95 GeV Higgs boson and nano-Hertz gravitational waves from domain walls in the N2HDM

We explore the diphoton and $b\bar{b}$ excesses at 95.4 GeV, as well as nano-Hertz gravitational waves originating from domain walls, within the framework of the next-to-two-Higgs-doublet model (N2HDM), which extends the two-Higgs-doublet model by introducing a real singlet scalar subject to a discrete $Z_2$ symmetry. The $Z_2$ symmetry is spontaneously broken by the non-zero vacuum expectation value of the singlet scalar, $v_s$, which leads to the formation of domain walls. We discuss two different scenarios: in scenario A, the 95.4 GeV Higgs boson predominantly originates from the singlet field, while in scenario B, it arises mainly from the CP-even components of the Higgs doublets. Taking into account relevant theoretical and experimental constraints, we find that scenario A can fully account for both the diphoton and $b\bar{b}$ excesses at 95.4 GeV within the $1σ$ range. Moreover, the peak amplitude of the gravitational wave spectrum at a peak frequency of $10^{-9}$ Hz can reach $2 \times 10^{-12}$ for $v_s = 100$ TeV. Scenario B only marginally accounts for the diphoton and $b\bar{b}$ excesses at the $1σ$ level, but the peak amplitude of the gravitational wave spectrum at the peak frequency of $10^{-9}$ Hz can reach $6\times 10^{-8}$ for $v_s=100$ TeV. The nano-Hertz gravitational wave signals predicted in both scenarios can be tested by the current and future pulsar timing array projects.