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

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.

💡 Research Summary

The paper investigates the physics reach of the Electron‑Ion Collider (EIC) during its “early science” phase—approximately the first five years of operation—focusing on inclusive electron‑proton deep‑inelastic scattering (DIS). Using realistic assumptions for the early‑stage machine (10 GeV electrons colliding with 130 GeV or 250 GeV protons, plus an optional 5 GeV × 130 GeV configuration), the authors generate pseudo‑data corresponding to an integrated luminosity of 1 fb⁻¹ per energy setting. The central values are derived from NNLO QCD predictions based on the HERAPDF2.0 set, and systematic uncertainties are modeled conservatively: a point‑to‑point uncorrelated component of 1.9 % (including 1 % radiative corrections and 1.6 % detector effects) and a 3.4 % normalisation uncertainty that is uncorrelated between energy configurations. Statistical errors are negligible except at the extreme edges of phase space.

The core of the analysis is the Rosenbluth separation of the reduced cross‑section σ_r into the transverse structure function F₂ and the longitudinal structure function F_L. With two centre‑of‑mass energies (√s = 72 GeV and 100 GeV) the authors employ a simplified linear‑fit method (using the two σ_r points at different y²/Y⁺ values) to extract F₂ (intercept) and F_L (slope). When a third energy (√s = 51 GeV) is added, a full χ² minimisation over all available y points is performed, dramatically improving the lever arm in y²/Y⁺ and thus the precision of F_L. To quantify uncertainties, 1000 Monte‑Carlo replicas of the pseudo‑data are generated; the mean and variance of the extracted structure functions are taken as the result.

Key findings include:

1. Structure Functions – Adding the third energy reduces the absolute uncertainty on F_L by roughly 10‑20 % across most of the kinematic region, never exceeding a 30 % improvement. F₂ is already well constrained, but the combined EIC+HERA dataset extends the measurable x range of F_L by up to two orders of magnitude, especially at low x where HERA alone had limited lever arm.
2. PDF Impact – Incorporating early‑science EIC data into global PDF fits (via the xFitter framework) yields noticeable reductions in PDF uncertainties at large Bjorken‑x (x > 0.3) for both valence quarks and the gluon. This is significant because high‑x PDFs are crucial for predictions at the LHC and future hadron colliders.
3. Strong Coupling αₛ – By exploiting the Q²‑dependence of F₂ and F_L, the authors perform an NNLO fit for αₛ(M_Z²). The three‑energy scenario achieves an experimental precision surpassing that of the HERA‑only determination by about 30 %, demonstrating that even modest early‑science luminosities can provide a competitive αₛ measurement.
4. Combination with HERA – When the pseudo‑data are combined with the final HERA inclusive cross‑section measurements, the overall precision improves further. The additional EIC points fill gaps in HERA’s coverage, especially at intermediate y where the Rosenbluth lever arm is maximal.

The study also discusses systematic treatment, noting that the assumed uncertainties are deliberately conservative; actual detector performance and luminosity monitoring are expected to be better, which would further tighten the results. Moreover, the analysis shows that statistical uncertainties are negligible for the bulk of the phase space, implying that the dominant limitation will be systematic control.

In conclusion, the paper demonstrates that even during the limited early‑science period, the EIC can deliver high‑precision measurements of F₂, F_L, PDFs, and αₛ. The inclusion of a third centre‑of‑mass energy is especially beneficial for the longitudinal structure function and the strong coupling extraction. These results underscore the EIC’s potential to become a leading facility for perturbative QCD studies and to provide essential inputs for high‑energy phenomenology well before its full‑capability era.