Abstract
The first full amplitude analysis of $B^+ \to J/\psi\phi K^+$ with $J/\psi \to \mu^+\mu^−$, $\phi \to K^+K^−$ 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 $\phi K^+$, and four $J/\psi\phi$ 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.