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Rare $|\Delta c|=|\Delta u|=1$ transitions into dineutrinos are stronglyGIM-suppressed and constitute excellent null tests of the standard model. Whilebranching ratios of $D \to P \,\nu \bar \nu$, $D \to P^+ P^- \, \nu \bar \nu$,$P=\pi, K$, baryonic $\Lambda_c^+ \to p \,\nu \bar \nu$, and $\Xi_c^+ \to\Sigma^+ \, \nu \bar \nu$ and inclusive $D \to X \nu \bar \nu$ decays areexperimentally unconstrained, signals of new physics can be just around thecorner. We provide model-independent upper limits on branching ratios reachingfew $\times 10^{-5}$ in the most general case of arbitrary lepton flavorstructure, $\sim 10^{-5}$ for scenarios with charged lepton conservation andfew $\times 10^{-6}$ assuming lepton universality. We also give upper limits in$Z^\prime$ and leptoquark models. The presence of light right-handed neutrinoscan affect these limits, a possibility that can occur for lepton numberviolation at a TeV, and that can be excluded with an improved bound on$\mathcal{B}(D^0 \to \text{invisibles})$ at the level of $\sim 10^{-6}$, abouttwo orders of magnitude better than the present one. Signatures of $c \to u \nu\bar \nu$ modes contain missing energy and are suited for experimental searchesat $e^+ e^-$-facilities, such as BES III, Belle II and future $e^+e^-$-colliders, such as the FCC-ee running at the $Z$.

Rare charm $\boldsymbol{c\to u\,\nu\bar{\nu}}$ dineutrino null tests for $\boldsymbol{e^+e^-}$-machines