Gross-Llewellyn Smith sum rule from lattice QCD

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 $0.5\lesssim Q^2\lesssim 10{\mathrm{GeV}}^2$, 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 $\hat{I}{\pm }_s(Q^2)$ from a hadronic quantity complementing the phenomenological and other lattice approaches, and electroweak box contributions crucial for Cabibbo-Kobayashi-Maskawa matrix unitarity studies.

16 pages, 12 figures