New opportunities for rare charm from $Z\rightarrow c\bar{c}$ decays
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 $D^0 → π^+ π^- v\bar{v}$ and in polarized $Λ^+_c → p ℓ^+ ℓ^-$ decays with $ℓ = e, μ$. 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 $D^0 → π^+ π^- v\bar{v}$ decays and work out the phenomenology of polarization-induced null-test observables in $Λ^+_c → p ℓ^+ ℓ^-$ 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 $Λ^+_c$ 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 x 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 $Λ^+_c → p ℓ^+ ℓ^-$ at $O$(1%) will be possible. Similar sensitivities are expected for dielectron final states, although robust predictions will require further dedicated studies.