Long-Range Plans in the Muon Sector: Mu2e-II and AMF

Charged lepton flavor violation (CLFV) is expected in a diverse set of BSM scenarios. The muon sector probes CLFV in three complementary channels: muon to electron conversion, muon to electron and gamma, and muon to three electrons. Current muon conversion experiments like Mu2e at Fermilab and COMET at J-PARC aim to enhance limits by four orders of magnitude. The proposed Mu2e-II experiment aims to improve the Mu2e limit by a further order of magnitude. To utilize existing infrastructure and expertise, Mu2e-II will reuse as much of the Mu2e apparatus as possible but will require upgrades in key areas. Beyond Mu2e-II, the proposed Advanced Muon Facility (AMF) at Fermilab introduces a transformative approach based on a muon storage ring to enable a full suite of muon CLFV experiments. R&D for both Mu2e-II and AMF is ongoing, following the 2023 P5 report's baseline recommendations. I will outline the state of the Mu2e-II and AMF efforts and highlight potential synergies with the proposed US-based muon collider.