General analysis ofB¯→K¯(*)ℓ+ℓ−decays at low recoil
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Abstract
We analyze the angular distributions of $\overline{B}\ensuremath{\rightarrow}{\overline{K}}^{*}(\ensuremath{\rightarrow}\overline{K}\ensuremath{\pi}){\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ and $\overline{B}\ensuremath{\rightarrow}\overline{K}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decays in the region of low hadronic recoil in a model-independent way by taking into account the complete set of dimension-six operators $[\overline{s}\ensuremath{\Gamma}b][\overline{\ensuremath{\ell}}{\ensuremath{\Gamma}}^{\ensuremath{'}}\ensuremath{\ell}]$. We obtain several novel low-recoil observables with high sensitivity to nonstandard-model Dirac structures, including $CP$ asymmetries, which do not require flavor tagging. The transversity observables ${H}_{T}^{(1,3,4,5)}$ are found to be insensitive to hadronic matrix elements and their uncertainties even when considering the complete set of operators. In the most general scenario we show that the low recoil operator product expansion can be probed at the few-percent level using the angular observable ${J}_{7}$. Higher sensitivities are possible assuming no tensor contributions, specifically by testing the low-recoil relation $|{H}_{T}^{(1)}|=1$. We explicitly demonstrate the gain in reach of the low-recoil observables in accessing the ratio $|{\mathcal{C}}_{9}/{\mathcal{C}}_{10}|$ compared to the forward-backward asymmetry, and probing $CP$-violating right-handed currents $\mathrm{Im}{\mathcal{C}}_{{10}^{\ensuremath{'}}}$. We give updated Standard Model predictions for key observables in $\overline{B}\ensuremath{\rightarrow}{\overline{K}}^{(*)}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decays.