Rare charm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>u</mml:mi><mml:mi>ν</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> dineutrino null tests for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> machines
Rigo Bause, Hector Gisbert, Marcel Golz, Gudrun Hiller
Abstract
Rare $|\mathrm{\ensuremath{\Delta}}c|=|\mathrm{\ensuremath{\Delta}}u|=1$ transitions into dineutrinos are strongly Glashow-Iliopoulos-Maiani-suppressed and constitute excellent null tests of the standard model. While branching ratios of $D\ensuremath{\rightarrow}P\ensuremath{\nu}\overline{\ensuremath{\nu}}$, $D\ensuremath{\rightarrow}{P}^{+}{P}^{\ensuremath{-}}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, $P=\ensuremath{\pi}$, $K$, baryonic ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}\ensuremath{\rightarrow}p\ensuremath{\nu}\overline{\ensuremath{\nu}}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ and inclusive $D\ensuremath{\rightarrow}X\ensuremath{\nu}\overline{\ensuremath{\nu}}$ 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 $\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ in the most general case of arbitrary lepton flavor structure, $\ensuremath{\sim}{10}^{\ensuremath{-}5}$ for scenarios with charged lepton conservation and few $\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ assuming lepton universality. We also give upper limits in ${Z}^{\ensuremath{'}}$ 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 $\mathcal{B}({D}^{0}\ensuremath{\rightarrow}\text{invisibles})$ at the level of $\ensuremath{\sim}{10}^{\ensuremath{-}6}$, about two orders of magnitude better than the present one. Signatures of $c\ensuremath{\rightarrow}u\ensuremath{\nu}\overline{\ensuremath{\nu}}$ modes contain missing energy and are suited for experimental searches at ${e}^{+}{e}^{\ensuremath{-}}$--facilities, such as BES III, Belle II and future ${e}^{+}{e}^{\ensuremath{-}}$--colliders, such as the FCC-ee running at the $Z$.