An amplitude analysis of the final state structure in the Bs->J/psi K+K- decay mode is performed using 1.0/fb of data collected by the LHCb experiment in 7 TeV center-of-mass energy pp collisions produced by the LHC. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. Resonant structures are observed in the K+K- mass spectrum as well as a significant non-resonant S-wave contribution. The largest resonant component is the phi(1020), accompanied by f0(980), f2(1525), and four additional resonances. The overall branching fraction is measured to be B(Bs->J/psi K+K-)=(7.70 +/-0.08 +/- 0.39 +/- 0.60)x 10^(-4), where the first uncertainty is statistical, the second systematic, and the third due to the ratio of the number of Bs to B- mesons produced. The mass and width of the f2(1525) are measured to be 1522.2 +/- 2.8^{+5.3}_{-2.0} MeV and 84 +/- 6^{+10}_{-5} MeV, respectively. The final state fractions of the other resonant states are also reported.
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