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QED nuclear medium effects at EicC

This paper evaluates non-negligible QED nuclear medium effects on various scattering processes at the future Electron-ion collider in China (EicC), presenting first-order opacity expansion calculations and the first computations for charged-current deep inelastic and polarized scattering across heavy and light nuclei to highlight their importance for extracting nucleon structure.

Original authors: Oleksandr Tomalak

Published 2026-09-02

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Oleksandr Tomalak

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep inside the heart of every atom lies a dense, bustling city of protons and neutrons, bound together by forces so strong they defy everyday intuition. To understand how these particles are built and how they behave, scientists fire high-speed beams of electrons at heavy atomic targets. By watching how these electrons bounce off, researchers can map the invisible architecture of matter itself. However, the path of an electron through a heavy nucleus is not a straight, clean line. As it zips through the crowded interior, the electron constantly bumps into the electric charges of the protons around it. These tiny, frequent interactions, known as quantum electrodynamics effects, can subtly alter the electron's path and the energy it carries. If scientists ignore these small nudges, their maps of the atomic interior will be slightly distorted, leading to incorrect conclusions about the fundamental building blocks of the universe.

A researcher has now performed a detailed calculation to measure exactly how much these internal bumps matter for the upcoming Electron-ion Collider in China, a massive machine designed to probe the deepest secrets of nuclear structure. The scientist focused on four specific types of collisions: electrons bouncing off nuclei without changing the nucleus's identity, and collisions where the electron transforms into a different particle, a neutrino. They also looked at scenarios where the electron is spinning in a specific direction versus when it is not. Using advanced computer simulations that account for the complex environment inside heavy atoms like gold, lead, and uranium, they calculated how the presence of the nuclear medium changes the probability of these events occurring.

The results reveal that these internal interactions are far from negligible. In the simplest case, where an electron bounces off a nucleus and keeps its identity, the presence of the surrounding protons increases the likelihood of the collision happening by more than one percent at certain angles. This might sound small, but in the precise world of particle physics, where experiments aim for extreme accuracy, a shift of this size is significant enough to skew the final results if left uncorrected. The effect is most pronounced when the electron grazes the nucleus at a shallow angle, a common occurrence in these high-energy experiments.

The story becomes even more interesting when the electron changes its identity, transforming into a neutrino during the collision. In this scenario, the influence of the nuclear medium does not just add to the collision rate; it can actually subtract from it, depending on the angle of the bounce. The researcher found that for these charged interactions, the correction can swing negative at small angles, effectively reducing the number of events scientists expect to see. This reversal of sign is a crucial detail, showing that the environment inside the nucleus affects different types of collisions in fundamentally different ways.

The study also explored what happens when the electron undergoes not just one, but many tiny interactions as it travels through the nucleus. Instead of a single sharp bump, the electron experiences a series of gentle shoves that gradually blur its path, much like a beam of light scattering through fog. They calculated that this "smearing" of the electron's trajectory distorts the kinematics of the collision, making the final energy and angle of the outgoing particle appear different from what they truly were. This distortion reduces the measured cross-section, or the effective target size, by a few percent across a wide range of conditions.

Perhaps most importantly, this work provides the first-ever calculations for these effects in specific, high-energy scenarios involving charged currents and polarized beams, which were previously unexplored. The researcher found that while the effects are generally smaller for these complex interactions compared to the simplest elastic collisions, they are still large enough to matter. For the lightest nucleus they studied, calcium, the corrections are smaller, but for the heavy nuclei like gold and uranium, the effects reach the percent level. The researcher concludes that to extract the true, process-independent structure of protons and neutrons from future experiments, scientists must account for these QED nuclear medium effects. Without these corrections, the high-precision data expected from the new collider could lead to a flawed understanding of the fundamental forces that hold our universe together.

Technical Summary: QED Nuclear Medium Effects at EicC

Problem Statement
Precision in electron scattering experiments, essential for extracting non-perturbative nucleon and nuclear structure information and testing Standard Model interactions, requires the accurate unfolding of Quantum Electrodynamics (QED) radiative corrections. While QED interactions with a medium have been studied for decades (e.g., the Landau–Pomeranchuk–Migdal effect and Coulomb corrections), the increasing precision of upcoming electron-ion collider experiments, specifically the Electron-ion collider in China (EicC), necessitates a rigorous evaluation of QED nuclear medium effects. These effects arise from the electromagnetic interaction of high-energy charged leptons with the electric charges (primarily protons) inside the nucleus. Previous work by the author established these corrections for neutral-current elastic and deep inelastic scattering (DIS) at first order in the opacity expansion. This paper extends that framework to charged-current processes and polarized scattering, addressing a gap in the theoretical description of lepton-nucleus interactions at EicC energies.

