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In GUT-scale constrained (GUTc) supersymmetric (SUSY) models, the mass ofsmuon $\tilde{\mu}_1$ is typically heavier than that of stau $\tilde{\tau}_1$,and stau co-annihilation is a typical annihilation mechanism of dark matter.However, light smuon is more favored by the muon $g-2$ anomaly, thussmuon-neutralino loop contribution to muon $g-2$ is usually smaller than thatof sneutrino-chargino. Inspired by the latest muon $g-2$ results, we take theGUTc- Next-to-Minimal Supersymmetric Model (NMSSM) as an example, where thegaugino (Higgs) masses are not unified to the usual parameter $M_{1/2}$($M_0$), exploring its possibility of light smuon and its contribution to muon$g-2$. After complicated calculations and discussions, we conclude that inGUTc-NMSSM the smuon can be lighter than stau. In this light-smuon scenario,the contribution of smuon-neutralino loop to the muon $g-2$ can be larger thanthat of the sneutrino-chargino loop. The annihilation mechanisms of dark matterare dominated by multiple slepton or chargino co-annihilation. In ourcalculations, we consider also other latest related constraints like Higgsdata, SUSY searches, dark matter relic density and direct detections, etc.

Smuon contribution to muon g-2 in Grand Unified supersymmetric theories