Observation of J/ψϕ Structures Consistent with Exotic States from Amplitude Analysis of B^{+}→J/ψϕK^{+} Decays.

The first full amplitude analysis of B^{+}→J/ψϕK^{+} with J/ψ→μ^{+}μ^{-}, ϕ→K^{+}K^{-} decays is performed with a data sample of 3  fb^{-1} of pp collision data collected at sqrt[s]=7 and 8 TeV with the LHCb detector. The data cannot be described by a model that contains only excited kaon states decaying into ϕK^{+}, and four J/ψϕ structures are observed, each with significance over 5 standard deviations. The quantum numbers of these structures are determined with significance of at least 4 standard deviations. The lightest has mass consistent with, but width much larger than, previous measurements of the claimed X(4140) state.