On Naturalness of the MSSM and NMSSM

Abstract: 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\sim125 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 \lambda and the doublet-singlet Higgs boson mixing effect pushing upward or pulling downward m_h. 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 \lambda-RGE running effect and vacuum stability. (2) A small \lambda 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.