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In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD),

The strength of strong interactions, parametrized by the scale-dependent coupling

In this Letter, we describe a novel method of estimating the running of the coupling or the

The strategy proposed in this Letter uses a combination of numerical lattice QCD calculations and high-order perturbative results. We concentrate on correlation functions of flavor nonsinglet bilinear quark operators of the form

We start with the bare lattice data for correlation functions

Subset of

At fixed lattice spacing and lattice distance, we extrapolate the correlators to the chiral limit. We use a fitting ansatz linear in the dimensionless combination

A significant step to reliably perform the continuum limit extrapolation is to reduce the size of discretization effects present in the data. To this aim, we perturbatively compute

Impact of the tree-level (red squares) and one-loop (blue circles) improvement of the massless axial current-current correlation function at

In order to perform the continuum extrapolations, we need to follow the lines of constant physics. In our case, the only relevant scale is the correlator distance

If discretization effects are under control, the continuum limits corresponding to the same physical distance should agree for each of the three lattice directions. We checked that this is the case and hence, we performed combined continuum fits of data for all three directions. Depending on the distance (and, thus, the available lattice spacings), we use from 6 to 12 data points and constrain the fit by a common value in the continuum,

The difference between the axial and vector correlation functions was estimated in various frameworks, for a review see Ref.

Continuum extrapolation of the axial (left) and vector (right) correlators at

Having the continuum-extrapolated

Running of

Results for

We consider several sources of uncertainty in our analysis and we decompose the error of our final result for the

To make our final result independent from the choice of the window of physical distances where

The final result for the

In this Letter, we presented and tested a novel method to estimate the

To conclude, we believe that the techniques described in this Letter provide a robust way of extracting the running of the QCD coupling and the QCD

We gratefully acknowledge discussions with V. Braun, F. Knechtli, and T. Korzec. This research was carried out with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM) University of Warsaw under Grants No. GA67-12, No. GA69-20, No. GA71-26, No. GA76-14, and AGH Cyfronet Computing Center under Grant ID pionda, nspt, hadronspectrum. This work was supported by Deutsche Forschungsgemeinschaft under Grant No. SFB/TRR 55 and in part by the Polish Narodowe Centrum Nauki (NCN) Grants No. UMO-2016/21/B/ST2/01492 (P. K. and S. C.) and No. 2016/22/E/ST2/00013 (K. C.). P. K. acknowledges support from the Narodowa Agencja Wymiany Akademickiej (NAWA) Bekker fellowship and thanks Università degli Studi di Roma “Tor Vergata” for hospitality during which this work was initiated. We thank our colleagues in the Coordinated Lattice Simulations (CLS) effort for the joint generation of the gauge field ensembles on which the computation described here is based. The gauge ensembles were generated with the help of the Gauss Centre for Supercomputing e.V. using computer time allocations on SuperMUC at Leibniz Supercomputing Centre (LRZ) and JUQUEEN at Jülich Supercomputing Center (JSC). GCS is the alliance of the three national supercomputing centers HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich) and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF). Additionally computer time provided by PRACE (Partnership for Advanced Computing in Europe) as part of the project ContQCD was used. Additional ensembles were generated on QPACE2 supercomputer at University of Regensburg and on the Wilson computer cluster at University of Mainz. For the NSPT computer resources of QPACE3 at the Juelich Supercomputing Center were used.