Numerical determination of the $\Lambda$-parameter in SU(3) gauge theory from the twisted gradient flow coupling

TL;DR

This paper non-perturbatively estimates the $b3$-parameter in SU(3) gauge theory using the twisted gradient flow method, confirming its consistency with known values.

Contribution

It introduces a non-perturbative approach to determine the $b3$-parameter in SU(3) gauge theory via the twisted gradient flow method, validating its effectiveness.

Findings

Estimated $b3$-parameter values are consistent with previous results.

Demonstrated the validity of the twisted gradient flow method for this calculation.

Provided precise numerical estimates for $b3$-parameter in the $bc$ scheme.

Abstract

We estimate the $\Lambda$-parameter in the $\overline{\mathrm{MS}}$ scheme for the SU(3) pure gauge theory with the twisted gradient flow method non-perturbatively. We obtain $\Lambda_{\overline{\mathrm{MS}}}/\sqrt{\sigma}=0.527(13)(10)$ and $r_{0}\Lambda_{\overline{\mathrm{MS}}}=0.605(15)(5)$ which are consistent with the known values.This demonstrates the validity of the present method.