Non-perturbative determination of the Λ-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling

Abstract

We evaluate the Λ-parameter in the $$ \overline{\mathrm{MS}} $$ scheme for the pure SU(3) gauge theory with the twisted gradient flow (TGF) method. A running coupling constant g TGF 2 (1/L) is defined in a finite volume box with size of L4 with the twisted boundary condition. This defines the TGF scheme. Using the step scaling method for the TGF coupling with lattice simulations, we can evaluate the Λ-parameter non-perturbatively in the TGF scheme. In this paper we determine the dimensionless ratios, $$ {\varLambda}_{\mathrm{TGF}}/\sqrt{\sigma } $$ and r0ΛTGF together with the Λ-parameter ratio ΛSF/ΛTGF on the lattices numerically. Combined with the known ratio $$ {\varLambda}_{\overline{\mathrm{MS}}}/{\varLambda}_{\mathrm{SF}} $$ , we obtain $$ {\varLambda}_{\overline{\mathrm{MS}}}/\sqrt{\sigma } = 0.5315(81)\left({}_{-48}^{+269}\right) $$ and $$ \mathrm{r}0{\varLambda}_{\overline{\mathrm{MS}}}=0.6062(92)\left({}_{-52}^{+309}\right) $$ , where the first error is statistical one and the second is our estimate of systematic uncertainty.