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Non-perturbative determination of the \(\Lambda\)-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling. (English) Zbl 1383.83023

Summary: We evaluate the \(\Lambda\)-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 \(g_{\mathrm{TGF}}^{2}(1/L)\) 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, \( {\Lambda}_{\mathrm{TGF}}/\sqrt{\sigma}\) and \(r_{0} {\Lambda}_{\mathrm{TGF}}\) together with the \(\Lambda\)-parameter ratio \({\Lambda}_{\mathrm{SF}}/{\Lambda}_{\mathrm{TGF}}\) on the lattices numerically. Combined with the known ratio \( {\Lambda}_{\overline{\mathrm{MS}}}/{\Lambda}_{\mathrm{SF}}\), we obtain \( {\Lambda}_{\overline{\mathrm{MS}}}/\sqrt{\sigma}=0.5315(81)\left({}_{-48}^{+269}\right) \) and \( {r}_0 {\Lambda}_{\overline{\mathrm{MS}}} = 0.6062(92)\left({}_{-52}^{+309}\right) \), where the first error is statistical one and the second is our estimate of systematic uncertainty.

MSC:

83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory
81T25 Quantum field theory on lattices
81T17 Renormalization group methods applied to problems in quantum field theory
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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