A smuon in the NMSSM confronted with the muon g-2 and SUSY searches

Motivated by the recent supersymmetry (SUSY) search results which prefer most SUSY particles heavy, and muon g-2 anomaly which prefers colorless SUSY particles light, we explore the status of a light smuon (the SUSY partner of left-handed muon lepton) in the Next-to-Minimal Supersymmetric Standard Model (NMSSM). Assuming colored SUSY particles be heavy, and considering numerous experimental constraints including muon g-2, SUSY searches, and dark matter, we scan the parameter space in the NMSSM with Z3-symmetry, checking the status of colorless SUSY particles and their possible mass order, and paying special attention to the smuon. After calculation and discussions, we draw the following conclusions: (i) The dominated SUSY contributions to muon g-2 come from the chargino-sneutrino loops, but the muon g-2 anomaly can also constrain the mass of smuon seriously because of the mass-degenerate relation between smuon and muon sneutrino. To interpret the muon g-2 anomaly at $1\sigma$ ($2\sigma$) level, the smuon need to be lighter than 1 TeV (1.8 TeV). (ii) When $\tilde{\chi}^0_1$ is wino- or higgsino-dominated, the smuon can escape from the direct searches with low mass, e.g., 300 GeV. (iii) When smuon and $\tilde{\chi}^0_1$ are mass-degenerate, the smuon can be as light as 200 GeV, while the $\tilde{\chi}^0_1$ is usually bino-dominated, or some singlino-dominated, and its relic density can most likely reach the observed value, and the dominated annihilating mechanism is slepton annihilations. In addition, we also list several benchmark points for further studies.