Fine tuning in non-minimal supersymmetric models

Abstract

This thesis is based on work that investigates the fine tuning in low scale non-minimal supersymmetric models. 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 Z3 invariant NMSSM; the second is the NMSSM plus additional matter filling 3(5 + 5) representations of SU(5) and is called the NMSSM+; while the third model comprises 4(5 + 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 ? 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+ (? ~ 200) is significantly larger than in the NMSSM (? ~ 100), with fine tuning in the NMSSM++ (? ~ 600) being significantly larger than in the NMSSM+. Moreover, supersymmetric unified models in which the Z’ couples to the Higgs doublets, as in the E6 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 (cE6SSM) that is consistent with a Higgs mass mh ~ 125 GeV. Fixing tan ? = 10, and taking specific values of the mass of the Z’ boson, with MZ’ ~ 2-4 TeV. We find that the minimum fine tuning set predominantly from the mass of Z’ and varies from ~200-400 as we vary MZ’ from~ 2-4 TeV. However, this is lower than the fine tuning in the constrained Minimal Supersymmetic Standard Model (cMSSM) of 0(1000), arising from the large stop masses required to achieve the Higgs mass. Finally, it was found that varying tan ? below and above 10 does not correspond to lower fine tuning in the cE6SSM, nor does lowering the mass of the Z’ by lowering its associated coupling g’.

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