QCD Lambda Parameter from Gradient Flow

TL;DR

This paper analytically determines the QCD Lambda parameter in pure gauge theory using the gradient flow scheme, establishing a relationship with the reference scale and confirming it with numerical estimates.

Contribution

It introduces an analytical method to relate the QCD Lambda parameter to the gradient flow scale, emphasizing the role of the gluon condensate.

Findings

Good agreement with numerical estimates

Established a formal relationship between Lambda and w0

Highlighted the invariance of the gluon condensate

Abstract

Starting from the running coupling in the gradient flow scheme, the QCD Lambda parameter $\Lambda_{\,\overline{\!\rm MS\!}\;}$ is determined analytically with respect to the reference scale $w_0$ in the pure gauge theory. A key element is the gluon condensate, which, being invariant under RG transformations, establishes a formal relationship between $\Lambda_{\,\overline{\!\rm MS\!}\;}$ and $w_0$. Good agreement with numerical estimates is found.