We compute the Gross-Llewellyn Smith sum rule, i.e. the lowest odd moment of the parity-violating structure function, F3, of the nucleon from a lattice QCD calculation of the Compton amplitude. Our calculations are performed on 483×96 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≲Q2≲10GeV2, 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 αs(Q2) from a hadronic quantity complementing the phenomenological and other lattice approaches, and electroweak box contributions crucial for Cabibbo-Kobayashi-Maskawa matrix unitarity studies.
@article{arxiv.2502.19704,
title = {Gross-Llewellyn Smith sum rule from lattice QCD},
author = {K. Utku Can and Joshua A. Crawford and Roger Horsley and Paul E. L. Rakow and Thomas G. Schar and Gerrit Schierholz and Hinnerk Stüben and Ross D. Young and James M. Zanotti},
journal= {arXiv preprint arXiv:2502.19704},
year = {2025}
}