Implications of an enhanced $B \to K \nu \bar \nu$ branching ratio

Abstract

Rare decays mediated by $b \to s \nu \bar \nu$ transitions have been reported by the Belle II experiment. The branching ratio of the decay $B^+ \to K^+ \nu \bar \nu$ is found to be enhanced with respect to the standard model value. If taken at face value, the implications are profound: either lepton flavor universality is violated at the (multi)-TeV-scale, or light new physics is involved. This holds in general if $\mathcal{B}(B^+ \to K^+ \nu \bar \nu)$ exceeds $1.2 \cdot 10^{-5} \, (1.3 \cdot 10^{-5})$ at $1 \sigma$ ($2 \sigma$), which tightens with a decreasing upper limit on $\mathcal{B}(B \to K^*\nu \bar \nu)$, that is in reach of the Belle II experiment. In view of the strong constraints on electron-muon universality violation in $|\Delta b|=|\Delta s|=1$ processes, viable explanations are heavy, $(5-10)$-TeV tree-level new physics mediators that couple only to tau-flavors, or lepton flavor violating ones. In addition, couplings of similar size to both left- and right-handed quarks are generically required, implying non-minimal BSM sectors which are carefully balanced against flavor constraints. The decay $B_s^0 \to \text{invisibles}$ can shed light on whether new physics is light or heavy. In the former case, branching ratios can be as large as $10^{-5}$.