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The flavor-changing neutral current (FCNC) decays of charmed hadrons withmissing energy $(\not\!\!E)$ can serve as potentially promising hunting groundsfor hints of new physics, as the standard-model backgrounds are verysuppressed. A few of such processes have been searched for in recentexperiments, specifically $D^0\to\,\not\!\!E$ by Belle and$D^0\to\pi^0$$\not\!\!E$ and $\Lambda_c^+\to p\!\not\!\!E$ by BESIII, resultingin upper bounds on their branching fractions. We consider them to illuminatethe possible contributions of the quark transition $c\to u\!\not\!\!E$ with acouple of invisible spinless bosons carrying away the missing energy, assumingthat they are not charge conjugates of each other and hence can have unequalmasses. We find that these data are complementary in that they constraindifferent sets of the underlying operators and do not cover the same ranges ofthe bosons' masses, but there are regions not yet accessible. From the allowedparameter space, we show that other $D$-meson decays, such as$D\to\rho$$\not\!\!E$, and the charmed-baryon ones$\Xi_c\to(\Sigma,\Lambda)$$\not\!\!E$ can have sizable branching fractions andtherefore may offer further probes of the new-physics interactions. We pointout the importance of $D^0\to\gamma\!\not\!\!E$ which are not yet searched forbut could access parts of the parameter space beyond the reach of the othermodes. In addition, we look at a scenario where the invisibles are insteadfermionic, namely sterile neutrinos, and a scalar leptoquark mediates $c\tou\!\not\!\!E$. We discuss the implications of the aforesaid bounds for thismodel. The predictions we make for the various charmed-hadron decays in thedifferent scenarios may be testable in the near future by BESIII and Belle II.

FCNC charmed-hadron decays with invisible singlet particles in light of recent data