⚛️ nuclear theory

Exclusive Quark and Gluon Dijet Production as Probes of GPDs at Collider Energies

This paper investigates exclusive electroproduction of quark and gluon dijets as probes of generalized parton distributions by extending theoretical frameworks to include helicity contributions and form factor channels, comparing predictions with HERA data, and providing projections for future Electron-Ion Collider measurements.

Original authors: Zhuoyi Pang, Paweł Sznajder, Lech Szymanowski, Jakub Wagner

Published 2026-07-15

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CC BY 4.0

Original authors: Zhuoyi Pang, Paweł Sznajder, Lech Szymanowski, Jakub Wagner

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

The Cosmic Lego Set: Unlocking the 3D Map of Matter

Imagine the universe is built from a massive, invisible Lego set. For decades, scientists have known the basic bricks: protons and neutrons, which make up the nuclei of every atom in your body. But knowing a brick exists is different from understanding how it's put together. Inside these protons, a chaotic dance of tiny particles called quarks and gluons is constantly happening. They zip around, stick together, and spin, creating the mass and spin of the matter we see.

To understand this dance, physicists use a special map called "Generalized Parton Distributions" (GPDs). Think of a GPD not as a flat, 2D photograph, but as a high-tech, 3D hologram. While old maps could only tell you where a particle was, these holograms tell you where it is, how fast it's moving, and how it's spinning, all at the same time. This is crucial because it helps us answer big questions: Why does a proton have mass if the quarks inside are so light? How is the spin of a proton created? To read this hologram, scientists smash electrons into protons at incredible speeds. When the electron hits the proton, it knocks out a pair of particles that fly off together like a pair of skaters spinning away from each other. By studying how these pairs fly, scientists can reverse-engineer the 3D map of the proton's interior.

The Paper's Story: A New Lens on the Proton's Dance

In this paper, a team of researchers from the National Centre for Nuclear Research in Poland takes a fresh look at how we can read these 3D maps. They focus on a specific type of collision where an electron hits a proton and knocks out a "dijet"—a pair of particles flying out together. They looked at two types of pairs: one made of quarks (the main bricks) and one made of gluons (the glue holding the bricks together).

The authors did something clever: they didn't just look at the main collision path. They also calculated the effects of a "side channel," a less obvious way the particles can interact that involves pure electromagnetism (like the force that makes magnets stick). They call this the "QED channel." In their simulations, they found that while this side channel is usually a whisper compared to the main roar of the collision, it gets surprisingly loud when the particles fly off at certain angles. It's like realizing that in a crowded concert, the background music you thought was just noise actually carries a secret message if you listen closely enough.

They also discovered that the "glue" particles (gluons) play a much bigger role in these collisions at future facilities than they did at older ones. At the famous HERA collider in the past, the quark pairs were the stars of the show. But when they simulated what will happen at the future Electron-Ion Collider (EIC), they found that the gluon pairs become much more prominent, almost as common as the up-quark pairs. This is a big deal because it means the EIC will be a perfect place to study the "glue" that holds our universe together.

The researchers also checked if the "spin" of the particles (helicity) mattered. They found that while it does contribute, it's a much smaller effect than the main, non-spinning contributions. They didn't find any magic new particles, but they did provide a much more detailed recipe for how to calculate these collisions. They showed that if we want to get the most accurate map of the proton, we can't ignore the side channels or the gluon pairs.

One interesting twist they found is that the "side channel" (the QED part) becomes very important when the particles fly off with high energy but low sideways momentum. It's like a specific trick in a magic show that only works when the magician is standing in a very specific spot. If we ignore this trick, our calculations of the proton's map will be slightly off.

The paper concludes that while we have a good handle on the basics, we need to be very careful with our math to get the full picture. They suggest that at future colliders, we will be able to separate the quark pairs from the gluon pairs much better than before. This separation is like having a pair of glasses that lets you see the glue and the bricks as distinct colors instead of a blurry mix. The authors are confident in their calculations for the leading level of physics, but they admit that to get the perfect picture, we will eventually need to add even more complex corrections (like accounting for how the particles turn into actual hadrons after the crash). For now, they have provided a solid, updated foundation for the next generation of experiments to build upon.

Technical Summary: Exclusive Quark and Gluon Dijet Production as Probes of GPDs at Collider Energies

Problem and Motivation
Generalized Parton Distributions (GPDs) encode the three-dimensional structure of hadrons and provide access to fundamental quantities such as spin, mass, and internal force distributions. While hard exclusive processes within the collinear factorization framework are the primary experimental avenue for accessing GPDs, the exclusive electroproduction of dijets remains a process requiring further theoretical development. Previous studies, such as those by Braun and Ivanov and subsequent numerical analyses, have focused primarily on quark dijet production considering unpolarized GPDs. However, a comprehensive leading-order (LO) treatment that includes helicity GPDs, the exclusive gluon dijet channel, and previously neglected electromagnetic (QED) contributions is necessary to fully exploit the potential of future facilities like the Electron-Ion Collider (EIC) and the Electron-ion collider in China (EicC).

