The rare multi-body decays B¯→K¯πℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ \overline{B}\to \overline{K}\pi \ell \ell $$\end{document} and B¯s→K¯Kℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ {\overline{B}}_s\ \to \overline{K}K\ell \ell $$\end{document} are both important as backgrounds to precision analyses in the benchmark modes B¯→K¯*ℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ \overline{B}\to {\overline{K}}^{*}\ell \ell $$\end{document} and B¯s→ϕℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ {\overline{B}}_s\to \phi \ell \ell $$\end{document} as well as sensitive probes of flavor physics in and beyond the standard model. We work out non-resonant contributions to B¯→K¯πℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ \overline{B}\to \overline{K}\pi \ell \ell $$\end{document} and B¯s→K¯Kℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ {\overline{B}}_s\ \to \overline{K}K\ell \ell $$\end{document} amplitudes, where ℓ = e,μ, at low hadronic recoil in a model-independent way. Using the operator product expansion in 1/mb, we present expressions for the full angular distribution. The latter allows to probe new combinations of |ΔB| = |ΔS| = 1 couplings and gives access to strong phases between non-resonant and resonant contributions. Exact endpoint relations between transversity amplitudes based on Lorentz invariance are obtained. Several phenomenological distri- butions including those from the angular projections to the S-, P-, D-waves are given. Standard model branching ratios for non-resonant B¯→K¯πℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ \overline{B}\to \overline{K}\pi \ell \ell $$\end{document} and B¯s→K¯Kℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ {\overline{B}}_s\ \to \overline{K}K\ell \ell $$\end{document} decays are found to be in the few 10−8 region, but drop significantly if cuts around the K* or ϕ mass are employed. Nevertheless, the non-resonant contributions to B¯→K¯πℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ \overline{B}\to \overline{K}\pi \ell \ell $$\end{document} provide the dominant background in the B¯→K¯*ℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ \overline{B}\to {\overline{K}}^{*}\ell \ell $$\end{document} signal region with respect to the low mass scalars. In B¯s→K¯Kℓℓ\documentclass[12pt]{minimal}
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\begin{document}$$ {\overline{B}}_s\ \to \overline{K}K\ell \ell $$\end{document}, the narrowness of the ϕ allows for more efficient background control. We briefly discuss lepton-flavor non-universal effects, also in view of the recent data on RK.
