"Massive" Perturbative QCD, regular in the IR limit

TL;DR

This paper proposes a modified perturbative QCD approach with an added mass parameter to ensure regularity in the IR region, aiming to improve data analysis below 1 GeV.

Contribution

It introduces 'massive analytic pQCD', combining a gluon mass regulator with ghost-free analytic perturbation theory for IR regularity.

Findings

The modified theory remains finite in the IR limit.

It effectively suppresses the blow-up of the series below 1 GeV.

Provides a practical framework for low-energy QCD data analysis.

Abstract

The goal of research is to devise a modification of the perturbative QCD that should be regular in the low-energy region and could serve as a practical means for the analysis of data below 1 \GeV up to the IR limit. Recent observation of the four-loop pQCD series "blow-up" in the region below 1 \GeV for the Bjorken Sum Rule gave an impetus to this attempt. The proposed {\sf "massive analytic pQCD"} is constructed on the two grounds. The first is the pQCD with only one parameter added, the effective "glueball mass" $m_{gl}\lesssim 1 \GeV,$ serving as an IR regulator. The second stems out of the ghost-free Analytic Perturbation Theory comprising non-power perturbative expansion that makes it compatible with linear integral transformations. In short, the proposed MAPT differs from the minimal APT by simple ansatz $Q^2 \to Q^2+m_{gl}^2.$