The singlet contribution to the Bjorken sum rule for polarized deep inelastic scattering

TL;DR

This paper discusses the importance of including singlet diagrams in the four-loop calculation of the Bjorken sum rule for polarized deep inelastic scattering, highlighting their impact on QCD predictions.

Contribution

It identifies the need to incorporate singlet diagram contributions into the four-loop perturbative QCD calculations of the Bjorken sum rule.

Findings

Singlet diagrams contribute significantly at four-loop order.

A coincidence between non-singlet and singlet diagram contributions is explained.

The results refine the theoretical predictions for polarized deep inelastic scattering.

Abstract

It is shown that the existing four-loop result for the Bjorken polarized sum rule for deep inelastic electron-nucleon scattering obtained within perturbative Quantum Chromodynamics should be supplemented by the calculation of the diagrams of the so called singlet type. We also give an explanation of the interesting coincidence of two different classes of diagrams, one of the non-singlet and one of the singlet type, contributing the $\alpha_s^4$-approximation to the total cross-section of electron-positron annihilation into hadrons.