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 $a^{-1}\sim 3\mathrm{GeV}$. We calculate masses of heavy-light (charmed) and heavy-heavy (charmonium) mesons with spin-parity $J^P=0^{\mp }$ and $1^{\mp }$, leptonic decay constants of the charmed pseudoscalar mesons ($D$ and $D_s$), and the $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing parameter. The charm quark mass is found to be $m_c^{\overline{\mathrm{MS}}}(m_c)=1.24(1{)}_{\mathrm{stat}}(18{)}_{\mathrm{syst}}\mathrm{GeV}$. The mass splittings in charmed-meson parity partners ${\Delta }_{q,J=0}$ and ${\Delta }_{q,J=1}$ are degenerate within statistical errors, in accordance with experiment, and they satisfy a relation ${\Delta }_{q=ud,J}>{\Delta }_{q=s,J}$, also consistent with experiment. Using our lattice calculation of the splitting between $h_c$ and ${\chi }_{c1}$ and the experimental ${\chi }_{c1}$ mass, we obtain a parity-odd axial-vector charmonium state $m_{h_c}=3533(11{)}_{\mathrm{stat}}(336{)}_{\mathrm{syst}}\mathrm{MeV}$, with a systematic error dominated by heavy quark discretization at order $(a{m}_c{)}^2$. 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 $f_D=232(7{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+6}{-0}{)}_{\mathrm{chiral}}(17{)}_{\mathrm{syst}}\mathrm{MeV}$ and $f_{D_s}/f_D=1.05(2{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+0}{-2}{)}_{\mathrm{chiral}}(2{)}_{\mathrm{syst}}$, 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 $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing bag parameter, which enters the $\Delta C=2$ transition amplitude, is found to be $B_D(2\mathrm{GeV})=0.845(24{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+24}{-6}{)}_{\mathrm{chiral}}(105{)}_{\mathrm{syst}}$. All the above systematic errors include our estimates of quenching errors.

• Received 21 August 2006

DOI:https://doi.org/10.1103/PhysRevD.74.114506