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

Rare $|\mathrm{\Delta }c|=|\mathrm{\Delta }u|=1$ transitions into dineutrinos are strongly Glashow-Iliopoulos-Maiani-suppressed and constitute excellent null tests of the standard model. While branching ratios of $D\to P\nu \overline{\nu }$, $D\to P^{+}{P}^{-}\nu \overline{\nu }$, $P=\pi$, $K$, baryonic ${\mathrm{\Lambda }}_c^{+}\to p\nu \overline{\nu }$, and ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}\nu \overline{\nu }$ and inclusive $D\to X\nu \overline{\nu }$ 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 $c\to u\nu \overline{\nu }$ 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 $Z$.

Figure 1

Relative statistical uncertainty of the branching ratio $\delta \mathcal{B}$ versus the branching ratio $\mathcal{B}$ for decays of the $D^0$ (upper plot to the left), the $D^{+}$ (upper plot to the right) and the ${\mathrm{\Lambda }}_c^{+}$ (lower plot to the left). The shaded areas correspond to the reach for ${\eta }_{\mathrm{eff}}=1$, whereas the solid tilted lines illustrate the impact of reconstruction efficiencies ${\eta }_{\mathrm{eff}}={10}^{-3}$ for the FCC-ee (lilac) and Belle II (green). Horizontal $3\sigma$ (dotted) and $5\sigma$ (dashed) black lines correspond to $\delta \mathcal{B}=1/3$ and $\delta \mathcal{B}=1/5$, respectively. Vertical lines represent upper limits assuming LU (solid), cLFC (dotted) and generic lepton flavor (dashed) for different modes, given in Table 3. To improve readability the three lines for each decay mode are grouped together by a shaded band. Upper limits for $D_s^{+}\to K^{+}\nu \overline{\nu }$, ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}\nu \overline{\nu }$ and the inclusive modes can be seen in Table 3.

Figure 2

Differential branching ratios for $D^0\to {\pi }^0\nu \overline{\nu }$, $D^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $D_s^{+}\to K^{+}\nu \overline{\nu }$ in red, brown, and green, respectively for the LU (cLFC) limit in solid (dotted) lines from Eq. (10) [Eq. (11)]. The uncertainty bands are due to the form factors, the vertical dashed lines illustrate the cuts (16) needed to avoid the $\tau$ background.

Figure 3

Differential branching ratios for $D^0\to {\pi }^0{\pi }^0\nu \overline{\nu }$, $D^0\to {\pi }^{+}{\pi }^{-}\nu \overline{\nu }$ and $D^0\to K^{+}{K}^{-}\nu \overline{\nu }$ decays in orange, deep pink and cyan, respectively for the LU (cLFC) limit in solid (dotted) lines from Eq. (10) [Eq. (11)]. The upper plot shows $\mathrm{d}\mathcal{B}/\mathrm{d}{q}^2$, whereas the lower plot $\mathrm{d}\mathcal{B}/\mathrm{d}{p}^2$, as in (20). The differential branching ratio of $D^0\to K^{+}{K}^{-}\nu \overline{\nu }$ is multiplied by a factor 100 to be visible in the plots. The band widths illustrate 10% uncertainty originating from form factors.

Figure 4

Differential branching ratios for ${\mathrm{\Lambda }}_c^{+}\to p\nu \overline{\nu }$ and ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}\nu \overline{\nu }$ decays in brown and blue, respectively for the LU (cLFC) limit in solid (dotted) lines from Eq. (10) [Eq. (11)]. The band widths correspond to the form factor uncertainties, see main text.

Figure 5

Differential branching ratios for $D^0\to X\nu \overline{\nu }$, $D^{+}\to X\nu \overline{\nu }$, and $D_s^{+}\to X\nu \overline{\nu }$ decays in magenta, lime and green, respectively for the LU (cLFC) limit in solid (dotted) lines from Eq. (10) [Eq. (11)]. The band widths illustrate 10% uncertainties from power corrections. The distributions are cut at $q_{\max }^2=m_c^2$ and at the physical limit $q_{\max }^2={(m_D-m_K)}^2$ for the $D^{0,+}$ and $D_s^{+}$ modes, respectively [20].