Short- vs. long-distance physics in $$B\rightarrow K^{(*)} \ell ^+\ell ^-$$ B → K ( ∗ ) ℓ + ℓ - : a data-driven analysis

Abstract

Abstract We analyze data on $$B\rightarrow K\mu ^+\mu ^-$$ B → K μ + μ - and $$B\rightarrow K^*\mu ^+\mu ^-$$ B → K ∗ μ + μ - decays in the whole dilepton invariant mass spectrum with the aim of disentangling short- vs. long-distance contributions. The sizable long-distance amplitudes from $$c \overline{c}$$ c c ¯ narrow resonances are taken into account by employing a dispersive approach. For each available $$q^2=m^2_{\mu \mu }$$ q 2 = m μ μ 2 bin and each helicity amplitude an independent determination of the Wilson coefficient $$C_9$$ C 9 , describing $$b\rightarrow s\ell ^+\ell ^-$$ b → s ℓ + ℓ - transitions at short distances, is obtained. The consistency of the $$C_9$$ 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 $$b\rightarrow s \mu ^+\mu ^-$$ b → s μ + μ - amplitude of short-distance origin.