In calculations of the hyperfine splitting in charmonium, the contributions of the disconnected diagrams are considered small and are typically ignored. We aim to estimate nonperturbatively the size of the resulting correction, which may eventually be needed in high precision calculations of the charmonium spectrum. We study this problem in the quenched and unquenched QCD cases. On dynamical ensembles the disconnected charmonium propagators contain light modes which complicate the extraction of the signal at large distances. In the fully quenched case, where there are no such light modes, the interpretation of the signal is simplified. We present results from lattices with $aapprox 0.09$ fm and $aapprox 0.06$ fm.
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