Redesigning Lattice QCD

TL;DR

The work argues that lattice QCD can be accurately simulated on coarse lattices by combining perturbative corrections for high-momentum modes with nonperturbative Monte Carlo methods for infrared physics. Central to this approach is tadpole improvement, which rescales link variables to remove large ultraviolet renormalizations, and the construction of improved actions (gluon and quark) that cancel leading discretization errors. The result is a coherent framework (including SW, D234, and NRQCD formulations, anisotropic lattices, and t-staggered schemes) that achieves percent-level accuracy at lattice spacings around 0.3–0.4 fm, dramatically reducing computational costs while preserving continuum-like physics. This methodology enables rapid, first-principles QCD studies of hadron spectra, decays, and structure, with strong cross-checks against perturbation theory and experimental data, signaling a potential paradigm shift in lattice QCD research.

Abstract

There has been major progress in recent years in the development of improved discretizations of the QCD action, current operators, etc for use in numerical simulations that employ very coarse lattices. These lectures review the field theoretic techniques used to design these discretizations, techniques for testing and tuning the new formalisms that result, and recent simulation results employing these formalisms.

Figures (13)

• Figure 1: One-loop amplitudes contributing to: a) $qq\!\to\! qq$, and b) the quark self energy.
• Figure 2: The $\chi_{22}$ Creutz ratio of Wilson loops versus loop size. Results from Monte Carlo simulations (exact), and from tadpole-improved (new) and traditional (old) lattice perturbation theory are shown.
• Figure 3: The critical bare quark mass for Wilson's lattice quark action versus lattice spacing. Monte Carlo data points are compared with perturbation theories in a theory with no tadpole improvement (T.I), tadpole-improved gluon dynamics, and tadpole-improved quark and gluon dynamics.
• Figure 4: Static-quark potential computed on $6^4$ lattices with $a\approx 0.4$ fm using the Wilson action and the improved action. The dotted line is the standard infrared parameterization for the continuum potential, $V(r)=Kr-\pi/12r + c$, adjusted to fit the on-axis values of the potential.
• Figure 5: The static-quark potential computed on an anisotropic lattice in different orientations. Results are shown for $a_t/a_s$ equal $1/2$. Except as shown, analysis errors are smaller than the plot symbols. The fit in each plot is to the open circles; the fitting function is $V(r)=Kr-b/r+c$.