Implications of $$B \rightarrow K \nu {\bar{\nu }}$$ under rank-one flavor violation hypothesis

We study the implications of the observed excess in B+→K+νν¯ under the assumption of Rank-One Flavour Violation, i.e. that New Physics couples to a single specific direction in flavour space. By varying this direction we perform analyses at the level of the low-energy EFT, the SMEFT, and with explicit mediators such as leptoquarks and colorless vectors (Z′ and V′). We study correlations with other flavour, electroweak and collider observables, finding that the most interesting ones are with K→πνν¯, Bs→μ+μ-, meson mixing and the LHC searches in τ+τ- high-energy tails. Among the various mediators, the scalar leptoquarks R~2 and S1 offer the best fits of the Belle-II excess, while being consistent with the other bounds. On the other hand, colorless vectors are strongly constrained by meson mixing and resonance searches in pp→τ+τ-. In all cases we find that a flavour alignment close to the third generation is generically preferred.