We report the results of a search for the $X(1835)$ state in the process $e^+e^-to J/psi+X(1835)$ using a data sample of 672 fb$^{-1}$ collected with the Belle detector at and near the $Upsilon(4S)$ resonance at the KEKB asymmetric-energy $e^+e^-$ collider. No significant evidence is found for this process, and an upper limit is set on its cross section times the branching fraction: $sigma_{rm Born}(e^+e^- to J/psi X(1835)) cdot$ {${cal B}(X(1835)to ge 3$ charged tracks)} $< 1.3 {rm fb}$ at 90% confidence level.
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