Abstract
We present the first study of the charmonium spectrum using overlap fermions, on quenched configurations. Simulations are performed on 16 3 × 72 lattices, with Wilson gauge action at β = 6.3345 . We demonstrate that we have discretization errors, as indicated by the dispersion relation, at about 5%. We obtain 88(4) MeV for the 1 S hyperfine splitting using the r 0 scale, and 121(6) MeV using the ( 1 P ¯ − 1 S ¯ ) scale. This Letter should encourage the pursuit of using the same chiral fermions for both heavy and light quarks on the same lattice.
Highlights
Over the last few years, numerical simulations of chiral fermions have matured
The stage of testing has passed for simulating valence chiral fermions, and physically relevant results have been reported in lattice simulations
We have presented the first study of the charmonium spectrum using overlap fermions
Summary
Over the last few years, numerical simulations of chiral fermions have matured. The stage of testing has passed for simulating valence chiral fermions, and physically relevant results have been reported in lattice simulations. Using the unequal mass Gell-Mann–Oakes–Renner relation as the renormalization condition, the renormalization factor in the heavy-light current can be determined non-perturbatively to a high precision for overlap fermions [1]. We demonstrate the value of overlap fermions to simulate heavy quarks, by studying hyperfine splitting in the charmonium system. It is harder to study the dispersion relation on the configurations we use for this Letter, because on the small volume lattice box we use, one unit of momentum corresponds to about 1.6 GeV This is a huge momentum, and as a result, the data is noisier. This figure indicates that we have discretization errors at about the 5–7% level near the charm mass, which is near ma ≈ 0.35
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