On naturalness of the MSSM and NMSSM

With a bottom-up approach, we consider naturalness in the MSSM and NMSSM. Assuming the light stops. the LHC gluino search implies that the degree of fine tuning in both models is less than 2.5%. Taking the LHC hints for the SM-like Higgs boson mass m(h) similar to 125 GeV seriously, we find that naturalness will favor the NMSSM. We study the Higgs boson mass for several scenarios in the NMSSM: (1) A large A and the doublet-singlet Higgs boson mixing effect pushing upward or pulling downward nth. The former case can readily give the di-photon excess of the Higgs boson decay whereas the latter case can not. However, we point out that the former case has a new large fine-tuning related to strong A ROE running effect and vacuum stability. (2) A small A and the mixing effect pushing m(h) upward. Naturalness status becomes worse and no significant di-photon excess can be obtained. In these scenarios, the lightest supersymmetric particle (LSP) as a dark matter candidate is strongly disfavored by the XENON100 experiment. Even if the LSP can be a viable dark matter candidate, there does exist fine-tuning. The above naturalness evaluation is based on a high mediation scale for supersymmetry breaking, whereas for a low mediation scale, fine-tuning can be improved by about one order.