Domain wall QCD with physical quark masses (1411.7017v2)

Abstract: We present results for several light hadronic quantities ($f_\pi$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit' with a number of other ensembles with heavier pion masses. We use the physical values of $m_\pi$, $m_K$ and $m_\Omega$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_\pi$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11).

• The paper demonstrates that domain wall fermions with nearly physical quark masses can accurately reproduce key QCD observables such as fπ = 130.2(9) MeV and fK = 155.5(8) MeV.
• The paper employs simulations on two ensembles (48I and 64I) using an improved o formulation to maintain chiral symmetry while optimizing computational resources.
• The paper shows that advanced methods like all-mode-averaging and EigCG significantly reduce finite-volume effects and enhance the precision of lattice QCD predictions.

Insights on "Domain Wall QCD with Physical Quark Masses"

"Domain Wall QCD with Physical Quark Masses" exemplifies a significant step forward in lattice gauge theory simulations, utilizing domain wall fermion (DWF) methodology to probe QCD with nearly physical quark masses. The use of domain wall fermions is crucial as it retains the symmetry properties of quarks in the continuum limit, while controlling chiral symmetry breaking—a nontrivial issue in lattice QCD computations.

The paper presents results from simulations on two ensembles, denoted as 48I and 64I, with different lattice spacings and configurations that accurately correspond to the details of strong interactions as described by QCD. The physical quark masses used in these simulations are particularly noteworthy as they closely approximate the up, down, and strange quark masses, with the lightest pion mass used being just a few percent above its physical value.

Methodological Advances

The introduction of the o formulation of domain wall fermions, as opposed to the more traditional Shamir formulation, is a key methodological advance documented in this manuscript. By varying parameters such as the scaling factor $b+c$ and the length of the fifth dimension $L_s$, the authors have managed to maintain a tight control over the chiral symmetry breaking whilst using fewer resources than the traditional DWF approach would require. Significantly, these parameters provide a thorough improvement over previous simulations by effectively approximating the overlap action of the continuum limit, which is crucial in obtaining reliable predictions from lattice QCD.

Results and Interpretations

The paper reports several important quantities: the pion decay constant $f_\pi$, the kaon decay constant $f_K$, the neutral kaon mixing parameter $B_K$, and the average up, down, and strange quark masses. Notably, the values $f_\pi = 130.2(9)$ MeV and $f_K = 155.5(8)$ MeV fall in line with experimental results, signaling a significant triumph in bridging lattice calculations with experimental observations.

Additionally, $B_K$ in $\overline{\rm MS}$ scheme, documented at $0.5293(17)(106)$, agrees closely with established values, thereby validating the methodologies used in simulating such strong interactions.

Implications and Future Directions

The research elucidates how finite-volume effects and scale-setting ambiguities can be controlled and significantly diminished, as demonstrated by the high degree of consistency and precision across different extrapolation techniques and fitting methods. The introduction and successful execution of all-mode-averaging (AMA) and EigCG in the simulation show the advances in computational efficiency, allowing large-volume, high-resolution simulations that were previously prohibitive in computational cost.

In the future, applying these improved DWF methodologies to simulate QCD with a dynamically evolving charm quark may push the frontier further, granting insights into even more complex multi-scale interactions in QCD and potentially hinting at physics beyond the Standard Model. Additionally, the exploration of isospin-breaking effects and electromagnetic corrections using this lattice configuration could yield further refinement in theoretical predictions, influencing both phenomenology and the extraction of fundamental constants.

This paper not only consolidates the domain wall method's position as a powerful tool in lattice QCD but also lays the groundwork for progressively detailed explorations of strong interactions, with precision and scalability that enable relevant inferences about fundamental quark dynamics in the universe.