Simulation of dark scalar particle sensitivity in $\eta$ rare decay channels at HIAF

Searching dark portal particle is a hot topic in particle physics frontier. We present a simulation study of an experiment targeted for searching the scalar portal particle at Huizhou $\eta$ factory. The HIAF high-intensity proton beam and a high event-rate spectrometer are suggested for the experiment aimed for the discovery of new physics. Under the conservative estimation, $5.9\times 10^{11}$ $\eta$ events could be produced in one month running of the experiment. The hadronic production of $\eta$ meson ($p + ^7\text{Li} \rightarrow \eta X$) is simulated at beam energy of 1.8 GeV using GiBUU event generator. We tend to search for the light dark scalar particle in the rare decay channels $\eta \rightarrow S \pi^0 \rightarrow \pi^+ \pi^- \pi^0$ and $\eta \rightarrow S \pi^0 \rightarrow e^+ e^- \pi^0$. The detection efficiencies of the channels and the spectrometer resolutions are studied in the simulation. We also present the projected upper limits of the decay branching ratios of the dark scalar particle and the projected sensitivities to the model parameters.