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

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 $K^{\ast }$ 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, $A_{\mathrm{FB}\mathrm{L}}^K$, 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 non-resonant backgrounds.

14 pages

References in corpus (9)

• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• New strategies for New Physics search in B -> K* nu anti-nu, B -> K nu anti-nu and B -> X(s) nu anti-nu decays
• Rare $B$ Decays as Tests of the Standard Model
• Tree-level contributions to the rare decays B+ --> pi+ nu anti-nu, B+ --> K+ nu anti-nu, and B+ --> K*+ nu anti-nu in the Standard Model
• Analysis of the D+ --> K- pi+ e+ nu_e decay channel
• The effect of S-wave interference on the $B^0\to K^{\ast 0}{\ell }^{+}{\ell }^{-}$ angular observables
• Analysis of rare (B -> K_0*(1430) l^+ l^- decay) within QCD sum rules
• Differential branching fraction and angular moments analysis of the decay $B^0\to K^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ in the $K_{0,2}^{\ast }(1430{)}^0$ region

Cited by in corpus (7)

• Understanding the first measurement of $\mathcal{B}(B\to K\nu \bar{\nu })$
• Prospects for searches of $b\to s\nu \bar{\nu }$ decays at FCC-ee
• Consequences of $b\to s{\mu }^{+}{\mu }^{-}$ anomalies on $B\to K^{(\ast )}\nu \bar{\nu }$, $B_s\to (\eta ,{\eta }^{\prime })\nu \bar{\nu }$ and $B_s\to \varphi \nu \bar{\nu }$ decay observables
• Helicity amplitudes in $B\to D^{\ast }\bar{\nu }l$ decay
• $c\to u\nu \bar{\nu }$ transitions of $B_c$ mesons: 331 model facing Standard Model null tests
• The asymmetries of the $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ decay and the search of new physics beyond the Standard Model
• Helicity amplitudes in the $\bar{B}\to D^{\ast }{\bar{\nu }}_{\tau }\tau$ decay with $V-A$ breaking in the quark sector