A bstract We perform a frequentist analysis of q _(2)-dependent B → K _(?)(→ Kπ ) ? _(+) ? _(?)angular observables at large recoil, aiming at bridging the gap between current theoretical analyses and the actual experimental measurements. We focus on the most appropriate set of observables to measure and on the role of the q _(2)-binning. We highlight the importance of the observables P ~( i )exhibiting a limited sensitivity to soft form factors for the search for New Physics contributions. We compute predictions for these binned observables in the Standard Model, and we compare them with their experimental determination extracted from recent LHCb data. Analysing b → s and b → s? _(+) ? _(?)transitions within four different New Physics scenarios, we identify several New Physics benchmark points which can be discriminated through the measurement of P ~( i )observables with a fine q _(2)-binning. We emphasise the importance (and risks) of using observables with (un)suppressed dependence on soft form factors for the search of New Physics, which we illustrate by the different size of hadronic uncertainties attached to two related observables ( P ~(1)and S ~(3)). We illustrate how the q _(2)-dependent angular observables measured in several bins can help to unravel New Physics contributions to B → K _(?)(→ Kπ ) ? _(+) ? _(?), and show the extraordinary constraining power that the clean observables will have in the near future. We provide semi-numerical expressions for these observables as functions of the relevant Wilson coefficients at the low scale.
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