Unified Interpretation of Muon g-2 anomaly, 95 GeV Diphoton, and $b\bar{b}$ Excesses in the General Next-to-Minimal Supersymmetric Standard Model

We investigate three intriguing anomalies within the framework of the General Next-to-Minimal Supersymmetric Standard Model. These anomalies include a significant deviation of the experimental results for the muon anomalous magnetic moment from its Standard Model prediction, with a confidence level of $5.1\sigma$; a joint observation by the CMS and ATLAS collaborations of a diphoton excess with a local significance of $3.1 \sigma$ in the invariant mass distribution around 95.4 GeV; and a reported excess in the $b\bar{b}$ production at LEP with a local significance of $2.3 \sigma$. Through analytical and numerical analyses, we provide unified interpretations across an extensive parameter space that remain consistent with current experimental restrictions from data on the Higgs boson at 125 GeV, B-physics measurements, dark matter observables, as well as existing searches for supersymmetry and extra Higgs bosons. We attribute the muon anomaly to loops involving muon-smuon-neutralino and muon-sneutrino-chargino interactions, while attributing the diphoton and $b \bar{b}$ excesses to the resonant production of a singlet-dominated scalar. These proposed solutions are poised for experimental tests at the high-luminosity LHC and future linear colliders.