95 GeV Diphoton and $b \bar{b}$ Excesses in the General Next-to-Minimal Supersymmetric Standard Model

The CMS and ATLAS collaborations recently published their results searching for light Higgs bosons, using the complete Run 2 data of the LHC. Both reported an excess in the diphoton invariant mass distribution at $m_{\gamma \gamma} \simeq 95.4~{\rm GeV}$ with compatible signal strengths. The combined result corresponded to a local significance of $3.1\sigma$. Besides, the mass of the diphoton signal coincided with that of the $b\bar{b}$ excess observed at the LEP. Given the remarkable theoretical advantages of the general Next-to-Minimal Supersymmetric Standard Model, we interpret these excesses by the resonant productions of the singlet-dominated CP-even Higgs boson predicted by the theory. Using both analytic formulae and numerical results, we show that the idea can interpret the excesses by broad parameter space without contradicting current experimental restrictions, including those from the 125~{\rm GeV} Higgs data, the dark matter relic abundance and direct detection experiments, and the collider searches for supersymmetry and extra Higgs bosons. Although the explanations are scarcely affected by present Higgs data and the LHC search for supersymmetry, the dark matter physics may leave footprints on them. We also survey the other signals of the light Higgs boson at the LHC.