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 J^P=0^∓ and 1^∓, leptonic decay constants of the charmed pseudoscalar mesons (D and D_s), and the D⁰-D̅ ⁰ mixing parameter. The charm quark mass is found to be m_c^MS̅ (m_c)=1.24(1)_stat(18)_syst  GeV. The mass splittings in charmed-meson parity partners Δ_q,J=0 and Δ_q,J=1 are degenerate within statistical errors, in accordance with experiment, and they satisfy a relation Δ_q=ud,J>Δ_q=s,J, also consistent with experiment. Using our lattice calculation of the splitting between h_c and χ_c1 and the experimental χ_c1 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 (am_c)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 D_s mesons are found to be f_D=232(7)_stat(+6/-0)_chiral(17)_syst  MeV and f_Ds/f_D=1.05(2)_stat(+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-D̅ ⁰ mixing bag parameter, which enters the ΔC=2 transition amplitude, is found to be B_D(2  GeV)=0.845(24)_stat(+24/-6)_chiral(105)_syst. All the above systematic errors include our estimates of quenching errors.