The Hyperfine Splitting in Charmonium: Lattice Computations using the Wilson and Clover Fermion Actions

We compute the hyperfine splitting mJ/ψ − mηc on the lattice, using both the Wilson and O(a)-improved (clover) actions for quenched quarks. The computations are performed on a 243×48 lattice at β = 6.2, using the same set of 18 gluon configurations for both fermion actions. We find that the splitting is 1.83 + 13 − 15 times larger with the clover action than with the Wilson action, demonstrating the sensitivity of the spinsplitting to the magnetic moment term which is present in the clover action. However, even with the clover action the result is less than half of the physical mass-splitting. We also compute the decay constants fηc and f −1 J/ψ, both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio f J/ψ/f −1 ρ we find 0.32 + 1 − 2 with the Wilson action and 0.48 ± 3 with the clover action (the physical value is 0.44(2)). The Hyperfine Splitting Lattice computations of the vector-pseudoscalar mass-splittings mD∗ − mD and mJ/ψ − mηc , using the standard Wilson action for the quarks in the quenched approximation, give results which are much too small [1, 2]. At β = 6.2, for which the inverse lattice spacing (a) is approximately 2.7 GeV, the discrepancy is about a factor of 2 for mD∗ − mD and a factor of about 4 for mJ/ψ −mηc . In this letter we compute the hyperfine splitting mJ/ψ −mηc using both the Wilson fermion action, S F = a 4 ∑