Probing invisible particles with charm

We point out opportunities to probe invisible particles, left- and right-handed neutrinos, axion-like particles (ALPs) and dark photons $(Z^\prime)$ with rare decays of charm hadrons. We employ and recast existing searches in $D \to (\pi, \omega) X$, $D^ 0 \to X$ and $\Lambda_c \to p X$, where $X$ denotes one of the above invisible final states including dineutrinos. The branching ratios are clean null tests of the standard model, yet, are essentially unconstrained for some parameters of light new physics, limited only by weak lifetime constraints at the level of $\mathcal{O}(10^{-1})$. On the other hand, if models are probed, branching ratios still reach up to $10^{-3}$ ($Z^\prime$) and $10^{-4}$ (ALPs). Chirality-preserving operators from heavy new physics in the dimension six standard model effective theory (SMEFT) imply tighter upper limits, up to few $\times 10^{-5}$. Constraints on chirality-flipping heavy new physics, such as lepton number violation from dimension seven SMEFT, or with light sterile neutrinos, are weaker, with branching ratios up to few$\times 10^{-4}$. Sensitivities to different couplings arise with $\Lambda_c \to p X$ and $D \to \pi \pi X$ decays, in particular in relation with the other modes. Processes can be studied at running and future experiments with high charm luminosities, BESIII, Belle II, a super-tau-charm factory (STCF) and $Z$-factories, such as the FCC-ee and the CEPC.