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

TL;DR

This study calculates the hyperfine splitting in charmonium using lattice QCD with Wilson and clover fermion actions, revealing the sensitivity of spin-splitting to the fermion action and comparing decay constants.

Contribution

It provides a comparative analysis of hyperfine splitting and decay constants in charmonium using Wilson and clover actions, highlighting the impact of the magnetic moment term.

Findings

Clover action increases hyperfine splitting by a factor of 1.83 compared to Wilson.

Both actions underestimate the physical hyperfine splitting.

Decay constants are larger with the clover action than with Wilson.

Abstract

We compute the hyperfine splitting $m_{J/\psi}-m_{\eta_c}$ on the lattice, using both the Wilson and $O(a)$-improved (clover) actions for quenched quarks. The computations are performed on a $24^3\times48$ 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 $f^{-1}_{J/\psi}$, both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio $f^{-1}_{J/\psi}/f^{-1}_{\rho}$ 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)).