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The rare decay $B\to K^\ast( \to K\pi) \nu\bar{\nu}$ is expected to play animportant role in searches for physics beyond the Standard Model at the nearfuture $B$-physics experiments. We investigate resonant and non-resonantbackgrounds that arise beyond the narrow-width approximation for the $K^\ast$.Non-resonant $B\to K\pi \nu\bar{\nu}$ decays are analyzed in the region of lowhadronic recoil, where $B \to K \pi$ form factors fromHeavy-Hadron-Chiral-Perturbation Theory are available. In a Breit-Wigner-typemodel interference-induced effects in the $K^*$ signal region are found to besizable, as large as $20\%$ in the branching ratio. Corresponding effects inthe longitudinal polarization fraction $F_L$ are smaller, at most around few\%. Effects of the broad scalar states $K_0^\ast$ and $\kappa$ are at the levelof percent in the branching fraction in the $K^\ast$ signal region andnegligible in $F_L$. Since the backgrounds to $F_L$ are small this observableconstitutes a useful probe of form factors calculations, or alternatively, ofright-handed currents in the entire $q^2$-region. The forward-backwardasymmetry in the $K \pi$-system, $A_{\rm FB \, L}^K$, with normalization to thelongitudinal decay rate probes predominantly S,P-wave interference free ofshort-distance coefficients and can therefore be used to control the resonantand non-resonant backgrounds.

Revisiting $B\to K^\ast( \to K\pi) \nu\bar{\nu}$ decays