Inclusive electron-proton measurement prospects in the Electron-Ion Collider early science stage

TL;DR

The paper evaluates the potential of the Electron-Ion Collider's early science phase to illuminate proton structure by extracting $F_2$, $F_L$, PDFs, and $\alpha_s(M_Z^2)$ using Rosenbluth separation on simulated pseudo-data. It compares two- and three-energy EIC configurations, both standalone and combined with HERA data, and quantifies gains in structure-function precision, PDF constraints (notably at high $x$), and $\alpha_s$ precision, highlighting substantial benefits from adding a third, lower-energy beam. The results show that $F_L$ can be measured with significantly improved precision when three energies are available, while $F_2$ gains are evident across approaches. The study demonstrates that early EIC data will provide competitive tests of perturbative QCD and markedly improve our understanding of proton structure within the first five years of operation.

Abstract

We explore the potential for extracting proton structure functions, proton parton density functions (PDFs), and the strong coupling $α_s(M_z^2)$, using early science data from the future Electron-Ion Collider (EIC), both standalone, and in combination with HERA data. Different scenarios are considered in which samples with modest luminosity are collected at either two or three EIC beam energy configurations. The Rosenbluth separation method is used to extract the proton structure functions $F_2$ and $F_L$ from simulated data in a model-independent manner, showing that $F_L$ can be extracted significantly more precisely with three centre of mass energies than with two, whilst also obtaining $F_2$ to higher precision than has been achieved previously. The inclusion of a third beam configuration is also beneficial in the extraction of the strong coupling $α_s(M_z^2)$ that is obtainable with unprecedented experimental precision with the early EIC data. Additionally, the precision of the proton PDFs is improved when adding these data, especially for large values of Bjorken-$x$, for both two and three EIC beam energy configurations. These studies show that EIC data will already be a highly competitive probe of perturbative Quantum Chromodynamics within the first five years of data taking.

Figures (13)

• Figure 1: Simulated extractions of $F_2$ and $F_{L}$ averaged over $1000$ replicas for the fits with the HERA and EIC data, for two EIC beam energy configurations. (The two EIC centre-of-mass energies are $100$ and $72$ GeV.) The error bars on the points represent the total experimental uncertainties. For the HERA+EIC $F_L$ measurements, points with absolute uncertainties larger than 0.5 are removed for visual clarity but all points for the $F_2$ measurements are shown.
• Figure 2: Simulated extractions of $F_2$ and $F_{L}$ averaged over $1000$ replicas for the fits with only two EIC beam energy configurations. (The two EIC centre-of-mass energies are $100$ and $72$ GeV.) The error bars on the points represent the total experimental uncertainties. For the EIC $F_L$ measurements, points with absolute uncertainties larger than 0.5 are removed for visual clarity but all points for the $F_2$ measurements are shown.
• Figure 3: Absolute uncertainties on the simulated EIC-only $F_L$ measurements averaged over 1000 replicas, corresponding to the three (left) and two (right) beam energy configurations, with the colours indicating the uncertainties. Note that different methods are applied in the two cases, with all three beam energies required to be available in the fits for the '3 EIC' extraction and just two required for the '2 EIC' case.
• Figure 4: Ratio of absolute uncertainties on the simulated EIC $F_L$ measurements for the three beam energy configuration over the two beam energy configuration, averaged over 1000 replicas. For the three beam energy configuration the EIC centre-of-mass energies are $100$, $72$ and $51$ GeV. For the two beam energy configuration the EIC centre-of-mass energies are $100$ and $72$ GeV. All three beam energies are required in the fits for the '3 EIC' extraction, whereas just two are required for the '2 EIC' case.
• Figure 5: Absolute uncertainties on the simulated HERA+EIC $F_L$ measurements averaged over 1000 replicas, corresponding to the three (left) and two (right) beam energy configurations, with the colours indicating the uncertainties. At least three data points are required for the Rosenbluth fits in both cases.