Methodology
The paper employs Soft-Collinear Effective Field Theory (SCET) to evaluate QED nuclear medium effects on scattering cross sections. The analysis is divided into two primary theoretical regimes:

First Order in the Opacity Expansion: The author calculates cross-section corrections ( $\delta\sigma_e$ ) arising from single and double exchanges of Glauber photons between the electron and the nuclear medium. The correction is formulated as an integral over the transverse momentum of the Glauber photon and the nuclear charge density ( $\rho$ ). The calculation assumes the no-recoil approximation and treats the nuclear medium via a Woods-Saxon distribution for protons. The author evaluates these corrections for neutral-current (NC) and charged-current (CC) elastic scattering, as well as unpolarized and polarized NC and CC inclusive DIS.
Resummation of Multiple Rescattering: Recognizing that ultrarelativistic electrons undergo a large number of soft interactions ( $\chi \sim 10^5 - 10^7$ ) within a nucleus, the author resums multiple rescattering effects. This leads to a broadening of the electron's transverse momentum distribution. The "true" cross section ( $\sigma_{broad}$ ) is obtained by averaging the hard scattering cross section over the transverse momentum distributions of the initial and final state electrons, weighted by the spectrum derived from the mean number of interactions. This is compared to the "expected" cross section ( $\sigma_{exp}$ ) derived from observed lepton kinematics without medium broadening.

The study performs numerical evaluations for four nuclei: $^{40}_{20}\text{Ca}$ , $^{197}_{79}\text{Au}$ , $^{208}_{82}\text{Pb}$ , and $^{238}_{92}\text{U}$ , using parton distribution functions (PDFs) appropriate for bound nucleons. Calculations are performed for the anticipated center-of-mass energies of the EicC.

Key Contributions

First Calculations of CC and Polarized Effects: The paper presents the first theoretical evaluations of QED nuclear medium effects for charged-current (CC) inclusive DIS and polarized neutral-current inclusive DIS.
Comprehensive Process Coverage: The analysis covers a complete set of scattering processes: NC and CC elastic scattering, and unpolarized/polarized NC and CC inclusive DIS.
Nuclear Size Dependence: The study explicitly investigates the dependence of these corrections on nuclear size by comparing light ( $^{40}\text{Ca}$ ) and heavy ( $^{197}\text{Au}$ , $^{208}\text{Pb}$ , $^{238}\text{U}$ ) nuclei.
Kinematic Dependence: The author maps the corrections across various kinematic variables, including the squared momentum transfer ( $Q^2$ ), the Bjorken scaling variable ( $x$ ), and the recoil lepton energy.

Results

First Order Corrections:
- Elastic Scattering: For NC elastic scattering, corrections are positive-definite and largest at small scattering angles (low $Q^2$ ), reaching the percent level for heavy nuclei. In contrast, CC elastic scattering exhibits a sign change; corrections are negative at small $Q^2$ and become positive at larger $Q^2$ , with magnitudes reaching a few percent for heavy nuclei.
- DIS: In NC inclusive DIS, corrections increase with nuclear size and are most significant at large $x$ and large $Q^2$ , generally reaching the percent level only near kinematic boundaries. For CC inclusive DIS, the magnitude of corrections is smaller than in unpolarized NC DIS and comparable to polarized NC DIS at small $x$ . Unlike NC DIS, CC DIS corrections do not increase monotonically with $x$ .
- Polarization: The magnitude of corrections for spin-dependent observables is generally smaller than for unpolarized cross sections.
Multiple Rescattering Effects:
- Resummation of multiple soft interactions leads to a broadening of the electron trajectory, reducing the reconstructed cross section ( $\sigma_{broad} < \sigma_{exp}$ ) by a few percent across a wide kinematic range, not just in the forward direction.
- The reduction is most pronounced at small scattering angles (high recoil energy) but remains finite at backward angles for CC scattering.
- The effects exhibit a non-monotonic dependence on nuclear size in certain kinematic regimes.
Comparison of Mechanisms: The author notes that the magnitudes of the first-order opacity corrections and the multiple rescattering effects are similar. Consequently, they cannot be distinguished experimentally and should be added incoherently. This leads to a numerical suppression of the total correction at forward angles, where multiple rescattering becomes the dominant mechanism in non-forward kinematics.

Significance and Claims
The paper asserts that QED nuclear medium effects are "non-negligible" for the extraction of process-independent, non-perturbative structure functions of nucleons and nuclei at the EicC. The author emphasizes that failing to account for these corrections—particularly the sign-changing nature in CC elastic scattering and the broadening effects from multiple rescattering—could distort the interpretation of experimental data. The work provides the necessary theoretical inputs to ensure that the high-precision goals of the EicC regarding nucleon and nuclear structure are met, specifically highlighting that these effects must be included in event generators and data analysis frameworks for both neutral and charged current processes.

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