Lattice QCD with two dynamical flavors of domain wall quarks

TL;DR

Two-flavor lattice QCD with domain wall fermions is demonstrated in a large-scale dynamical study on a $16^3\times32$ lattice at $a^{-1}\approx 1.7$ GeV, preserving chiral symmetry with $L_s=12$ and employing the DBW2 gauge action. The work reports hadron spectra and decay constants in good agreement with experiment, a robust static potential analysis establishing the lattice scale, and a BK determination $B_K^{\overline{MS}}(2\mathrm{GeV})\approx 0.50$, including effects from non-degenerate valence quarks and sea quarks. Chiral behavior is analyzed with PQChPT, revealing suppressed quenched chiral logs and small residual chiral symmetry breaking $a m_{res}\sim 10^{-3}$; significant auto-correlations and topology persistence are discussed. The results validate dynamical domain wall fermions as a viable path toward controlled continuum-like QCD calculations, while highlighting systematic uncertainties and the need for lighter masses and continuum extrapolations in future work.

Abstract

We present results from the first large-scale study of two flavor QCD using domain wall fermions (DWF), a chirally symmetric fermion formulation which has proven to be very effective in the quenched approximation. We work on lattices of size 16^3x32, with a lattice cut-off of a^{-1}\approx 1.7 GeV, and dynamical (or sea) quark masses in the range m_{strange}/2 \simle m_{sea} \simle m_{strange}. After discussing the algorithmic and implementation issues involved in simulating dynamical DWF, we report on the low-lying hadron spectrum, decay constants, static quark potential, and the important kaon weak matrix element describing indirect CP violation in the Standard Model, B_K. In the latter case we include the effect of non-degenerate quark masses (m_s \neq m_u = m_d), finding B_K(MS-bar, 2 GeV) = 0.495(18).

Figures (38)

• Figure 1: Conjugate gradient iteration count for the chronological inverter using the previous 7 vectors compared with a linear extrapolation of the previous two vectors for the $m_{\rm sea}=0.02$ ensemble.
• Figure 2: $d(U_\mu^{(n)},U^{(I)}_\mu)$ and $d_{max}(U_\mu^{(n)},U^{(I)}_\mu)$ in a trajectory of $m_{sea}=0.02$ on $16^3 \times 32$. The total step numbers are 10, 20, 50, 100, 200, and 500. The solid curves are $d(U_\mu^{(n)},U^{(I)}_\mu)$ while the dashed are $d_{max}(U_\mu^{(n)},U^{(I)}_\mu)$.
• Figure 3: The breaking of reversible dynamics measured by $d(U^{'(I)}_\mu,U^{(I)}_\mu)$ and $d_{max}(U^{'(I)}_\mu,U^{(I)}_\mu)$ as a function of the CG convergence criteria, $R_{conv}$. The dotted lines are observed upper bound of deviations due to the reunitarization process. The error-bar at $R_{conv}$ = 1e-8 was obtained using five configurations.
• Figure 4: The residues of CG, Eq. \ref{['eq:resCG']}, as a function of the number of CG iteration are plotted for various numbers of previous solutions, $N_p$, on a typical configuration of the $m_{\rm sea}=0.02$ ensemble.
• Figure 5: The individual contributions to the total change in the Hamiltonian from the various components of the Hamiltonian for the large step-size, old force term simulation described in Table \ref{['imp:nforce_small']}. The shaded bars represent the trajectories which failed the accept/reject step, while the empty bars tally all trajectories.