Kinematic scheme study of the $O(a^4)$ Bjorken sum rule and R ratio

TL;DR

This paper calculates the Bjorken sum rule and R ratio to fourth order in the coupling constant within specific schemes, analyzing convergence and scheme discrepancies to improve quantum field theory error estimation.

Contribution

It provides a detailed $O(a^4)$ calculation of key QCD observables in three momentum subtraction schemes, exploring convergence and scheme dependence.

Findings

Analysis of convergence properties in different schemes

Assessment of scheme discrepancies as error estimates

Insights into the reliability of perturbative expansions

Abstract

The Bjorken sum rule and R ratio are constructed to $O(a^4)$ in the Landau gauge in the three momentum subtraction schemes of Celmaster and Gonsalves where $a$ $=$ $g^2/(16\pi^2)$. We aim to examine the issue of convergence for observables in the various schemes as well as to test ideas on whether using the discrepancy in different scheme values is a viable and more quantum field theoretic alternative to current ways of estimating the theory error on a measureable.