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

## TL;DR

This paper analyzes backgrounds and interference effects in the rare decay $B\to K^*(\to K\pi) \nu\bar{\nu}$, highlighting their impact on measurements and the potential to probe form factors and new physics.

## Contribution

It provides a detailed study of resonant and non-resonant backgrounds beyond the narrow-width approximation, quantifying interference effects and their implications for experimental analyses.

## Key findings

- Interference effects in the $K^*$ signal region can be as large as 20% in branching ratio.
- Effects of broad scalar states are at the percent level in branching fractions and negligible in polarization.
- The observable $A_{\rm FB \, L}^K$ can effectively control backgrounds and probe form factors or right-handed currents.

## Abstract

The rare decay $B\to K^\ast( \to K\pi) \nu\bar{\nu}$ 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 non-resonant backgrounds 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 low hadronic recoil, where $B \to K \pi$ form factors from 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 few \%. Effects of the broad scalar states $K_0^\ast$ and $\kappa$ are at the level of percent in the branching fraction in the $K^\ast$ signal region and negligible in $F_L$. Since the backgrounds to $F_L$ are small this observable constitutes a useful probe of form factors calculations, or alternatively, of right-handed currents in the entire $q^2$-region. The forward-backward asymmetry in the $K \pi$-system, $A_{\rm FB \, L}^K$, 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 non-resonant backgrounds.