Prospects for measurements of the longitudinal proton structure function $F_L$ at the Electron Ion Collider

TL;DR

This paper assesses the Electron-Ion Collider's potential to precisely measure the proton's longitudinal structure function $F_L$, which is crucial for understanding gluon distributions, using Rosenbluth separation under various experimental conditions.

Contribution

It demonstrates that the EIC can achieve unprecedented precision in measuring $F_L$ across a broad kinematic range, even with modest luminosities, and highlights its potential to probe proton gluon density directly.

Findings

EIC can measure $F_L$ with high precision using Rosenbluth separation.

Measurement accuracy depends on sample size, systematics, and beam energies.

EIC data will complement existing fixed target and HERA data.

Abstract

We explore the potential for extracting the longitudinal proton structure function $F_{L}$ at the future Electron-Ion Collider (EIC) through a Rosenbluth separation method. The impacts of differing assumptions on sample sizes, systematic uncertainties and beam energy scenarios are investigated. With a sufficiently large number of centre of mass energy configurations and well-controlled systematics, the EIC will measure $F_{L}$ to an unprecedented precision, even with relatively modest luminosities. The accessible kinematic range complements both fixed target and HERA data. In the most optimistic scenarios, the EIC data will be a highly competitive direct probe of the proton gluon density.