Light dark matter confronted with the 95 GeV diphoton excess

The correlation between Higgs-like scalars and light dark matter is an interesting topic, especially now that a $125 GeV$ Higgs was discovered and dark matter (DM) searches got negative results. The $95 GeV$ excess reported by the CMS collaboration with $132 fb^{-1}$ data recently, and the DM search results by XENONnT and LZ collaborations motivate us to revise that. In this work, we study that in the GUT-scale constrained (GUTc) Next-to-Minimal Supersymmetric Model (NMSSM), where most parameters are input at the GUT scale, but with scalar and gaugino masses not unified there. In the calculation we also consider other recent experimental constraints, such as Higgs data, Supersymmetry (SUSY) searches, DM relic density, etc. After detailed analysis and discussion, we find that: (i) The light DM can be bino- or singlino-dominated, but can be mixed with minor components of Higgsino. (ii) Both cases can get right relic density and sizable Higgs invisible decay, by adjusting the dimensionless parameters $\lambda, \kappa$, or suitably mixing with Higgsino. (iii) Both cases can have four funnel annihilation mechanisms, i.e., annihilating through $Z, a_1, h_2, h_1$. (iv) Samples with right relic density usually get weak signal of Higgs invisible decay at future lepton collider, but the $95 GeV$ scalar can have sizable $b\bar{b}$ signal.