Abstract
We investigate the stability of the electroweak vacuum for two-Higgs doublet models with a supersymmetric UV completion. The supersymmetry breaking scale is taken to be of the order of the grand unification scale. We first study the case where all superpartners decouple at this scale. We show that contrary to the Standard Model with one Higgs doublet, matching to the supersymmetric UV completion is possible if the low-scale model contains two Higgs doublets. In this case vacuum stability and experimental constraints point towards low values of tan(beta) < 2 and pseudoscalar masses of at least about a TeV. If the higgsino superpartners of the Higgs fields are also kept light, the conclusions are similar and essentially independent of the higgsino mass. Finally, if all gauginos are also given electroweak-scale masses (split supersymmetry with two Higgs doublets), the model cannot be matched to supersymmetry at very high scales when requiring a 125 GeV Higgs. Light neutral and charged higgsinos therefore emerge as a promising signature of a supersymmetric UV completion of the Standard Model at the grand unification scale.
Highlights
In the past, the main motivation to consider supersymmetric extensions of the Standard Model used to be the hierarchy problem: electroweak-scale supersymmetry allows to stabilise a large hierarchy between the electroweak scale and a much higher fundamental scale against radiative corrections
For the two-Higgs-doublet model (THDM) with split supersymmetry, on the other hand, we find that the model cannot be extrapolated to the scale of Grand Unification because the predicted mass of the Standard Model-like Higgs boson is always too large in the parameter regions allowed by the other constraints
The constraint Mh = 125 GeV enforces MA 200 GeV at large tan β, and this parameter region is excluded by the constraint on the charged Higgs boson mass in a THDM from the measurement of BR(b → sγ) and by the limits from the LHC searches for H, A → τ τ
Summary
The standard procedure for treating theories with several hierarchically separated scales is to “run and match” the effective field theory parameters. While intermediate thresholds certainly offer interesting possibilities to generalise our work, here we will always assume that one set of particles decouples close to MS and that the remaining states will obtain masses at most of the order of a TeV. These “light” states will always include the Standard Model particles and a second Higgs doublet; we will investigate the cases where they include a pair of higgsinos, or a pair of higgsinos and all MSSM gauginos. We do not subscribe to these arguments; it seems to us that they rest on rather frail assumptions, and that even if anthropics should be related to the electroweak hierarchy, this would not necessarily preclude a (presently unknown) anthropic argument for a second light Higgs doublet
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