The rare decay $B\to K^{*}(\to K\pi )\nu \overline{\nu }$ is expected to play an important role in searches for physics beyond the Standard Model at the near future $B$-physics experiments. We investigate resonant and nonresonant backgrounds that arise beyond the narrow-width approximation for the $K^{*}$. Nonresonant $B\to K\pi \nu \overline{\nu }$ decays are analyzed in the region of low hadronic recoil, where $B\to K\pi$ form factors from the heavy-hadron-chiral-perturbation theory are available. In a Breit-Wigner–type model interference-induced effects in the $K^{*}$ signal region are found to be sizable, as large as 20% in the branching ratio. Corresponding effects in the longitudinal polarization fraction $F_L$ are smaller, at most around a few percent. Effects of the broad scalar states $K_0^{*}$ and $\kappa$ are at the level of percent in the branching fraction in the $K^{*}$ signal region and negligible in $F_L$. Since the backgrounds to $F_L$ are small, this observable constitutes a useful probe of form factor calculations or, alternatively, of right-handed currents in the entire $q^2$ region. The forward-backward asymmetry in the $K\pi$ system, $A_{\mathrm{FB}\mathrm{L}}^K$, with normalization to the longitudinal decay rate probes predominantly $S$, $P$-wave interference free of short-distance coefficients and can therefore be used to control the resonant and nonresonant backgrounds.

• Received 5 March 2017

DOI:https://doi.org/10.1103/PhysRevD.95.073001