Charmonium Spectrum from Quenched QCD with Overlap Fermions

Overlap fermions have the following desirable features: • Exact chiral symmetry on the lattice. • No additive quark mass renormalization. • No flavor symmetry breaking. • No O(a) error. • The O(ma) and O(ΛQCDma) errors are also small, from dispersion relation and renormalization constants. The first two features are especially significant for light quarks. Many exciting results at low quark masses have been reported using overlap fermions. Here we want to make the point that using overlap fermions can also alleviate some problems with simulating heavy quarks. The last feature, demonstrated in [1], is an unexpected bonus in this regard. The key observation is that the discretization errors are only about 5% all the way upto ma ≈ 0.5. We make our case using hyperfine splitting in the charmonium system. It is known that with staggered quarks, there is an ambiguity about Nambu-Goldstone (NG) and non-NG mode for the ηc, resulting in widely different estimates of hyperfine splitting – 51(6) MeV (non-NG) and 404(4) MeV (NG) [2]. NRQCD converges only slowly for charm [3]. Including O(v) terms changed the result from 96(2) MeV to 55(5) MeV. Wilson fermions have O(a) errors. Hyperfine splitting is very sensitive to the coefficient of the correction term, cSW . There are many studies [4] using Wilson type valence quarks, including some with non-perturbative cSW . The quenched clover estimate of hyperfine splitting has stabilized around 80 MeV. Result from a 2+1 dynamical simulation using tree-level cSW still falls short of the experimental value by about 20% [5]. Although costly, overlap fermions offer the best solution — they do not have flavor symmetry breaking, they guarantee that the O(a) error is absent without any tuning and they are relativistic. Furthermore, O(a) errors appear to be small [1].