Exploring charm decays with missing energy in leptoquark models

We investigate the possibility that scalar leptoquarks generate consequential effects on the flavor-changing neutral-current decays of charmed hadrons into final states with missing energy ($\not\!\!E$) carried away by either standard model or sterile neutrinos. We focus on scenarios involving the $R_2$, $\tilde R_2$, and $\bar S_1$ leptoquarks and take into account various pertinent constraints, learning that meson-mixing ones and those inferred from collider searches can be of significance. We find in particular that the branching fractions of charmed meson decays $D\to M\!\not\!\!E$, $M=\pi,\rho$, and $D_s\to K^{(*)}\!\not\!\!E$ and singly charmed baryon decays $\Lambda_c^+\to p\!\not\!\!E$ and $\Xi_c\to\Sigma\!\not\!\!E$ are presently allowed to attain the $10^{-7}$-$10^{-6}$ levels if induced by $R_2$ and that the impact of $\tilde R_2$ is comparatively much less. In contrast, the contributions of $\bar S_1$, which couples to right-handed up-type quarks and the sterile neutrinos, could lead to branching fractions as high as order $10^{-3}$. This suggests that these charmed hadron decays might be within reach of the BESIII and Belle II experiments or future super charm-tau factories and could serve as potentially promising probes of leptoquark interactions with sterile neutrinos.