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

Abstract

Abstract We evaluate the Λ-parameter in the MS¯ $$ \overline{\mathrm{MS}} $$ scheme for the pure SU(3) gauge theory with the twisted gradient flow (TGF) method. A running coupling constant g TGF2(1/L) is defined in a finite volume box with size of L 4 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, ΛTGF/σ $$ {\varLambda}_{\mathrm{TGF}}/\sqrt{\sigma } $$ and r0ΛTGF together with the Λ-parameter ratio ΛSF/ΛTGF on the lattices numerically. Combined with the known ratio ΛMS¯/ΛSF $$ {\varLambda}_{\overline{\mathrm{MS}}}/{\varLambda}_{\mathrm{SF}} $$, we obtain ΛMS¯/σ=0.531581−48+269 $$ {\varLambda}_{\overline{\mathrm{MS}}}/\sqrt{\sigma } = 0.5315(81)\left({}_{-48}^{+269}\right) $$ and r0ΛMS¯=0.606292−52+309 $$ \mathrm{r}0{\varLambda}_{\overline{\mathrm{MS}}}=0.6062(92)\left({}_{-52}^{+309}\right) $$, where the first error is statistical one and the second is our estimate of systematic uncertainty.

Keywords

• Lattice Quantum Field Theory
• Renormalization Group