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In calculations of the hyperfine splitting in charmonium, the contributionsof the disconnected diagrams is considered small and is typically ignored. Weaim to estimate nonperturbatively the size of the resulting error, which couldpotentially affect the high precision calculations of the charmonium spectrum.Following our work on the effects of the disconnected diagrams in unquenchedQCD presented at Lattice 2007, we study the same problem in the quenched case.On dynamical ensembles the disconnected charmonium propagators contain lightmodes which complicate the extraction of the signal at large distances. In thefully quenched case, where there are no such light modes, the interpretation ofthe signal is simplified. We present results from lattices with $a\approx 0.09$fm and $a\approx 0.063$ fm.

Contributions of charm anihilation to the hyperfine splitting in charmonium