Light Higgs boson in the NMSSM confronted with the CMS diphoton and ditau excesses

In 2018, the CMS collaboration reported a di-photon excess around 95.3 GeV with a local significance of 2.8 $\sigma$. Interestingly, the CMS collaboration also reported a di-tau excess recently at 95 $\sim$ 100 GeV with a local significance of 2.6 $\sim$ 3.1 $\sigma$. Besides, a $b\bar{b}$ excess at 98 GeV with a 2.3 $\sigma$ local significance was reported with LEP data about twenty years ago. In this work, we consider interpreting these excesses together with a light Higgs boson in the next-to-minimal supersymmetric standard model (NMSSM). We conclude that in NMSSM the 95 $\sim$ 100 GeV excesses are difficult to be satisfied simultaneously (not possible globally at $1\sigma$ level, or simultaneously at $2\sigma$ level), and we analyze two partial-satisfied scenarios: the globally $2\sigma$ scenario and small di-photon scenario. An approximate equation of global fit to the three excesses is derived, and two representative types of surviving samples are analyzed in detail. Since the mass regions of these excesses are near the Z boson, we also consider checking the light Higgs boson in the $t\bar{t}$-associated channels. The detailed results may be useful for further checking the low-mass-region excesses in the future.