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Impact of QED Radiation on SMEFT Constraints in Deep Inelastic Scattering

This paper investigates how collision-induced QED radiation affects Standard Model Effective Field Theory (SMEFT) constraints in deep-inelastic scattering, revealing that while cross sections undergo significant order-one corrections, longitudinal electron spin asymmetries remain robust at the few-percent level, thereby offering a more reliable observable for future precision studies at facilities like SoLID and the Electron-Ion Collider.

Original authors: Sonny Mantry, Jian-Wei Qiu, Jia-Yue Zhang

Published 2026-07-10

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CC BY 4.0

Original authors: Sonny Mantry, Jian-Wei Qiu, Jia-Yue Zhang

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

Imagine you are a detective trying to solve a mystery about the fundamental building blocks of the universe. You are looking at a high-speed collision between an electron and a proton, a process called Deep Inelastic Scattering (DIS). Your goal is to find clues about "New Physics"—things that don't fit the current rulebook known as the Standard Model. To do this, you use a magnifying glass called the Standard Model Effective Field Theory (SMEFT), which helps you spot tiny deviations that might hint at hidden, heavier particles.

But there's a catch. When these particles zoom past each other, they don't just crash; they also throw off sparks. In the world of physics, these sparks are photons (light particles) radiated by the electrically charged electrons and quarks. This is called QED radiation.

For a long time, scientists treated these sparks like annoying static on a radio. They thought, "If we just subtract the static, we'll hear the music clearly." They tried to calculate how much static there was and subtract it from their measurements to find the "true" signal.

However, in this paper, the authors suggest that this "subtract the static" approach is a bit like trying to clean a muddy window by guessing how much mud is there. It's messy and prone to errors. Instead, they propose a new way of looking at the whole picture: the "Joint QCD+QED Factorization" framework. Think of this as realizing that the sparks are actually part of the show, not just noise. They are a feature of the collision that needs to be included in the script, just like the main actors.

The Big Surprise: The "Spin" Trick

The authors ran some simulations (computer experiments) to see what happens when you include these sparks properly. They looked at two different ways of measuring the collision:

The Total Score (Cross Section): This measures the total amount of "stuff" happening in the collision.
The Spin Asymmetry: This measures a specific difference in behavior when the electron spins one way versus the other (like a top spinning clockwise vs. counter-clockwise).

Here is the twist: The sparks (QED radiation) completely mess up the "Total Score." In some areas of the experiment, the sparks change the score by a huge amount—so much that the number could double or even disappear! It's like if a sudden gust of wind changed the score of a soccer game by 10 goals. If you try to use this messy score to find clues about New Physics, you might get the wrong answer entirely.

But, the "Spin Asymmetry" is a superhero. Even with all the sparks flying around, the spin measurement barely flinches. The authors found that the sparks only change the spin measurement by a tiny bit—just a few percent. It's as if the wind blew the soccer ball, but the referee's whistle (the spin measurement) remained perfectly clear.

What This Means for Future Experiments

The authors used this new understanding to make predictions for two upcoming super-lab facilities: SoLID at Jefferson Lab and the Electron-Ion Collider (EIC). They simulated millions of fake collision events to see how well these labs could find New Physics.

The Danger Zone: If these labs try to find New Physics using the "Total Score" (the cross section) and ignore the sparks, they will get very confused. Their maps of where New Physics might be hiding will be shifted and distorted. The authors showed that depending on how they model the sparks, the results could look completely different.
The Safe Zone: If they use the "Spin Asymmetry," the results are much more stable. Even with the sparks, the clues point to the same place.

The simulations suggest that the SoLID experiment is so precise that it could even tell the difference between different theories about how the sparks behave. The EIC, which will be even more powerful, might need to run for a long time (collecting about 100 inverse femtobarns of data) to see these differences clearly.

The Bottom Line

The paper doesn't claim to have found New Physics yet. Instead, it suggests that if we want to find it in the future, we have to stop ignoring the sparks. We need to treat the radiation as a key part of the collision, not just a nuisance to subtract. And the best news? If we focus on the "Spin Asymmetry" measurements, we are much less likely to get fooled by the chaos of the sparks, making our search for the universe's hidden secrets much more reliable.

Technical Summary: Impact of QED Radiation on SMEFT Constraints in Deep Inelastic Scattering

Problem Statement
Precision Deep Inelastic Scattering (DIS) measurements at facilities like the proposed SoLID experiment at Jefferson Laboratory and the Electron-Ion Collider (EIC) offer a powerful probe for physics beyond the Standard Model (BSM) via the Standard Model Effective Field Theory (SMEFT). While previous SMEFT analyses have incorporated higher-order perturbative QCD corrections, resummation, and extensive datasets, they have historically neglected the effects of collision-induced Quantum Electrodynamics (QED) radiation from charged leptons and quarks.

