Lattice QCD: a critical status report

TL;DR

This status report surveys the rapid progress of lattice QCD, attributing the advancement to algorithmic breakthroughs, hardware growth, and improved actions with non-perturbative renormalization. It highlights near-physical simulations (e.g., $m_{PS}\approx 250$ MeV, $a\approx 0.05$ fm) and demonstrates how multiple observables, such as the baryon spectrum and low-energy constants, can be computed with controlled systematics. A central theme is universality: different lattice fermion formulations should yield the same continuum limits, though clear inconsistencies (notably in $f_{PS}$ scaling) indicate that thorough cross-formulation checks and better understanding of systematics are still required. The report also discusses practical challenges—mixed actions, non-perturbative renormalization for $N_f=2+1$, finite-volume and topology effects—and urges data sharing and detailed methodological reporting to solidify lattice QCD’s role in precision phenomenology.

Abstract

The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized.

Figures (13)

• Figure 1: The values of the lattice spacing $a$ and pseudo scalar masses $m_\mathrm{PS}$ as employed presently in typical QCD simulations by various collaborations as (incompletely) listed in the legend. The blue dot indicates the physical point where in the continuum the pseudo scalar assume assumes its experimentally measured value. The black cross represents a state of the art simulation by the JLQCD collaboration in 2001.
• Figure 2: The Baryon spectrum as obtained by the Budapest-Marseille-Wuppertal collaboration bmw2008.
• Figure 3: Confronting lattice QCD results for the pseudo scalar decay constant with chiral perturbation theory.
• Figure 4: The Berlin wall plots.
• Figure 5: Schwinger model results for the lightest pseudo scalar particle mass $\sqrt{\beta}M_\pi$ as a function of $a^2=1/\beta$. The continuum limit scaling is shown for Wilson, maximally twisted mass, hypercube and overlap fermions for a fixed value of the quark mass. The common continuum limit value for all these kind of lattice fermions demonstrates universality for this model.