Charm as a domain wall fermion in quenched lattice QCD

We report a study describing the charm quark by a domain-wall fermion (DWF) in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of a^-1~3 GeV. We calculate masses of heavy-light (charmed) and heavy-heavy (charmonium) mesons with spin-parity JP=0^∓ and 1^∓, leptonic decay constants of the charmed pseudoscalar mesons (D and Dₛ), and the D⁰-D̄⁰ mixing parameter. The charm quark mass is found to be mcMS̄(mc)=1.24(1)ₛₜₐₜ(18)syst GeV. The mass splittings in charmed-meson parity partners Δq,J=0 and Δq,J=1 are degenerate within statistical errors, in accordance with experiment, and they satisfy a relation Δq=ud,J>Δq=s,J, also consistent with experiment. Using our lattice calculation of the splitting between hc and χc1 and the experimental χc1 mass, we obtain a parity-odd axial-vector charmonium state m_hc=3533(11)ₛₜₐₜ(336)syst MeV, with a systematic error dominated by heavy quark discretization at order (amc)². However, in this regard, we emphasize significant discrepancies in the calculation of hyperfine splittings on the lattice. The leptonic decay constants of D and Dₛ mesons are found to be fD=232(7)ₛₜₐₜ(0+6-0)chiral(17)syst MeV and f_Dₛ/fD=1.05(2)ₛₜₐₜ(0+0-2)chiral(2)syst, where the first error is statistical, the second is systematic due to chiral extrapolation, and the third error is a combination of other known systematics. The D⁰-D̄⁰ mixing bag parameter, which enters the ΔC=2 transition amplitude, is found to be BD(2 GeV)=0.845(24)ₛₜₐₜ(0+24-6)chiral(105)syst. All the above systematic errors include our estimates of quenching errors.