The plan for a super $\eta$ factory at Huizhou accelerator complex

As an approximate Goldstone boson with zero quantum number and zero standard model charge, the decay processes of long-lived $\eta$ meson offer a unique opportunity to explore new physics beyond the standard model and new sources of CP violation, as well as test the low-energy QCD theory and measure the fundamental parameters of light quarks. To pursue these goals in the physics frontiers, we propose a plan to construct a super $\eta$ factory at HIAF high-energy terminal or at CiADS after its energy upgrade. The high-intensity proton beam at HIAF enables the production of a vast number of $\eta$ samples, exceeding $10^{13}$ events per year in the first stage, utilizing multiple layers of thin targets made of light nucleus. This paper presents the physics goals, the first-version conceptual design of the spectrometer, and some preliminary simulation results.