⚛️ nuclear theory

Probing the Collins effect at photon-photon colliders

This paper proposes studying the Collins effect in photon-photon collisions producing back-to-back hadrons at future colliders like the FCC and LHC, predicting sizable azimuthal asymmetries of up to 10–15% that could significantly advance the understanding of quark fragmentation and distinguish between existing Collins function models.

Original authors: Simone Anedda, Carlo Flore, Francesco Murgia, Cristian Pisano

Published 2026-10-27

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CC BY 4.0

Original authors: Simone Anedda, Carlo Flore, Francesco Murgia, Cristian Pisano

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

Inside the heart of every atom, a chaotic dance of invisible particles called quarks and gluons holds the universe together. These particles carry a property known as "color," a charge that binds them so tightly they can never be seen alone. When high-energy collisions smash these particles apart, they do not simply vanish; they must transform into the stable, colorless particles we can actually detect, such as protons and pions. This transformation process, called hadronization, is one of the most difficult puzzles in modern physics. Because the forces involved are too complex to calculate from first principles, scientists rely on mathematical maps called fragmentation functions to describe how a single quark turns into a spray of detectable matter. While scientists have mapped some of these processes, a specific aspect known as the Collins effect remains elusive. This effect describes how a spinning quark, when it breaks apart, tends to shoot its resulting particles in a specific sideways direction, creating a subtle tilt in the spray. Understanding this tilt is crucial because it reveals the hidden spin of the quark and the intricate mechanics of how matter is born from energy.

A team of researchers has now proposed a new way to catch this elusive effect in the act, using a different kind of cosmic collision than those typically studied. Instead of smashing electrons into protons or colliding heavy ions, they suggest looking at collisions between two photons, the particles of light. In this scenario, two beams of light, generated either by speeding electrons or by the electromagnetic fields of heavy lead nuclei, crash into each other. When these photons collide, they can briefly transform into a pair of quarks moving in opposite directions. As these quarks fly apart, they fragment into pairs of pions. The researchers calculated that if the original quarks were spinning, the resulting pions would not be distributed evenly around the path of the jets; instead, they would show a distinct wobble, a specific pattern in their angles that signals the presence of the Collins effect.

The team performed detailed calculations to see if this wobble would be strong enough to be seen by future experiments. They focused on two specific environments where such light-by-light collisions could be observed: the Future Circular Collider, a planned machine that would smash electrons and positrons together, and the Large Hadron Collider, where heavy lead nuclei pass each other at incredible speeds without actually touching. By simulating the collisions that would occur in these machines, the researchers found that the predicted wobble is surprisingly large. In certain conditions, the asymmetry in the distribution of the pions could reach levels between 10 and 15 percent. This is a significant signal, large enough to be measured with the precision instruments planned for these facilities.

The study also explored how different theoretical models for the fragmentation process would affect the results. The researchers tested their predictions against two leading sets of mathematical descriptions for how quarks turn into pions. They discovered that in specific regions of the collision data, these two models predicted noticeably different sizes for the wobble. This means that if the experiments are performed, the data could do more than just confirm the effect exists; it could help scientists decide which of the current theories best describes reality. The researchers noted that while the calculations are robust, they are based on simulations and theoretical estimates. The true test will come when the actual data arrives from the colliders.

What makes this proposal particularly valuable is the unique perspective it offers. Previous experiments have studied similar effects, but they often involve complex mixtures of different forces that make it hard to isolate the specific behavior of the quark spin. In these photon-photon collisions, the environment is much cleaner, dominated by the final stages of the interaction. This clarity could allow scientists to separate the contributions of different types of quarks, such as up quarks versus down quarks, with much greater precision than before. The researchers emphasize that their work is a proposal and a set of predictions, a roadmap for what to look for rather than a report of a discovery already made. However, the potential payoff is high: confirming these measurements would provide a new, independent way to map the fragmentation functions, refining our understanding of how the fundamental building blocks of matter assemble themselves into the visible world. If the upcoming experiments at the Large Hadron Collider and the Future Circular Collider can capture these patterns, they will open a fresh window into the mechanics of the strong force, turning a theoretical possibility into a concrete observation of how spin shapes the birth of matter.

Problem and Motivation
The hadronization of colored quarks and gluons into colorless hadrons remains a nonperturbative challenge in Quantum Chromodynamics (QCD), typically described by fragmentation functions (FFs). While Transverse Momentum Dependent (TMD) FFs offer detailed insights into the intrinsic transverse momentum of final hadrons, their extraction is currently limited. In Semi-Inclusive Deep Inelastic Scattering (SIDIS), FFs are convoluted with TMD Parton Distribution Functions (PDFs), complicating the analysis. Conversely, in semi-inclusive $e^+e^-$ annihilation (SIA), where only FFs are involved, experimental data remains relatively scarce. Furthermore, existing extractions of the Collins function (which describes the fragmentation of a transversely polarized quark into an unpolarized hadron) are limited. The authors propose investigating the Collins effect in photon-photon collisions ( $\gamma\gamma \to h_1 h_2 X$ ) as a complementary process. This channel offers a distinct advantage: due to the fourth power of the fractional electric charge in the cross-section, contributions from $d, s, b$ quarks are suppressed by a factor of $1/16$ relative to $u, c$ quarks (compared to $1/4$ in other processes), potentially allowing for more efficient flavor separation.

