An empirical model of the long-distance contributions to $\bar{B}^{0} \rightarrow \bar{K}^{*0}\mu^{+}\mu^{-}$ transitions

Abstract

A method for analysing the hadronic resonance contributions in $\bar{B}^{0} \rightarrow \bar{K}^{*0}\mu^{+}\mu^{-}$ decays is presented. This method uses an empirical model that relies on measurements of the branching fractions and polarisation amplitudes of final states involving $J^{PC}=1^{--}$ resonances, relative to the short-distance component, across the full dimuon mass spectrum of $\bar{B}^{0} \rightarrow \bar{K}^{*0}\mu^{+}\mu^{-}$ transitions. The model is in good agreement with existing calculations of hadronic non-local effects. The effect of this contribution to the angular observables is presented and it is demonstrated how the narrow resonances in the $q^{2}$ spectrum provide a dramatic enhancement to $CP$-violating effects in the short-distance amplitude. Finally, a study of the hadronic resonance effects on lepton universality ratios, $R_{K^{(*)}}$, in the presence of new physics is presented.