Disentangling new physics in K→πνν¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K\to \pi \nu \overline{\nu} $$\end{document} and B→KK∗νν¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ B\to K\left({K}^{\ast}\right)\nu \overline{\nu} $$\end{document} observables

We investigate the possibility of disentangling different new physics contributions to the rare meson decays [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext] through kinematic distributions in the missing energy [inline-graphic not available: see fulltext]. We employ dimension-6 operators within the Low-Energy Effective Field Theory (LEFT), identifying the invisible part of the final state as either active or sterile neutrinos. Special emphasis is given to lepton-number violating (LNV) operators with scalar and tensor currents. We show analytically that contributions from vector, scalar, and tensor quark currents can be uniquely determined from experimental data of kinematic distributions. In addition, we present new correlations of branching ratios for K and B-decays involving scalar and tensor currents. As there could a priori also be new invisible particles in the final states, we include dark-sector operators giving rise to two dark scalars, fermions, or vectors in the final state. In this context, we present new calculations of the inclusive decay rate [inline-graphic not available: see fulltext] for dark operators. We show that careful measurements of kinematic distributions make it theoretically possible to disentangle the contribution from LEFT operators from most of the dark-sector operators, even when multiple operators are contributing. We revisit sum rules for vector currents in LEFT and show that the latter are also satisfied in some new dark-physics scenarios that could mimic LEFT. Finally, we point out that an excess in rare meson decays consistent with a LNV hypothesis would point towards highly flavor non-democratic physics in the UV, and could put high-scale leptogenesis under tension.