Gross-Llewellyn Smith sum rule from lattice QCD

TL;DR

This paper presents a lattice QCD calculation of the Gross-Llewellyn Smith sum rule, providing insights into nucleon structure, higher-twist effects, and the strong coupling constant across different energy regimes.

Contribution

It introduces a lattice QCD approach to compute the sum rule's moments across a range of Q^2 values, bridging nonperturbative and perturbative regimes.

Findings

Agreement with the sum rule within uncertainties

Insights into higher-twist contributions

Potential to determine α_s(Q^2) from lattice data

Abstract

We compute the Gross-Llewellyn Smith sum rule, i.e. the lowest odd moment of the parity-violating structure function, $F_3$, of the nucleon from a lattice QCD calculation of the Compton amplitude. Our calculations are performed on $48^3 \times 96$ lattices at the $SU(3)$ symmetric point for two lattice spacings. We extract the moments for several values of the current momenta in the range $0.5 \lesssim Q^2 \lesssim 10 \; {\rm GeV}^2$, covering both the nonperturbative and perturbative regimes. We compare our moments to the Gross-Llewellyn Smith sum rule and discuss the implications for higher-twist effects, a determination of $\alpha_s(Q^2)$ from a hadronic quantity complementing the phenomenological and other lattice approaches, and electroweak box contributions crucial for Cabibbo-Kobayashi-Maskawa matrix unitarity studies.