Perturbative reliability of the Higgs-boson coupling in the standard electroweak model

Abstract

We apply Pade summation to the β(λ) function for the quartic Higgs coupling λin the standard electroweak model. We use the βfunction calculated to five loops in the minimal subtraction scheme to demonstrate the improvement resulting from the summation, and then apply the method to the more physical on-mass-shell renormalization scheme where βis known to three loops. We conclude that the OMS βfunction and the running coupling λ(μ) are reliably known over the range of energies and Higgs-boson masses of current interest.