Supersymmetric unified models in which the Z couples to the Higgs doublets, as in the E 6 class of models, have large fine tuning dominated by the experimental mass limit on the Z . To illustrate this we investigate the degree of fine tuning throughout the parameter space of the Constrained Exceptional Supersymmetric Standard Model (cE 6 SSM) that is consistent with a Higgs mass m h ∼ 125 GeV. Fixing tan β = 10, and taking specific values of the mass of the Z boson, with M Z ∼ 2 − 4 TeV. We find that the minimum fine tuning is set predominantly from the mass of Z and varies from ∼ 200−400 as we vary M Z from ∼ 2−4 TeV. However, this is significantly lower than the fine tuning in the Constrained Minimal Supersymmetric Standard Model (cMSSM), of O(1000), arising from the large stop masses required to achieve the Higgs mass.
We present a comparative and systematic study of the fine tuning in Higgs sectors in three scale-invariant NMSSM models: the first being the standard $Z_3$-invariant NMSSM; the second is the NMSSM plus additional matter filling $3(5+\bar{5})$ representations of SU(5) and is called the NMSSM+; while the third model comprises $4(5+\bar{5})$ and is called the NMSSM++. Naively, one would expect the fine tuning in the plus-type models to be smaller than that in the NMSSM since the presence of extra matter relaxes the perturbativity bound on $\lambda$ at the low scale. This, in turn, allows larger tree-level Higgs mass and smaller loop contribution from the stops. However we find that LHC limits on the masses of sparticles, especially the gluino mass, can play an indirect, but vital, role in controlling the fine tuning. In particular, working in a semi-constrained framework at the GUT scale, we find that the masses of third generation stops are always larger in the plus-type models than in the NMSSM without extra matter. This is an RGE effect which cannot be avoided, and as a consequence the fine tuning in the NMSSM+ ($\Delta \sim 200$) is significantly larger than in the NMSSM ($\Delta \sim 100$), with fine tuning in the NMSSM++ ($\Delta \sim 600$) being significantly larger than in the NMSSM+.Comment: 31 pages, 22 figures, published versio
We analyze the Next-to-minimal supersymmetric Standard Model with Grand unification boundary conditions under current theoretical and experimental constraints. We compute the mass spectrum of the model and focus on the three lightest particles in the Higgs sector (two CP-even scalars, [Formula: see text], [Formula: see text] and one CP-odd, [Formula: see text]). The reduced couplings of such particles, singlet-doublet components, their branching ratios to bosons and reduced cross-section to photons and massive gauge bosons via gluon fusion are thoroughly and systematically scrutinized. Our analysis is focused on the parameter space where the singlet-doublet coupling [Formula: see text] is as large as possible (keeping the perturbativity bound intact) and the ratio between the vacuum expectation values of the up-type and down-type Higgses [Formula: see text] is as small as possible, which is the region representing the most natural case of the NMSSM. We show the impact of recent constraints from the LHC on the SM-Higgs couplings to bosons and fermions on the parameter space of the model and the consequent implications on the Higgs sector. The results show that while the model is still able to account for current data, and provide an opportunity for discovery of extended Higgs sectors, recent LHC Higgs couplings constraints rule-out parts of the parameter space where [Formula: see text] (non-SM-like) and [Formula: see text] are non-singlet with masses below 400 GeV.
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