Revisiting B → K * ( → K π ) ν ν ¯ decays

TLDR: In this paper, the authors investigate resonant and non-resonant backgrounds that arise beyond the narrow-width approximation for the rare decay of the standard model and show that interference-induced effects in the signal region are sizable, as large as 20% in the branching ratio.

Abstract: The rare decay $B\ensuremath{\rightarrow}{K}^{*}(\ensuremath{\rightarrow}K\ensuremath{\pi})\ensuremath{\nu}\overline{\ensuremath{\nu}}$ 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 $B\ensuremath{\rightarrow}K\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ decays are analyzed in the region of low hadronic recoil, where $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ 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 $\ensuremath{\kappa}$ 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 $K\ensuremath{\pi}$ system, ${A}_{\mathrm{FB}\text{ }\mathrm{L}}^{K}$, 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.