Non-parametric and continuous extraction of amplitudes in electroweak penguin decays

Abstract

We introduce a novel approach to extract the decay-amplitudes in $B\to V(\to M_1{M}_2){\ell }^{+}{\ell }^{-}$ processes, where $V$ represents a meson with either $J=0$ (S-wave) or $J=1$ (P-wave). This approach enables the decay-amplitudes across the dihadron and dilepton invariant-masses to be extracted from data in a model-independent and continuous way. To achieve this, the angular decay rate is expressed in a way that allows the application of the \sPlot technique to likelihood fits of the decay angles. We illustrate the abilities of this method on simulated $B^0\to K^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ data, containing both S- and P-wave contributions to the $K^{+}{\pi }^{-}$ system. We provide the weight functions and show that they allow the extraction of the absolute value of the P-wave and S-wave transversity amplitudes as a function of the dihadron and dimuon invariant-masses in a continuous, unbiased, and statistically-powerful way, while only relying on the angular distribution. As a consequence, the extracted amplitude shapes are model-independent -- up to the angular terms included in the fit -- and can be directly compared to theoretical predictions. A measurement using this technique can improve the sensitivity to potential new physics effects in $b\to s{\ell }^{+}{\ell }^{-}$ transitions, as well as the understanding of hadronic form factors, particularly in the S-wave system.

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