Abstract
Recently the DiracNMSSM has been proposed as a possible solution to reduce the fine tuning in supersymmetry. We determine the degree of fine tuning needed in the DiracNMSSM with and without non-universal gaugino masses and compare it with the fine tuning in the GNMSSM. To apply reasonable cuts on the allowed parameter regions we perform a precise calculation of the Higgs mass. In addition, we include the limits from direct SUSY searches and dark matter abundance. We find that both models are comparable in terms of fine tuning, with the minimal fine tuning in the GNMSSM slightly smaller.
Highlights
The discovery of the Higgs boson with a mass of about 125 GeV [1, 2] has a strong impact on the parameter range of supersymmetric models
The best example is the NMSSM with large λ. This has been demonstrated for the NMSSM in ref. [36] and we show an example for the DiracNMSSM in section 2.3.2. (ii) the effective potential approach corresponding to p2 = 0 can differ significantly from a full one-loop correction demanding p2 = m2h
We show the fine tuning as function of vs. While the fine tuning in the GNMSSM shows hardly any dependence on the singlet vacuum expectation values (VEVs) after all cuts, the fine tuning in the DiracNMSSM increases with increasing |vs|
Summary
The discovery of the Higgs boson with a mass of about 125 GeV [1, 2] has a strong impact on the parameter range of supersymmetric models. One option to generate the necessary operators is an underlying R symmetry, ZR4 or ZR8 After supersymmetry breaking, both the singlet mass and the μ term are generated but both are constrained to be of order the supersymmetry breaking mass [19, 20]. Other phenomenologically interesting aspects of the GNMSSM include a possible enhancement of the diphoton decay rate of the Higgs boson [27] as well as a potential simultaneous explanation of the Fermi line at 130 GeV [28] Such signals would require λ to become non-perturbative well below the scale of a grand unified theory (GUT), making an interpretation in terms of an underlying GUT model difficult, see [29]. Our estimate of the fine tuning is based on a full two-loop running of the renormalisation group equations and we perform a precise mass calculation in the Higgs sector. In the appendix we present all renormalisation group equations, mass matrices and vertices which are changed in comparison to the MSSM and explain in great detail the renormalisation of the CP even Higgs sector in the DiracNMSSM
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