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

We evaluate the Lambda-parameter in the (MS) over bar 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 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 Lambda-parameter non-perturbatively in the TGF scheme. In this paper we determine the dimensionless ratios, Lambda(TGF)/root sigma and r(0)Lambda(TGF) together with the Lambda-parameter ratio Lambda(SF)/Lambda(TGF) on the lattices numerically. Combined with the known ratio Lambda((MS) over bar)/Lambda(SF), we obtain Lambda((MS) over bar)/Lambda root sigma = 0.5315(81)((+269)(-48)) and ro Lambda((MS) over bar) = 0.6062(92)((+309)(-52)), where the first error is statistical one and the second is our estimate of systematic uncertainty.