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

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.