New opportunities for rare charm from $$Z\rightarrow c\bar{c}$$ decays

Abstract 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 $$D^0 \rightarrow \pi ^+ \pi ^- \nu \bar{\nu }$$ D 0 → π + π - ν ν ¯ and in polarized $$\varLambda _c^+ \rightarrow p \ell ^+ \ell ^-$$ Λ c + → p ℓ + ℓ - decays with $$\ell =e, \mu $$ 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 $$D^0 \rightarrow \pi ^+ \pi ^- \nu \bar{\nu }$$ D 0 → π + π - ν ν ¯ decays and work out the phenomenology of polarization-induced null-test observables in $$\varLambda _c^+ \rightarrow p \ell ^+ \ell ^-$$ Λ c + → p ℓ + ℓ - decays. In regions of dilepton mass near the $$\phi $$ ϕ resonance, polarization asymmetries can reach $$O(5 \%)$$ O ( 5 % ) for muons and $$O(14 \%)$$ O ( 14 % ) for electrons times the $$\varLambda _c^+$$ 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 $$\sim 2 \times 10^{-7}$$ ∼ 2 ×