Short- vs. long-distance physics in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$: a data-driven analysis

Abstract

We analyze data on $B\to K\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ and $B\to K^{\ast }\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ decays in the whole dilepton invariant mass spectrum with the aim of disentangling short- vs. long-distance contributions. The sizable long-distance amplitudes from $c\bar{c}$ narrow resonances are taken into account by employing a dispersive approach. For each available $q^2=m_{\hat{I}¼\hat{I}¼}^2$ bin and each helicity amplitude an independent determination of the Wilson coefficient $C_9$, describing $b\to s{\ell }^{+}{\ell }^{-}$ transitions at short distances, is obtained. The consistency of the $C_9$ values thus obtained provides an a posteriori check of the absence of additional, sizable, long-distance contributions. The systematic difference of these values from the Standard Model expectation supports the hypothesis of a non-standard $b\to s\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ amplitude of short-distance origin.

19 pages, 3 figures, v2: accepted on EPJC