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arXiv · 1607.06423

Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\rm f}=3$ QCD

Mattia Dalla Brida·Patrick Fritzsch·Tomasz Korzec·Alberto Ramos·Stefan Sint·Rainer Sommer
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Abstract

Using a finite volume Gradient Flow (GF) renormalization scheme with Schr\"odinger Functional (SF) boundary conditions, we compute the non-perturbative running coupling in the range $2.2 \lesssim {\bar g}_\mathrm{GF}^2(L) \lesssim 13$. Careful continuum extrapolations turn out to be crucial to reach our high accuracy. The running of the coupling is always between one-loop and two-loop and very close to one-loop in the region of $200\,{\rm MeV} \lesssim \mu=1/L \lesssim 4\,{\rm GeV}$. While there is no convincing contact to two-loop running, we match non-perturbatively to the SF coupling with background field. In this case we know the $\mu$ dependence up to $\sim 100\,{\rm GeV}$ and can thus connect to the $\Lambda$-parameter.

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Mattia Dalla Brida, Patrick Fritzsch, Tomasz Korzec, Alberto Ramos, Stefan Sint, Rainer Sommer. 2016-07-21. Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\rm f}=3$ QCD. https://doi.org/10.1103/physrevd.95.014507

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