Past, present, and future of precision determinations of the QCD coupling from lattice QCD

Abstract

Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task. In this contribution we focus on the case of the QCD coupling. We critically address the common challenges that state-of-the-art lattice determinations have to face in order to be significantly improved. In addition, we review a novel strategy that has been recently put forward in order to solve this non-perturbative renormalization problem and discuss its implications for future precision determinations. The new ideas exploit the decoupling of heavy quarks to match $N_{\mathrm{f}}$-flavor QCD and the pure Yang-Mills theory. Through this matching the computation of the non-perturbative running of the coupling in QCD can be shifted to the computationally much easier to solve pure-gauge theory. We shall present results for the determination of the $\Lambda$-parameter of $N_{\mathrm{f}}=3$-flavor QCD where this strategy has been applied and proven successful. The results demonstrate that these techniques have the potential to unlock unprecedented precision determinations of the QCD coupling from the lattice. The ideas are moreover quite general and can be considered to solve other non-perturbative renormalization problems.

Contribution to the EPJA special issue "Lattice Field Theory during the COVID-19 pandemic" in replacement of a plenary talk at the 38th International Symposium on Lattice Field Theory (Lattice 2020); LaTeX source, 36 pages. Matches published version in EPJA

References in corpus (27)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
• The five-loop beta function of Yang-Mills theory with fermions
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Critical slowing down and error analysis in lattice QCD simulations
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Towards the five-loop Beta function for a general gauge group
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• The chirally rotated Schrödinger functional with Wilson fermions and automatic O(a) improvement
• Step scaling and the Yang-Mills gradient flow
• On the effects of heavy sea quarks at low energies
• Logarithmic corrections to O(a^2) lattice artifacts
• The Yang-Mills gradient flow in finite volume
• The gradient flow running coupling with twisted boundary conditions
• Power corrections from decoupling of the charm quark
• A novel approach to the study of conformality in the SU(3) theory with multiple flavors
• Improved strong coupling determinations from hadronic decays of electroweak bosons at N${}^3$LO accuracy
• Lattice artefacts in the Schrödinger Functional coupling for strongly interacting theories
• Status and challenges of simulations with dynamical fermions
• Testing universality and automatic O(a) improvement in massless lattice QCD with Wilson quarks
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• ${\alpha }_s$(2019): Precision measurements of the QCD coupling
• Case studies of near-conformal $\beta$-functions