Fine tuning in the constrained exceptional supersymmetric standard model

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 m_h∼125 GeV. Fixing tan =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 to 400 as we vary M_Z ^′ from ∼2 to 4 TeV. However, this is significantly lower than the fine tuning in the constrained minimal supersymmetric standard model, of O(1000), arising from the large stop masses required to achieve the Higgs mass.