Precise determination of the strong coupling constant in Nf=2+1 lattice QCD with the Schr\"odinger functional scheme

TL;DR

This paper non-perturbatively evaluates the strong coupling constant in Nf=2+1 lattice QCD using the Schrödinger functional scheme, covering a wide energy range and carefully addressing systematic errors.

Contribution

It provides a precise determination of the running coupling in Nf=2+1 QCD with a detailed non-perturbative approach and systematic error analysis across multiple energy scales.

Findings

Successful non-perturbative running coupling calculation from low to high energy.

Quantification of systematic errors near the charm quark mass threshold.

Continuum limit extrapolation at multiple scales.

Abstract

We present an evaluation of the running coupling constant for Nf=2+1 QCD. The Schroedinger functional scheme is used as the intermediate scheme to carry out non-perturbative running from the low energy region, where physical scale is introduced, to deep in the high energy perturbative region, where conversion to the MS-bar scheme is safely performed. Possible systematic errors due to the use of perturbation theory occur only in the conversion from three-flavor to four-flavor running coupling constant near the charm mass threshold, where higher order terms beyond 5th order in the $\beta$ function may not be negligible. For numerical simulations we adopted Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy region and three lattice spacings to take the continuum limit at each scale. A physical scale is introduced from the previous Nf=2+1 simulation of the CP-PACS/JL-QCD collaboration, which covered the up-down quark mass range heavier than $m_\pi\sim 500$ MeV.