We search for bottomonium states in Upsilon(2S)-> (bb-bar) gamma decays with an integrated luminosity of 24.7fb^-1 recorded at the Upsilon(2S) resonance with the Belle detector at KEK, containing (157.8+-3.6) X 10^6 Upsilon(2S) events. The (bb-bar) system is reconstructed in 26 exclusive hadronic final states composed of charged pions, kaons, protons, and K^0_S mesons. We find no evidence for the state recently observed around 9975 MeV (X_(bb-bar)) in an analysis based on a data sample of 9.3 X 10^6 Upsilon(2S) events collected with the CLEO III detector. We set a 90 % confidence-level upper limit on the branching fraction B[Upsilon(2S)-> X_(bb-bar) gamma] X sum_i{B[X_(bb-bar)-> h_i]}< 4.9 X 10^-6, summed over the exclusive hadronic final states employed in our analysis. This result is an order of magnitude smaller than the measurement reported with CLEO data. We also set an upper limit for the eta_b(1S) state of B[Upsilon(2S)-> eta_b(1S) gamma] X sum_i{B[eta_b(1S)-> h_i]}< 3.7 X 10^-6.
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