Abstract
We determine the degree of fine-tuning needed in a generalised version of the NMSSM that follows from an underlying Z4 or Z8 R-symmetry. We find that it is significantly less than is found in the MSSM or NMSSM and extends the range of Higgs mass that have acceptable fine-tuning. Remarkably the minimal fine-tuning is achieved for Higgs masses of around 130 GeV.
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