BKT-40A Belle II results for B+ → K+ν ¯ν in the formalism of USC relational couplings

BKT–40A is a standalone satellite annex to BKT–40. The document explains how the public model-agnostic Belle II likelihood for the B⁺ → K⁺νν̄ channel can be used as a shape test for the phenomenological BKT–40 benchmark. The aim is not to claim the discovery of a new particle or to validate the global USC framework empirically, but to define a controlled interface between the Belle II result, the WET description and the hypothesis of a local invisible component B⁺ → K⁺X_inv. The test point is the two-body hypothesis: B⁺ → K⁺X_inv, with the invisible-state mass: mₓ = 2.10 (+0.20, −0.10) GeV, corresponding to the generator-level location: qₓ² = mₓ² = 4.41 (+0.88, −0.41) GeV². The effective invisible normalization of the benchmark is: B(B⁺ → K⁺X)Pₓ,inv = 9.2 (+1.8, −3.4) × 10⁻⁶. The formal test is defined as a deformation of the differential spectrum relative to the SM description: dB_test/dq² = dB_SM/dq² + Δ_BKT40(q²; λ), and as a reweighting of the Belle II templates: ν₁,ₓ = Σⱼ ν₀,ₓⱼ wⱼ,wⱼ = σ₁,ⱼ / σ₀,ⱼ. BKT–40A emphasizes that the decisive observable is not only the total branching fraction, but the reconstructed q²-shape. In the minimal benchmark, the signal is expected to concentrate in the region 4 < q²_rec < 8 GeV², with a strongly suppressed high-q² tail. This shape condition distinguishes a local two-body invisible contribution from smooth WET-like deformations of the b → sνν̄ transition. The document follows the BK/BKA standard: empirical result, hypothesis, calibrated parameter, derived quantity, detector approximation, model interpretation and falsification condition are kept separate. Agreement of a future q²-shape test may support only the sectoral BKT–40 benchmark; it does not constitute proof of the broader PJM–GTWSSF–USC–GTCW interpretation. Failure to reproduce the localized q² pattern, conflict with direct B → hX_inv limits, or correlated tauonic enhancement outside the minimal control conditions falsifies the minimal BKT–40 benchmark.