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

We study the implications of the observed excess in B⁺ → K⁺ ν ν̄ 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 → π ν ν̄, Bₛ → μ⁺ μ⁻, meson mixing and the LHC searches in τ⁺ τ⁻ high-energy tails. Among the various mediators, the scalar leptoquarks R̃₂ 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 p p → τ⁺ τ⁻. In all cases we find that a flavour alignment close to the third generation is generically preferred.