for Heavy Higgs Boson Masses

We consider dominant 3-, 4-, and 5-loop contributions to $\lambda$, the quartic scalar coupling-constant's $\beta$-function in the Standard Model. We find that these terms accelerate the evolution of $\lambda$ to nonperturbative values, thereby lowering the unification bound for which scalar-couplings are still perturbative. We also find that these higher order contributions imply a substantial lowering of $\lambda$ itself before the anticipated onset of nonperturbative physics in the Higgs sector.