Renormalization Group Summation of Laplace QCD Sum Rules for Scalar Gluon Currents

TL;DR

This paper uses renormalization group summation to improve QCD sum rules for scalar gluon currents, reducing scale dependence, providing bounds on scalar glueball mass, and showing better convergence than traditional perturbative methods.

Contribution

It introduces RG summation techniques to extend Laplace QCD sum rules for scalar gluon currents, reducing scale dependence and bounding glueball masses.

Findings

Reduced renormalization scale dependence with RG summation

RG summed results bound perturbative 3- and 4-loop results

Improved convergence of sum rule calculations

Abstract

We employ renormalization group (RG) summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter $\mu^2$ once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.