Charm as a domain wall fermion in quenched lattice QCD

Abstract

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 $a^{-1}\sim 3$ 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 $D^0$-$\overline{D^0}$ mixing parameter. The charm quark mass is found to be $m_c^{\overline{\mathrm{MS}}}(m_c)=1.24(1)(18)$ GeV. The mass splittings in charmed-meson parity partners ${\Delta }_{q,J=0}$ and ${\Delta }_{q,J=1}$ are degenerate within statistical errors, in accord with experiment, and they satisfy a relation ${\Delta }_{q=ud,J}>{\Delta }_{q=s,J}$, also consistent with experiment. A C-odd axial vector charmonium state, $h_c),lies22(11)MeVabovethe$\chi_{c1}$meson,or$m_{h_{c}} = 3533(11)_{\rm stat.}$MeVusingtheexperimental$\chi_{c1}) mass. 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 $f_D=232(7{)}_{stat.}{(}_{-0}^{+6}{)}_{\mathrm{chiral}}(11{)}_{syst.}$ MeV and $f_{D_s}/f_D=1.05(2{)}_{stat.}{(}_{-2}^{+0}{)}_{\mathrm{chiral}}(2{)}_{syst.}$, where the first error is statistical, the second a systematic due to chiral extrapolation and the third error combination of other known systematics. The $D^0$-$\overline{D^0}$ mixing bag parameter, which enters the $\Delta C=2$ transition amplitude, is found to be $B_D(2GeV)=0.845(24{)}_{stat.}{(}_{-6}^{+24}{)}_{\mathrm{chiral}}(105{)}_{syst.}$.

Comments: 49 pages, 15 figures