This omission presents a critical theoretical challenge. Initial and final state leptons can radiate energetic, collinear photons, leading to a mismatch between the reconstructed momentum transfer ( $Q^2 = -(\ell - \ell')^2$ ) and the true momentum transfer delivered to the proton ( $\hat{Q}^2$ ). In specific kinematic regions, this mismatch can reduce the true momentum transfer to the scale of $\Lambda_{QCD}^2$ , potentially invalidating the standard QCD factorization framework by introducing higher-twist effects and quasielastic tails. Furthermore, traditional approaches treating QED radiation as radiative correction (RC) factors added to the Born cross section face difficulties in experimentally accounting for all radiation and require arbitrary infrared cutoff parameters.

Methodology
To address these issues, the authors employ a rigorous, systematically improvable joint QCD+QED factorization framework. In this approach, QED radiation is not treated as a subtractive correction but as an intrinsic contribution to the DIS process, handled on equal footing with QCD radiation.

The methodology involves:

Factorization Formula: The cross section is expressed as a convolution of Lepton Distribution Functions (LDFs), Lepton Fragmentation Functions (LFFs), Parton Distribution Functions (PDFs), and a hard scattering function ( $\hat{H}$ ). The hard function includes Standard Model (SM) contributions (photon and Z-boson exchange) and their interference with dimension-six SMEFT operators.
Evolution: LDFs, LFFs, and PDFs satisfy DGLAP evolution equations that resum logarithmically enhanced collinear QED and QCD radiation. The evolution kernels are calculated at leading order in $\alpha_s$ and $\alpha_{em}$ .
Parameterization: The study utilizes three distinct parameterizations (LF1, LF2, LF3) for the LDFs and LFFs at the input scale ( $\mu_0 = 1.3$ GeV) to assess the sensitivity of results to the functional form of these distributions.
Observables: The analysis focuses on the unpolarized cross section ( $d\sigma_0$ ) and the parity-violating longitudinal single-spin electron asymmetry ( $A_e$ ). The impact of QED radiation is quantified by deviation factors $\delta\sigma$ and $\delta A$ .
SMEFT Analysis: The study performs $\chi^2$ fits to pseudo-data generated for SoLID ( $\sqrt{s} = 4.7$ GeV) and the EIC ( $\sqrt{s} = 105$ GeV). The analysis extracts constraints on Wilson coefficients (specifically the $C_{\ell d}$ and $C_{ed}$ pair) for dimension-six operators, comparing scenarios where QED radiation is included versus excluded.

Key Results

Magnitude of QED Effects: The impact of collision-induced QED radiation on the unpolarized DIS cross section is substantial, producing order-one corrections ( $\delta\sigma \sim \mathcal{O}(1)$ ), particularly at moderate to large Bjorken- $x_B$ and lower $Q^2$ values where the phase space for radiation is larger.
Robustness of Asymmetries: In contrast, the longitudinal electron spin asymmetry ( $A_e$ ) is affected only at the few-percent level ( $\delta A \sim \text{few } \%$ ). This indicates that asymmetry-based observables are significantly more robust against QED radiation effects than cross-section measurements.
Bias in SMEFT Fits: Neglecting QED radiation in theoretical predictions leads to large, significant shifts in the extracted best-fit values of SMEFT Wilson coefficients and alters the size of the 95% confidence level contours.
Experimental Sensitivity:
- SoLID: With an integrated luminosity of $10^6$ fb $^{-1}$ , the experiment has sufficient precision to distinguish between different LDF/LFF parameterizations (e.g., LF1 vs. LF2/LF3) using cross-section measurements.
- EIC: Distinguishing between parameterizations using cross sections requires approximately $100$ fb $^{-1}$ of integrated luminosity.
- Asymmetries: While asymmetries are stable against QED radiation, they are less sensitive to distinguishing between certain parameterizations (e.g., LF1 vs. LF2) compared to cross sections, though they can still distinguish LF3 from LF1/LF2 at high luminosity.

Significance and Claims
The paper claims to be the first to systematically address the impact of collision-induced QED radiation on SMEFT analyses of DIS. The authors assert that the joint QCD+QED factorization framework is an essential ingredient for future precision DIS analyses at SoLID and the EIC.

The primary significance lies in the demonstration that while cross-section measurements are highly susceptible to QED-induced biases in SMEFT constraints, longitudinal spin asymmetries offer a more robust observable. This finding suggests that global fits combining both cross sections and asymmetries can effectively disentangle the effects of QED radiation, PDF/LDF uncertainties, and genuine BSM physics. The work provides benchmark projections to guide the interpretation of future data, ensuring that SMEFT constraints derived from DIS are not compromised by unaccounted radiative effects.

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