Measurement of the local and nonlocal amplitudes in $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ decays

This paper presents a thorough study of the local and nonlocal amplitudes in $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ transitions through an amplitude analysis of the dimuon mass spectrum of the decay. The analysis is based on $pp$ collision data corresponding to an integrated luminosity of 8.4fb${}^{-1}$ collected by the LHCb experiment. This measurement employs a model that describes both one-particle and two-particle nonlocal amplitudes across the entirety of the dimuon mass spectrum, enabling the determination of both short- and long-distance contributions to the decay. The compatibility of the Wilson coefficient combinations $C_9+C_9^{\mathrm{\prime }}$ and $C_{10}+C_{10}^{\mathrm{\prime }}$ with the Standard Model prediction is found to vary between $1.6\sigma$ and $4\sigma$, depending on the choice of local form factors.