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

Using a finite volume gradient flow renormalization scheme with Schrödinger Functional boundary conditions, we compute the nonperturbative running coupling in the range 2.2≲g¯GF2(L)≲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 MeV≲μ=1/L≲4 GeV. While there is no convincing contact to two-loop running, we match nonperturbatively to the Schrödinger functional coupling with background field. In this case, we know the μ-dependence up to ∼100 GeV and can thus connect to the Λ-parameter.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