Adler Function, DIS sum rules and Crewther Relations

TL;DR

This paper reviews the Adler function and related DIS sum rules, introduces a new high-order calculation for the Gross-Llewellyn Smith sum rule, and uses Crewther relations to determine color structures in the Adler function at four loops.

Contribution

It presents the first analytical calculation of the Gross-Llewellyn Smith sum rule coefficient function at order alpha_s^4 in a generic gauge theory and applies Crewther relations to fix color structures.

Findings

Analytical O(alpha_s^4) coefficient function for the sum rule.

Crewther relation constrains color structures in the Adler function.

Enhanced understanding of DIS sum rules and their theoretical connections.

Abstract

The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.