Observation of J /ψ ϕ Structures Consistent with Exotic States from Amplitude Analysis of B+→J /ψ ϕ K+ Decays

The first full amplitude analysis of B⁺→J /ψ ϕ K⁺ with J /ψ →μ⁺μ^-, ϕ →K⁺K^- decays is performed with a data sample of 3 fb^-1 of p p collision data collected at √{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 ϕ K⁺, and four J /ψ ϕ 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.