The hyperfine splitting in charmonium. Lattice computations using the Wilson and clover fermion actions

Abstract We compute the hyperfine splitting m J ψ −m η c on the lattice, using both the Wilson and O (α)-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 1.83−15+13 times larger with the clover action than with the Wilson action, demonstrating the sensitivity of the spin-splitting 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 ƒηc and ƒ J ψ −1 both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio ƒ J ψ −1 ƒ ϱ −1 we find 0.32−2+1 with the Wilson action and 0.48±3 with the clover action (the physical value is 0.44 (2)).