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

We compute the hyperfine splitting $m_{J\mathrm{/}\psi }-m_{{\eta }_c}$ on the lattice, using both the Wilson and $O(a)$-improved (clover) actions for quenched quarks. The computations are performed on a ${24}^3\times 48$ lattice at $\beta =6.2$, using the same set of 18 gluon configurations for both fermion actions. We find that the splitting is 1.83\err{13}{15} 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 $f_{{\eta }_c}$ and $f_{J\mathrm{/}\psi }^{-1}$, both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio $f_{J\mathrm{/}\psi }^{-1}\mathrm{/}{f}_{\rho }^{-1}$ we find 0.32\err{1}{2} with the Wilson action and $0.48\pm 3$ with the clover action (the physical value is 0.44(2)).