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An amplitude analysis of the $B^{0}\to K^{*0}\mu^+\mu^-$ decay is presentedusing a dataset corresponding to an integrated luminosity of $4.7$ fb$^{-1}$ of$pp$ collision data collected with the LHCb experiment. For the first time, thecoefficients associated to short-distance physics effects, sensitive toprocesses beyond the Standard Model, are extracted directly from the datathrough a $q^2$-unbinned amplitude analysis, where $q^2$ is the $\mu^+\mu^-$invariant mass squared. Long-distance contributions, which originate fromnon-factorisable QCD processes, are systematically investigated and the mostaccurate assessment to date of their impact on the physical observables isobtained. The pattern of measured corrections to the short-distance couplingsis found to be consistent with previous analyses of $b$- to $s$-quarktransitions, with the largest discrepancy from the Standard Model predictionsfound to be at the level of 1.8 standard deviations. The global significance ofthe observed differences in the decay is 1.4 standard deviations.

Amplitude analysis of the $B^{0}\to K^{*0}\mu^+\mu^-$ decay