The semi-constrained NMSSM in light of muon g-2, LHC, and dark matter constraints

The semi-constrained NMSSM (scNMSSM) extends the MSSM by a singlet field, and requires unification of the soft SUSY breaking terms in the squark and slepton sectors, while it allows that in the Higgs sector to be different. We try to interpret the muon g-2 in the scNMSSM, under the constraints of 125 GeV Higgs data, B physics, searches for low and high mass resonances, searches for SUSY particles at the LHC, dark matter relic density by WMAP/Planck, and direct searches for dark matter by LUX, XENON1T, and PandaX-II. We find that under the above constraints, the scNMSSM can still (i) satisfy muon g-2 at 1$\sigma$ level, with a light muon sneutrino and light chargino; (ii) predict a highly-singlet-dominated 95~GeV Higgs, with a diphoton rate as hinted at by CMS data, because of a light higgsino-like chargino and moderate $\lambda$; (iii) get low fine tuning from the GUT scale with small $\mu_{\rm eff},\, M_0,\, M_{1/2},\, {\rm and}\, A_0$, with a lighter stop mass which can be as low as about 500 GeV, which can be further checked in future studies with search results from the 13~TeV LHC; (iv) have the lightest neutralino be singlino-dominated or higgsino-dominated, while the bino and wino are heavier because of high gluino bounds at the LHC and universal gaugino conditions at the GUT scale; (v) satisfy all the above constraints, although it is not easy for the lightest neutralino, as the only dark matter candidate, to get enough relic density. Several ways to increase relic density are discussed.