CANTON-$\mu$ Proposal: A Next-Generation Muon $g-2$ Measurement at Sub-0.1 ppm Precision
We propose a next-generation precision measurement of the muon anomalous magnetic moment (muon g-2) at the High Intensity Heavy-Ion Accelerator Facility (HIAF) in Huizhou, China. We refer to this proposed experimental programme as CANTON-$\mu$ (Coherent Anomalous magNetic momenT ObservatioN with muon). HIAF's intense, pulsed GeV-scale muon beams, particularly for negative muons, provide a promising basis for this programme. Building on two previously proposed storage-ring concepts, this work develops HIAF-specific experimental schemes that relax the conventional magic-momentum constraint and allow greater flexibility in the choice of beam momentum. We assess the expected muon intensity at HIAF and the corresponding statistical sensitivity. For each scheme, we identify its distinctive systematic effects, examine feasible control strategies, and propose quantitative systematic-uncertainty targets. Together, the statistical projections and systematic-uncertainty targets indicate prospective total precisions of 0.1 ppm in Phase-I, comparable to the current Fermilab precision, with the potential to reach the 0.05 ppm level in in Phase-II following the planned HIAF upgrade. At the ultimate projected precision, the measurement would provide a stringent test of the Standard Model and probe new physics at multi-TeV scales. A focus on negative-muon measurements would enable direct comparison with existing high-precision positive-muon results and strengthen tests of CPT symmetry in the muon sector within the Standard-Model Extension, with a projected sensitivity at the $10^{-24}$ GeV level, an order of magnitude beyond current limits.