Higgs sectors beyond leading order: matching, perturbativity and vacuum stability

Non-supersymmetric, weakly-interacting models with an extended Higgs sector are gaining popularity these days. For studying their properties, one can apply a bottom-up approach and use masses and mixing angles to characterize parameter regions, using leading-order relations to the Lagrangian parameters. For this approach one implies that an on-shell renormalization can always be performed to keep these observables fixed.
I will show in my talk that this approach can be dangerous as large loop corrections must to be absorbed in large counter-terms, casting doubts on the validity of the perturbative expansion in certain scenarios. I will discuss simple perturbativity checks based on these finite counter-terms and show how they compare to perturbativity conditions in an MS-bar scheme.
For determining the high-scale behaviour of these models, it is a widely-spread habit to use leading-oder parameters as starting values for the RGE flow. However, for reliable predictions, a proper matching beyond leading order must be performed. I will discuss how this can lead to significant deviations in the predictions of the UV behaviour as well as the stability of the electroweak vacuum.