Methodology
The authors derive leading-order expressions for the scattering amplitudes and differential cross sections for two processes:

Exclusive quark dijet production: $e(l) N(p) \to e(l') N(p') q(q_1)\bar{q}(q_2)$
Exclusive gluon dijet production: $e(l) N(p) \to e(l') N(p') g(q_1) g(q_2)$

The calculations are performed within the collinear factorization framework. The non-perturbative physics is parametrized using leading-twist GPDs (unpolarized $H, E$ and helicity $\tilde{H}, \tilde{E}$ ) and elastic nucleon form factors (EFFs). The authors utilize the Sudakov basis for four-momentum decomposition and define kinematic variables including the skewness parameter $\xi$ , the virtuality $Q^2$ , and the dijet invariant mass $M^2$ .

Key theoretical components include:

Amplitude Derivation: The authors calculate LO amplitudes for both quark and gluon dijet production. For quark dijets, they include contributions from quark and gluon GPDs (the "QCD channel") and a new analysis of the QED channel, where a photon is exchanged in the $t$ -channel (analogous to the Bethe-Heitler channel in Double Deeply Virtual Compton Scattering).
Helicity GPDs: The study extends previous work by explicitly including contributions from helicity GPDs ( $\tilde{H}, \tilde{E}$ ) for both quark and gluon channels.
Gluon Dijet Production: The paper derives the LO amplitude for exclusive gluon dijet production, noting that due to charge conjugation symmetry, this process is sensitive only to C-odd (valence) quark GPDs at any order in perturbation theory.
Compton Form Factors (CFFs): The amplitudes are expressed in terms of CFFs, which are convolutions of hard scattering kernels with GPDs. The authors address the mathematical consistency of these convolutions, particularly regarding the behavior of gluon GPD derivatives at $x = \pm \xi$ .
Numerical Implementation: Phenomenological predictions are generated using the Goloskokov–Kroll GPD model and the PARTONS framework. The renormalization and factorization scales are set to $\mu_R^2 = \mu_F^2 = m_q^2 + q_\perp^2 + z\bar{z}Q^2$ .

Key Contributions

Extension of Quark Dijet Formalism: The authors provide a complete LO derivation for quark dijet production that incorporates helicity GPDs and assesses the impact of the QED channel, which was previously neglected in this specific context.
First LO Analysis of Gluon Dijets: The paper presents the first derivation of LO expressions for exclusive gluon dijet production within the collinear factorization framework, establishing the sensitivity of this channel to valence quark GPDs.
QED Channel Assessment: The study quantifies the contribution of the QED channel (elastic form factors) to the cross section, finding it to be subdominant in most regions but becoming sizable in specific kinematic regimes (large $\beta'$ ).
Phenomenological Projections: The authors provide detailed numerical predictions for differential cross sections ( $d\sigma/d\beta'$ , $d\sigma/dz$ , $d\sigma/d\phi$ , etc.) for both HERA and EIC kinematics, comparing theoretical results with existing HERA data.

Results

Comparison with HERA Data: The theoretical predictions for quark dijet production at HERA energies are consistent with ZEUS collaboration data for $\beta' \gtrsim 0.5$ . The model fails to describe data at $\beta' \lesssim 0.5$ , a discrepancy attributed to the enhanced phase space for real gluon radiation at lower $\beta'$ (higher invariant mass), which is not captured by the LO collinear factorization.
Gluon vs. Quark Dijets at EIC: In HERA kinematics, gluon dijet production is significantly smaller than quark dijet production. However, at EIC energies (specifically $5 \text{ GeV} \times 41 \text{ GeV}$ ), the contribution from gluon dijet production becomes comparable to that of up-quark dijet production. This enhancement is attributed to the larger skewness $\xi$ accessible at lower $y$ values in EIC, which enhances contributions from the valence region of GPDs.
QED Contributions: The QED contribution to the cross section is generally small but becomes significant (reaching ~20% of the QCD contribution) at large $\beta'$ (e.g., $\beta' \sim 0.9$ ) and large $q_\perp^2$ .
Valence Sensitivity: Unlike HERA kinematics where sea quarks and gluons dominate (leading to symmetric $d\sigma/dz$ distributions), EIC kinematics show a significant deviation from symmetry in the $z$ -distribution. This indicates a dominant role for valence quark GPDs at EIC energies.
Helicity GPDs: Across all observables studied, contributions from helicity GPDs are found to be subdominant compared to those from unpolarized GPDs.
Angular Distributions: The study confirms that gluon dijets, similar to quark dijets in certain exchange configurations, exhibit a preference for production perpendicular to the leptonic plane ( $\phi = \pi/2, 3\pi/2$ ).

Significance and Claims
The authors position this work as an important first step toward a detailed Next-to-Leading Order (NLO) analysis of quark- and gluon-dijet production. They claim that the systematic study of LO contributions from different channels (QCD vs. QED, quark vs. gluon, unpolarized vs. helicity) is essential for interpreting future data.

The paper modestly claims that while NLO corrections are likely important, the current LO framework provides the necessary baseline. It highlights that the exclusive electroproduction of dijets is a viable probe for GPDs, particularly at the EIC where valence quark contributions are enhanced. The authors note that distinguishing between quark- and gluon-initiated jets is crucial for these measurements and relies on ongoing developments in jet-tagging techniques. They also acknowledge that a realistic description requires connecting partonic pairs to hadronic final states (hadronization), which is left for future work. Finally, they suggest that extending the study to proton-to-neutron transition GPDs could offer a unique method to isolate quark contributions by eliminating gluon backgrounds.

The Cosmic Lego Set: Unlocking the 3D Map of Matter

The Paper's Story: A New Lens on the Proton's Dance

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