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 varLambda -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.
Highlights
Renormalization is a fundamental step in order to extract phenomenologically relevant results from lattice QCD calculations
As one can see from the figure, as expected, the continuum limit extrapolations become more challenging as z becomes larger
In this respect we note that, as expected from the discussion in Sect. 3.2.2, the perturbative uncertainties in ρ estimated from the effect of the last known terms of P0P,T3 are completely negligible compared to the other sources of uncertainties
Summary
Renormalization is a fundamental step in order to extract (meaningful) phenomenologically relevant results from lattice QCD calculations. In order to make the determinations accessible to phenomenologists, it is often necessary to translate the results obtained in the chosen hadronic schemes to results in the (perturbative) schemes and at the scales commonly considered in phenomenology. This requires the determination of the non-perturbative renormalization group (RG) running of the renormalized QCD parameters and operators in some convenient intermediate scheme, from the hadronic scales where they were originally defined, up to some highenergy scale, where perturbation theory eventually applies and a matching to phenomenological schemes can be performed. It is important that the development in strategies to compute (bare) lattice quantities is accompa-
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