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

Abstract

Rare $|\Delta c|=|\Delta u|=1$ transitions into dineutrinos are strongly GIM-suppressed and constitute excellent null tests of the standard model. While branching 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 are experimentally unconstrained, signals of new physics can be just around the corner. We provide model-independent upper limits on branching ratios reaching few $\times 10^{-5}$ in the most general case of arbitrary lepton flavor structure, $\sim 10^{-5}$ for scenarios with charged lepton conservation and few $\times 10^{-6}$ assuming lepton universality. We also give upper limits in $Z^{\prime }$ and leptoquark models. The presence of light right-handed neutrinos can affect these limits, a possibility that can occur for lepton number violation at a TeV, and that can be excluded with an improved bound on $\mathcal{B}(D^0\to \text{invisibles})$ at the level of $\sim 10^{-6}$, about two 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 searches at $e^{+}{e}^{-}$-facilities, such as BES III, Belle II and future $e^{+}{e}^{-}$-colliders, such as the FCC-ee running at the $Z$.

Comments: v2: 14 pages, 5 figures, 8 tables; typos fixed and minor numerical changes in inclusive results, conclusions unchanged; published version