Radiative generation of chiral vector operators in $b\to s \nu\bar{\nu}$ transition
The recent Belle II evidence for $B^+ \to K^+ \nu \bar{\nu}$, combined with a suppressed branching fraction ratio $R \equiv \mathcal{B}(B^0 \to K^{*0} \nu \bar{\nu}) / \mathcal{B}(B^+ \to K^+ \nu \bar{\nu})$, necessitates new physics contributing to both left- and right-handed vector operators. We perform a systematic topological classification of one-loop completions that radiatively generate both operators without tree-level mediation, and construct two minimal benchmark scenarios: a scalar-rich model and a fermion-rich model. Evaluating these frameworks under specific benchmark mass schemes and four distinct flavor structures, we find a generic anti-correlation where enhancing one decay channel typically suppresses the other. A notable exception is a decoupled flavor configuration within the scalar-rich model, which yields simultaneous constructive interference, reducing $R$ by $4.22\%$ while satisfying all complementary flavor bounds. Under a universal coupling assumption, the scalar-rich model yields exact cancellation in the charged mode, highlighting the non-trivial interplay between flavor structure and loop-generated Wilson coefficients.