Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD

TL;DR

This paper uses lattice QCD to extract moments of proton structure functions $F_2$ and $F_L$, revealing significant power corrections and providing the first quantification of the $Q^2$ dependence of the lowest $F_2$ moment.

Contribution

It introduces a novel lattice QCD method to simultaneously determine moments of $F_2$ and $F_L$ across various $Q^2$ values, including power corrections.

Findings

Good agreement with experimental moments of $F_2$ and $F_L$

Power corrections are significant in the analysis

First quantification of $Q^2$ dependence of the lowest $F_2$ moment

Abstract

We present a simultaneous extraction of the moments of $F_2$ and $F_L$ structure functions of the proton for a range of photon virtuality, $Q^2$. This is achieved by computing the forward Compton amplitude on the lattice utilizing the second-order Feynman-Hellmann theorem. Our calculations are performed on configurations with two different lattice spacings and volumes, all at the $SU(3)$ symmetric point. We find the moments of $F_{2}$ and $F_{L}$ in good agreement with experiment. Power corrections turn out to be significant. This is the first time the $Q^2$ dependence of the lowest moment of $F_2$ has been quantified.