Methodology
The authors propose studying the production of almost back-to-back unpolarized hadrons (specifically charged pions) in quasi-real photon-photon collisions. The initial photons are generated via two mechanisms:

Emission from scattering leptons in $e^+e^-$ colliders (specifically the Future Circular Collider, FCC-ee).
Coherent emission from highly charged heavy nuclei in Ultra-Peripheral Collisions (UPCs) at the Large Hadron Collider (LHC).

Theoretical Framework:

Formalism: The calculation employs the helicity formalism assuming TMD factorization, valid when two distinct energy scales exist ( $q_T \ll Q$ ). The small scale is the transverse momentum of the hadrons relative to the jet thrust axis, while the hard scale is the transverse momentum of the thrust axis relative to the beam.
Cross-Section Derivation: The authors derive the invariant differential cross-section for $\ell^+\ell^- \to h_1 h_2 X$ and $N_1 N_2 \to h_1 h_2 X$ at leading order. The calculation incorporates Weizsäcker-Williams (WW) photon distributions for both leptons and nuclei.
Observables: The primary observables are the azimuthal distributions of the hadrons around the jet thrust axis. The authors calculate the unpolarized differential cross-section and azimuthal moments, specifically $\langle d\sigma_{unp} | \cos \phi_{12} \rangle$ and the double longitudinal spin asymmetry moment $\langle A_{LL} | \cos \phi_{12} \rangle$ .
Parametrizations: Numerical predictions utilize two recent phenomenological extractions of TMD FFs:
1. TO-CA24 (Ref. [15]): Based on global fits of SIDIS and $e^+e^-$ data with a specific Gaussian ansatz for $p_\perp$ dependence.
2. JAM3D-2022-nolat (Ref. [14]): A global fit including SIDIS, $e^+e^-$ , and inclusive $pp$ single-spin asymmetry data (excluding lattice QCD inputs).

Key Results
The authors provide numerical estimates for kinematic configurations accessible at the FCC-ee ( $\sqrt{s} = 92$ GeV) and the LHC ( $\sqrt{s_{NN}} = 5.36$ TeV) for various detectors (ATLAS, CMS, ALICE, LHCb).

FCC-ee ( $e^+e^-$ ):
- The unpolarized cross-section decreases with increasing $z_2$ (momentum fraction), ranging from $\mathcal{O}(100)$ nb to $\mathcal{O}(10^{-2})$ nb depending on kinematic cuts.
- The azimuthal moment $\langle d\sigma_{unp} | \cos \phi_{12} \rangle$ is predicted to be positive for unlike-sign pion pairs and negative for like-sign pairs.
- Magnitudes are estimated between 2–3% for unlike-sign pairs and 5–10% for like-sign pairs, potentially reaching 10–20% in specific high- $z$ bins.
- The double longitudinal spin asymmetry $\langle A_{LL} | \cos \phi_{12} \rangle$ (induced by polarized photons) is predicted to be of the order of a few percent for TO-CA24 and up to 10% for JAM3D-2022-nolat, though with larger uncertainties.
- Discrepancies between the two parametrizations are noted, particularly in the magnitude of the asymmetry and uncertainty bands, with JAM3D-2022-nolat generally showing larger uncertainties.
LHC (UPCs):
- In heavy-ion UPCs, only unpolarized photons contribute, so only $\langle d\sigma_{unp} | \cos \phi_{12} \rangle$ is predicted.
- Cross-sections are significantly larger (mb scale) due to the $Z^4$ enhancement, though they vary by detector pseudorapidity coverage.
- Azimuthal asymmetries are predicted to be sizable, reaching up to 10–15% in certain kinematic regions.
- The TO-CA24 parametrization predicts asymmetries ranging from 5% to 10%, while JAM3D-2022-nolat shows lower predictions at small $z_1$ but converges at larger $z_1$ .
- The authors note that the ALICE and LHCb configurations, particularly at lower $z_1$ bins, could potentially distinguish between the two extraction models if sufficient statistics are collected.

Significance and Claims
The paper claims that the proposed measurements would:

Shed light on the fragmentation mechanism: By providing data in a process where only final-state interactions are present (similar to SIA but with different initial states), the study offers a cleaner probe of TMD FFs.
Enable flavor separation: The specific charge-weighting in $\gamma\gamma$ collisions offers a unique handle to disentangle flavor contributions ( $u, c$ vs. $d, s, b$ ) to quark TMD FFs, which is difficult in SIDIS or standard $e^+e^-$ annihilation.
Discriminate between models: The authors assert that there are kinematic regions where the TO-CA24 and JAM3D-2022 parametrizations yield different predictions for the asymmetries. Measuring these regions with sufficient precision could allow for the discrimination between existing models of the Collins function.
Complement existing data: The results would provide complementary information at different energy scales and flavor combinations, aiding in the improvement of current phenomenological extractions.

The authors maintain a modest tone regarding theoretical uncertainties, noting that full TMD evolution is not implemented (though argued to be mild for asymmetries) and that a full evaluation of theoretical uncertainties has not yet been performed. They identify the work as a "first and exploratory" step, suggesting future extensions to electron-nucleus collisions and other hadron species (kaons, $\Lambda$ baryons).

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