Joint ECFA-NuPECC-APPEC Workshop “Synergies between the EIC and the LHC”

We present a determination of the gluon density $xg$ from simulated measurements of the longitudinal structure function of the proton at the Electron-Ion Collider (EIC). Using the Rosenbluth separation method, we show that the EIC can achieve high precision in the extraction of $F_L$, even with modest luminosities. We further show the complementarity between the EIC, HERA, and fixed-target results.