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 $${N_{\mathrm{f}}}$$ N 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 $$\varLambda $$ Λ -parameter of $${N_{\mathrm{f}}}=3$$ N 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.

Erratum to: Topical issue on Lattice Field Theory during the Covid-19 pandemic

“…In the original editorial paper, there was a typo in the title in the table of contents for refs. [ 1 ] and [ 7 ]. The corrected table of contents can be found below.…”

“… Flavor-diagonal CP violation: the electric dipole moment (A. Shindler) [ 6 ]. Past, present, and future of precision determinations of the QCD coupling from lattice QCD (M. Dalla Brida) [ 7 ]. The large limit of QCD on the lattice (P. Hernández, F. Romero-López) [ 8 ].…”

“…Past, present, and future of precision determinations of the QCD coupling from lattice QCD (M. Dalla Brida) [ 7 ].…”

Mass effects on the QCD $\beta$-function

“…Nonperturbative estimations of the strong coupling 𝛼, in several renormalization schemes, through numerical simulations of the corresponding lattice theories, are being studied by a number of groups at present (see e.g., Refs. [2,3] and references therein).…”