2+1 Flavor Lattice QCD toward the Physical Point (0807.1661v1)

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 $m\pi$, $m_K$ and $m_\Omega$ 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 $f_\pi=134.0(4.2)$MeV, $f_K=159.4(3.1)$MeV and $f_K/f_\pi=1.189(20)$ 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.

• The paper demonstrates that employing a nonperturbatively improved Wilson action and DDHMC algorithm reduces up-down quark masses to near physical values.
• The use of SU(2) and SU(3) Chiral Perturbation Theory quantifies significant NLO corrections and estimates key low-energy constants.
• The study achieves hadron spectrum and decay constant results within a few percent of experimental values, validating the lattice QCD approach.

2+1 Flavor Lattice QCD toward the Physical Point

The paper investigates 2+1 flavor lattice QCD simulations carried out by the PACS-CS collaboration, aiming to approach the physical point using the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. The ultimate goal of such simulations is to enable precise calculations of hadronic observables and to facilitate a deeper understanding of nonperturbative QCD dynamics.

Simulation Setup and Methodology

The authors conduct their simulations on a $32^3 \times 64$ lattice at $\beta=1.9$, leading to a lattice spacing of approximately 0.0907 fm. One of the critical aspects of the paper is the use of the domain-decomposed Hybrid Monte Carlo (DDHMC) algorithm to reduce the up-down quark masses significantly down to the physical point, complemented by mass preconditioning techniques. The pseudoscalar meson masses achieved throughout range from 702 MeV down to 156 MeV, exhibiting chiral logarithms indicative of the correct low-mass behavior anticipated by chiral perturbation theory (ChPT).

Chiral Perturbation Theory Analysis

The paper employs SU(3) and SU(2) Chiral Perturbation Theory (ChPT) to analyze the pseudoscalar meson sector. The analysis reveals significant next-to-leading order (NLO) corrections at the physical strange quark mass, illustrating the critical role these corrections play. This insight is essential, as it confirms the necessity of including higher-order corrections in understanding the QCD spectrum at low energies. The continuum ChPT forms applied to the pseudoscalar masses lead to estimates of SU(2) low-energy constants $\bar{l}_3$ and $\bar{l}_4$, which are difficult to tackle accurately without such analytical benchmarks.

Numerical Results and Physical Implications

The obtained hadron spectrum, extrapolated to the physical point, exhibits alignment with experimental values within a few percent statistical error margin. This agreement is notable, considering potential remaining cutoff effects. The decay constants $f_\pi$ and $f_K$, alongside the ratio $f_K/f_\pi$, are found to be compatible with experimental measures when perturbative renormalization is applied.

For physical quark masses, the axial-vector Ward-Takahashi identity reinforced by perturbatively derived renormalization factors provides $m_{\rm ud} = 2.527(47)$ MeV and $m_{\rm s} = 72.72(78)$ MeV. These are promising estimates that contribute to a more precise determination of fundamental parameters within the Standard Model.

Future Perspectives

While the current paper achieves remarkable convergence toward the physical point, ongoing efforts are essential to mitigate residual systematic errors—particularly at finer lattice spacings. Simulations at and beyond the physical point, accompanied by advancements in nonperturbative renormalization techniques, stand to refine further the understanding and application of lattice QCD.

Overall, the paper showcases the feasibility and effectiveness of modern lattice QCD techniques in achieving physical point simulations, paving the way for high-precision exploration of QCD and its implications in particle physics and cosmology. Future work will undoubtedly build upon these findings to further elucidate the rich tapestry of strong interactions at the fundamental level.