We analyze the potential of rare charm decays as probes of new physics at a high-luminosity flavor facility operating at the Z pole, such as the FCC-ee or CEPC. In particular, we identify clean null-test observables in D⁰ π^+ π^- νν and in polarized Λc^+ p ^+ ^- decays with =e, μ. Complementarity with the LHC and HL-LHC flavor programs arises from the characteristic features of a Tera-Z environment: the capability to study missing-energy modes and charm production with significant polarization. We improve the theoretical description of D⁰ π^+ π^- νν decays and work out the phenomenology of polarization-induced null-test observables in Λc^+ p ^+ ^- decays. In regions of dilepton mass near the ϕ resonance, polarization asymmetries can reach O (5 \%) for muons and O (14 \%) for electrons times the Λc^+ polarization. We also point out synergies between the dineutrino and the dilepton modes using the SMEFT framework of heavy new physics. Using the IDEA detector concept at FCC-ee, we find in simulation studies that dineutrino branching fractions as low as 2 10^-7 can be probed, which reaches well into the parameter space of new physics, and also allows for discrimination of lepton flavor structures. Furthermore, the measurement of asymmetries in Λc^+ p μ^+ μ^- at O (1 \%) will be possible. Similar sensitivities are expected for dielectron final states, although robust predictions will require further dedicated studies.
Canto et al. (Fri,) studied this question.