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

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.