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The properties of charmonium states are or will be intensively studied by theB-factories Belle II and BESIII, the LHCb and PANDA experiments and at a futureSuper-c-tau Factory. Precise lattice calculations provide valuable input andseveral results have been obtained by simulating up, down and strange quarks inthe sea. We investigate the impact of a charm quark in the sea on thecharmonium spectrum, the renormalization group invariant charm-quark mass andthe scalar charm-quark content of charmonium. The latter is obtained by thedirect computation of the mass-derivatives of the charmonium masses. We do thisinvestigation in a model, QCD with two degenerate charm quarks. The absence oflight quarks allows us to reach very small lattice spacings down to 0.023 fm.By comparing to pure gauge theory we find that charm quarks in the sea affectthe hyperfine splitting at a level below 2%. The most significant effects are5% in the quark mass and 3% in the value of the charm quark content of theeta_c meson. Given that we simulate two charm quarks these estimates are upperbounds for the contribution of a single charm quark. We show that latticespacings <0.06 fm are needed for safe continuum extrapolations of thecharmonium spectrum with O(a) improved Wilson quarks. A useful relation for theprojection to the desired parity of operators in two-point functions computedwith twisted mass fermions is proven.

How much do charm sea quarks affect the charmonium spectrum?