Perturbative reliability of the Higgs-boson coupling in the standard   electroweak model
  We apply Pade summation to the \beta(\lambda) function for the quartic Higgs coupling \lambda in the standard electroweak model. We use the \beta function 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 \beta is known to three loops. We conclude that the OMS \beta function and the running coupling \lambda(\mu) are reliably known over the range of energies and Higgs-boson masses of current interest. 
Loyal Durand and Gregory Jaczko