Theoretical constraints on supersymmetric models: Perturbative unitarity vs. vacuum stability

Florian Staub

doi:10.1016/j.physletb.2018.12.039

Abstract

There are nowadays strong experimental constraints on supersymmetric theories from the Higgs measurements as well as from the null results in Sparticle searches. However, even the parameter spaces which are in agreement with experimental data can be further constrained by using theoretical considerations. Here, we discuss for the MSSM and NMSSM the impact of perturbative unitarity as well as of the stability of the one-loop effective potential. We find in the case of the MSSM, that vacuum stability is always the stronger constraint. On the other side, the situation is more diverse in the NMSSM and one should always check both kind of constraints.

Highlights

The discovery of a standard model (SM)-like Higgs boson with a mass of about 125 GeV [1,2] seems to be a good argument that supersymmetry (SUSY), and in particular the minimal supersymmetric standard model (MSSM), is the correct extension of the SM: in contrast to other ideas to extend the SM, the MSSM predicts that the Higgs boson shouldn’t be significantly heavier than the Z -boson if new physics comes into play at the TeV scale, see e.g. Ref. [3] and references therein
We have summarised in this letter the situation concerning the impact of perturbative unitarity and vacuum stability on the MSSM and next-to-minimal supersymmetric standard model (NMSSM) parameter spaces
We showed that the constraints from vacuum stability are important in the MSSM because they can rule out phenomenological interesting parameter regions

Summary

Introduction

The discovery of a standard model (SM)-like Higgs boson with a mass of about 125 GeV [1,2] seems to be a good argument that supersymmetry (SUSY), and in particular the minimal supersymmetric standard model (MSSM), is the correct extension of the SM: in contrast to other ideas to extend the SM, the MSSM predicts that the Higgs boson shouldn’t be significantly heavier than the Z -boson if new physics comes into play at the TeV scale, see e.g. Ref. [3] and references therein. The second problem with highly mixed stops is that perturbative unitarity could be violated: the large trilinear stop couplings which are responsible for the mixing can induce scalar scattering processes which violate unitarity at leading order. While this is cured at higher loop-level, it indicates a breakdown of perturbation theory. One can alleviate the need for large loop corrections from the stop sector by considering SUSY models in which the Higgs mass is already enhanced at tree-level. Large trilinear couplings or light states in the extended Higgs sector can cause scattering cross sections which violate perturbative unitarity at leading order.

Calculation of the unitarity constraints

Checking the vacuum stability

Results

Z and the additional heavy

Stop scattering

Conclusion