Four-loop QCD analysis of the Bjorken sum rule vs data

TL;DR

This paper compares four-loop perturbative and analytic QCD approaches to the Bjorken sum rule at low energies, showing APT's effectiveness in describing data and extracting higher twist corrections.

Contribution

It provides a detailed four-loop QCD analysis of the Bjorken sum rule, highlighting the advantages of analytic perturbation theory at low energies.

Findings

APT describes low-energy data down to 300 MeV

Four-loop PT and APT give similar accuracy above 700 MeV

APT enables reliable extraction of higher twist corrections

Abstract

We study the polarized Bjorken sum rule at low momentum transfers in the range $0.22<Q<1.73 {\rm GeV}$ with the four-loop N$^3$LO expression for the coefficient function $C_{\rm Bj}(\alpha_s)$ in the framework of the common QCD perturbation theory (PT) and the singularity-free analytic perturbation theory (APT). The analysis of the PT series for $C_{\rm Bj}(\alpha_s)$ gives a hint to its asymptotic nature manifesting itself in the region $Q<1$ GeV. It relates to the observation that the accuracy of both the three- and four-loop PT predictions happens to be at the same 10% level. On the other hand, the usage of the two-loop APT allows one to describe the precise low energy JLab data down to $Q\sim 300$ MeV and gives a possibility for reliable extraction of the higher twist (HT) corrections. At the same time, above $Q\sim 700$ MeV the APT two-loop order with HT is equivalent to the four-loop PT with HT compatible to zero and is adequate to current accuracy of the data.