Speaker
Description
We investigate the feasibility of a model-independent extraction of the proton structure functions $F_{2}$, $F_{L}$, and $xF_{3}$ at the future Electron-Ion Collider (EIC). The extraction of $xF_{3}$ typically relies on combining electron and positron scattering data to isolate its parity-violating contribution; however, positron beams are not currently foreseen at the EIC. The methodology we present may therefore provide the only viable approach to determine all three structure functions in this environment. The method relies on measurements of the reduced cross section at multiple beam energy configurations, corresponding to different center-of-mass energies. We study the impact of datasets composed of various combinations of beam configurations that are expected to be achievable at the EIC. Using five nominal beam-energy configurations, we demonstrate that a simultaneous extraction of all three structure functions is possible, with the precision significantly improved by the inclusion of additional configurations. The contribution of $xF_{3}$ becomes significant at $Q^{2} \sim 100$ GeV$^{2}$ and high Bjorken-$x$. Assuming $xF_{3} = 0$ in this kinematic regime results in a possible measurable bias in the extracted $F_{L}$, reflecting the intertwined dependence of the reduced cross section on these structure functions. These findings emphasize the importance of multi-energy datasets and of including $xF_{3}$ in the extraction of the proton structure functions.