Gross-Llewellyn Smith sum rule with analytic coupling

TL;DR

This paper examines the Gross-Llewellyn Smith sum rule using analytic QCD, showing that the analytic approach aligns well with experimental and lattice data, unlike conventional perturbation theory.

Contribution

It demonstrates the effectiveness of analytic QCD in accurately describing the sum rule, contrasting it with the failure of conventional perturbation theory.

Findings

Analytic QCD agrees with experimental data.

Conventional perturbation theory fails to match data.

Analytic approach aligns with lattice calculations.

Abstract

We investigate the Gross-Llewellyn Smith sum rule within the framework of analytic QCD. A comparison is performed between experimental data, lattice calculations, and perturbative QCD based on conventional and analytic versions of perturbation theory with different parametrizations for the twist-four contribution. We show that conventional perturbation theory fails to reproduce the data, while the analytic version demonstrates good agreement with experiment and lattice calculations. We also discuss the relation between the Gross-Llewellyn Smith sum rule and the Bjorken sum rule.