Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Past, present, and future of precision determinations of the QCD
  coupling from lattice QCD   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 $N_{\rm f}$-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 $N_{\rm f}=3$-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.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph