Bayesian naturalness of the CMSSM and CNMSSM

The recent discovery of the 125.5 GeV Higgs boson at the LHC has fueled interest in the next-to-minimal supersymmetric standard model (NMSSM) as it may require less fine-tuning than the minimal model to accommodate such a heavy Higgs. To this end we present Bayesian naturalness priors to quantify fine-tuning in the (N) MSSM. These priors arise automatically as Occam razors in Bayesian model comparison and generalize the conventional Barbieri-Giudice measure. In this paper we show that the naturalness priors capture features of both the Barbieri-Giudice fine-tuning measure and a simple ratio measure that has been used in the literature. We also show that according to the naturalness prior the constrained version of the NMSSM is less tuned than the CMSSM.