We point out opportunities to probe invisible particles, left- and right-handed neutrinos, axionlike particles 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 ${\mathrm{\Lambda }}_c\to pX$, 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 ${10}^{-4}$ (axionlike particles). Chirality-preserving operators from heavy new physics in the dimension-six standard model effective theory 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 standard model effective theory, or with light sterile neutrinos, are weaker, with branching ratios up to $\mathrm{few}\times {10}^{-4}$. Sensitivities to different couplings arise with ${\mathrm{\Lambda }}_c\to pX$ 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 and $Z$ factories, such as the Future Circular Collider and the Circular Electron Positron Collider.

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• Flavor changing neutral currents
• Invisible decays
• Particle decays
• Particle interactions
• Phenomenology
• Rare decays