2+1 Flavor Lattice QCD toward the Physical Point

TL;DR

The study advances 2+1 flavor lattice QCD toward the physical point using $O(a)$-improved Wilson quarks and Iwasaki gauge action, enabling $m_{ud}$ at its physical value via the DDHMC family of algorithms. Chiral analyses show SU(3) ChPT struggles with convergence at the physical strange mass, motivating SU(2) ChPT with analytic strange quark treatment, which yields consistent low energy constants and a stable description of $m_\pi$ and $f_\pi$, $f_K$. The resulting hadron spectrum and decay constants at the physical point agree with experimental values within a few percent, and the static potential measurements provide a cross-check of scale setting; nonperturbative renormalization is planned to reduce residual systematic errors. Overall, the work demonstrates feasibility and accuracy of near-physical point simulations, informing future studies with finer lattices and improved renormalization.

Abstract

We present the first results of the PACS-CS project which aims to simulate 2+1 flavor lattice QCD on the physical point with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at the lattice spacing of $a=0.0907(13)$fm on a $32^3\times 64$ lattice with the use of the DDHMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose ud quark mass is as light as the physical value. The resulting PS meson masses range from 702MeV down to 156MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the PS meson sector with SU(3) ChPT reveals that the NLO corrections are large at the physical strange quark mass. In order to estimate the physical ud quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) LECs ${\bar l}_3$ and ${\bar l}_4$ are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing $m_π$, $m_K$ and $m_Ω$ as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of $f_π=134.0(4.2)$MeV, $f_K=159.4(3.1)$MeV and $f_K/f_π=1.189(20)$ with the perturbative renormalization factors are compatible with the experimental values. For the physical quark masses we obtain $m_{\rm ud}^\msbar=2.527(47)$MeV and $m_{\rm s}^\msbar=72.72(78)$MeV extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors.

Figures (26)

• Figure 1: Simulation cost at $(\kappa_{\rm ud}, \kappa_{\rm s})=(0.13770,0.13640)$ by DDHMC (blue open circle) and $(\kappa_{\rm ud}, \kappa_{\rm s})=(0.13781,0.13640)$ by MPDDHMC (blue closed circle) for 10000 trajectories. Solid line indicates the cost estimate of $N_f=2+1$ QCD simulations with the HMC algorithm at $a=0.1$ fm with $L=3$ fm for 100 independent configurations. Vertical line denotes the physical point.
• Figure 2: Plaquette history (left) and normalized autocorrelation function (right) for $(\kappa_{\rm ud}, \kappa_{\rm s})=(0.13727, 0.13640)$. Horizontal lines in the left denote the average value of the plaquette with one standard deviation error band.
• Figure 3: Effective masses for the mesons (left) and the baryons (right) at $(\kappa_{\rm ud},\kappa_{\rm s})=(0.13754,0.13640)$. Horizontal lines represent the fitting results with one standard deviation error band.
• Figure 4: Same as Fig. \ref{['fig:m_eff_kud54']} for $(\kappa_{\rm ud},\kappa_{\rm s})=(0.13754,0.13660)$.
• Figure 5: Same as Fig. \ref{['fig:m_eff_kud54']} for $(\kappa_{\rm ud},\kappa_{\rm s})=(0.13770,0.13660)$.