Lambda^{QCD}_{MS} from Renormalization Group Optimized Perturbation

TL;DR

This paper introduces a variationally optimized perturbation method combined with renormalization group properties to approximate nonperturbative QCD quantities, successfully estimating the QCD scale parameter Lambda from experimental data.

Contribution

It extends a variationally optimized perturbation approach with renormalization group techniques to evaluate nonperturbative QCD parameters, providing estimates consistent with lattice results.

Findings

Estimated Lambda(nf=2) ~ 255 MeV with uncertainties

Method aligns well with recent lattice simulations

Discusses potential for extrapolation to perturbative regimes

Abstract

A recent extension of a variationally optimized perturbation, combined with renormalization group properties in a straightforward way, can provide approximations to nonperturbative quantities such as the chiral symmetry breaking order parameters typically. We apply this to evaluate, up to third order in this modified perturbation, the ratio Fpi/Lambda, where Fpi is the pion decay constant and Lambda the basic QCD scale in the modified MS scheme. Using experimental Fpi input value we obtain Lambda(nf=2) ~ 255_{-15}^{+40} MeV, where quoted errors are estimates of theoretical uncertainties of the method. This compares reasonably well with some recent lattice simulation results. We briefly discuss prospects (and obstacles) for extrapolation to alpha_S(mu) at perturbative mu values.