| Summary: | We report four narrow peaks in the Ξ_{b}^{0}K^{-} mass spectrum obtained using pp collisions at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of 9 fb^{-1} recorded by the LHCb experiment. Referring to these states by their mass, the mass values are m[Ω_{b}(6316)^{-}]=6315.64±0.31±0.07±0.50 MeV, m[Ω_{b}(6330)^{-}]=6330.30±0.28±0.07±0.50 MeV, m[Ω_{b}(6340)^{-}]=6339.71±0.26±0.05±0.50 MeV, m[Ω_{b}(6350)^{-}]=6349.88±0.35±0.05±0.50 MeV, where the uncertainties are statistical, systematic, and the last is due to the knowledge of the Ξ_{b}^{0} mass. The natural widths of the three lower mass states are consistent with zero, and the 90% confidence-level upper limits are determined to be Γ[Ω_{b}(6316)^{-}]<2.8 MeV, Γ[Ω_{b}(6330)^{-}]<3.1 MeV and Γ[Ω_{b}(6340)^{-}]<1.5 MeV. The natural width of the Ω_{b}(6350)^{-} peak is 1.4_{-0.8}^{+1.0}±0.1 MeV, which is 2.5σ from zero and corresponds to an upper limit of 2.8 MeV. The peaks have local significances ranging from 3.6σ to 7.2σ. After accounting for the look-elsewhere effect, the significances of the Ω_{b}(6316)^{-} and Ω_{b}(6330)^{-} peaks are reduced to 2.1σ and 2.6σ, respectively, while the two higher mass peaks exceed 5σ. The observed peaks are consistent with expectations for excited Ω_{b}^{-} resonances.
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