An empirical model to determine the hadronic resonance contributions to [Formula: see text] transitions

A method for analysing the hadronic resonance contributions in [Formula: see text] decays is presented. This method uses an empirical model that relies on measurements of the branching fractions and polarisation amplitudes of final states involving [Formula: see text] resonances, relative to the short-distance component, across the full dimuon mass spectrum of [Formula: see text] 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 [Formula: see text] spectrum provide a dramatic enhancement to [Formula: see text] -violating effects in the short-distance amplitude. Finally, a study of the hadronic resonance effects on lepton universality ratios, [Formula: see text] , in the presence of new physics is presented.