Abstract
We investigate the high-scale behavior of Higgs sectors beyond the Standard Model, pointing out that the proper matching of the quartic couplings before applying the renormalization group equations (RGEs) is of crucial importance for reliable predictions at larger energy scales. In particular, the common practice of leading-order parameters in the RGE evolution is insufficient to make precise statements on a given model's UV behavior, typically resulting in uncertainties of many orders of magnitude. We argue that, before applying $N$-loop RGEs, a matching should even be performed at $N$-loop order in contrast to common lore. We show both analytical and numerical results where the impact is sizable for three minimal extensions of the Standard Model: a singlet extension, a second Higgs doublet and finally vector-like quarks. We highlight that the known two-loop RGEs tend to moderate the running of their one-loop counterparts, typically delaying the appearance of Landau poles. For the addition of vector-like quarks we show that the complete two-loop matching and RGE evolution hints at a stabilization of the electroweak vacuum at high energies, in contrast to results in the literature.
Highlights
Minimal extensions of the Standard Model (SM) are invaluable tools in the pursuit of physics beyond the SM (BSM)
We show in this work that higher-order corrections can be very important for the study of the UV behavior of a theory leading to four main conclusions: (1) The threshold corrections at low energy can lead to substantial shifts in the running parameters of a model: N-loop renormalization group equations (RGEs) with N-loop matching is required for consistency
We argued that the usual approach of using N − 1 matching when utilizing N-loop RGEs neglects important contributions in the presence of large couplings
Summary
Minimal extensions of the Standard Model (SM) are invaluable tools in the pursuit of physics beyond the SM (BSM). A parameter point can be discarded if the model becomes strongly interacting at energies already probed by the LHC, or if the lifetime of the electroweak breaking vacuum is too short on cosmological time scales Many of these effects have already been studied in the literature for a plethora of different models such as singlet extensions [5,6,7,8,9], triplet extensions [10,11], two-Higgsdoublet models (THDMs) [12,13,14,15,16,17,18,19,20] or models with vectorlike fermions [21].
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