Implications of B → K νν̅ under Rank-One Flavor Violation hypothesis

We study the implications of the observed excess in B^+ → K^+ νν̅ 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 →πνν̅, B_s →μ^+ μ^-, meson mixing and the LHC searches in τ^+ τ^- high-energy tails. Among the various mediators, the scalar leptoquarks R̃_2 and S_1 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 p p →τ^+ τ^-. In all cases we find that a flavour alignment close to the third generation is generically preferred.