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 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 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, ΛTGF/σ and r₀Λ_TGF together with the Λ-parameter ratio Λ_SF/Λ_TGF on the lattices numerically. Combined with the known ratio ΛMS¯/ΛSF, we obtain ΛMS¯/σ=0.531581−48+269 and r0ΛMS¯=0.606292−52+309, where the first error is statistical one and the second is our estimate of systematic uncertainty.