A Scheme Independent Definition of $\Lambda_{\rm QCD}$

TL;DR

This paper introduces a scheme-independent definition of 5_{ m QCD} using a connection on the space of the coupling constant, addressing scheme dependence issues in quantum chromodynamics.

Contribution

It proposes a novel, scheme-independent way to define 5_{ m QCD} by employing a connection on the coupling constant space, improving upon scheme-dependent definitions.

Findings

Defines 5_{ m QCD} independently of renormalization schemes

Shows how 5_{ m QCD} transforms under scheme changes

Provides a mathematical framework for scheme-independent 5_{ m QCD}

Abstract

Given a renormalization scheme of QCD, one can define a mass scale $\Lambda_{\rm QCD}$ in terms of the beta function. Under a change of the renormalization scheme, however, $\Lambda_{\rm QCD}$ changes by a multiplicative constant. We introduce a scheme independent $\Lambda_{\rm QCD}$ using a connection on the space of the coupling constant.