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

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.