New opportunities for rare charm from $Z\to c\bar{c}$ 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 $D^0\to {\pi }^{+}{\pi }^{-}\nu \bar{\nu }$ and in polarized ${\Lambda }_c^{+}\to p{\ell }^{+}{\ell }^{-}$ decays with $\ell =e,\mu$. 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 $D^0\to {\pi }^{+}{\pi }^{-}\nu \bar{\nu }$ decays and work out the phenomenology of polarization-induced null-test observables in ${\Lambda }_c^{+}\to p{\ell }^{+}{\ell }^{-}$ decays. In regions of dilepton mass near the $\varphi$ resonance, polarization asymmetries can reach $O(5\%)$ for muons and $O(14\%)$ for electrons times the ${\Lambda }_c^{+}$ 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 $\sim 2\times 10^{-7}$ 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 ${\Lambda }_c^{+}\to p{\mu }^{+}{\mu }^{-}$ at $O(1\%)$ will be possible. Similar sensitivities are expected for dielectron final states, although robust predictions will require further dedicated studies.

Comments: 35 pages, 11 figures, 3 tables v2: Clarifications added, conclusions unchanged. Version submitted to Eur. Phys. J. C