⚛️ phenomenology

Particle-level parton densities and uncertainties for the resolved photon at NLO

This paper introduces PL $\gamma$ 26, a new set of next-to-leading-order parton distribution functions for the resolved photon, which are uniquely fitted directly to particle-level jet measurements from HERA and LEP using SHERPA simulations that incorporate non-perturbative effects like hadronization and multi-parton interactions to minimize reliance on external corrections.

Original authors: Andy Buckley, Frank Krauss, Peter Meinzinger, Vithyaban Anjelo Narendran

Published 2026-10-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Andy Buckley, Frank Krauss, Peter Meinzinger, Vithyaban Anjelo Narendran

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

Light is usually thought of as a simple, pure thing, a stream of energy that carries no internal structure. Yet in the high-energy world of particle physics, light behaves in a strangely complex way. When a photon, the particle of light, travels through the vacuum, it can briefly transform into a cloud of other particles, specifically quarks and gluons, before turning back into light. This fleeting moment allows the photon to act like a tiny, hadronic particle, possessing an internal makeup similar to a proton. Physicists call this the "resolved" photon, and understanding its internal recipe is crucial for predicting what happens when light collides with matter at the highest energies. For decades, scientists have tried to map out this recipe, known as a parton distribution function, but the task has been difficult because the data often comes from low-energy collisions where the messy, non-pure effects of particle formation interfere with the clean signals scientists want to see.

A new study by a team of researchers from universities in the UK and Switzerland offers a fresh look at this problem, presenting a detailed map of the resolved photon's contents based on a wide range of collision data. Instead of trying to strip away the messy effects of particle formation to fit the data to a simple theory, the team decided to embrace the complexity. They used a sophisticated computer simulation that builds the entire collision event from the ground up, including the formation of particles and their subsequent interactions. By matching their theoretical models directly to the raw, particle-level data recorded by experiments at the HERA and LEP colliders, they were able to create a new, more accurate description of how quarks and gluons are distributed inside a photon. This approach allowed them to use a much larger and more diverse set of measurements than ever before, leading to a clearer picture of the photon's inner life.

The researchers focused on data from two major experiments: HERA, where electrons collided with protons, and LEP, where electrons collided with positrons. In these collisions, the photons involved can interact in two ways. Sometimes the photon acts as a single, point-like particle hitting a target directly. Other times, it acts as a resolved photon, where one of its internal parts, a quark or a gluon, does the hitting. The team analyzed the jets of particles produced in these collisions, which serve as a fingerprint of the underlying interaction. A significant challenge in this work was that these collisions occur at relatively low energy scales, where the effects of particles interacting with each other multiple times, known as multi-parton interactions, are very strong. If these effects are not modeled correctly, they can be mistaken for features of the photon's internal structure, leading to incorrect conclusions.

To solve this, the team first tuned their computer simulation to accurately reproduce the behavior of these multi-parton interactions for both the HERA and LEP environments. They adjusted the simulation's settings until it matched the experimental data for the production of particle jets, ensuring that the simulation was not hiding any unknown physics. Once the simulation was reliable, they used it to fit a new set of parameters that describe the photon's internal structure. This process involved testing thousands of different possible recipes for the photon's contents, running the simulation for each one, and seeing which recipe produced results that best matched the real-world data. The team used a clever statistical technique to speed up this process, allowing them to explore a vast landscape of possibilities without waiting days for each computer run to finish.

The result is a new set of values, named PLγ26, that describes the probability of finding a quark or a gluon with a specific amount of momentum inside a photon. The study found that the photon contains more up and strange quarks than previous maps suggested, while having fewer gluons. This difference is significant because it changes how scientists predict the outcomes of future high-energy collisions. The new map also comes with a detailed estimate of uncertainty, showing exactly where the data is strong and where it is still vague. For instance, the team found that while they have a good handle on the behavior of the photon at certain energy levels, the data is less precise at very low momentum fractions, leaving some room for future refinement.

This work represents a shift in how particle physicists approach the problem of understanding complex particles. By fitting their models directly to the final, messy state of the collision rather than trying to clean the data first, the researchers were able to include many more measurements and get a more robust result. Their findings suggest that the internal structure of the photon is more nuanced than previously thought, with a balance between quarks and gluons that differs from older models. While this is not the final word on the subject, it provides a solid foundation for future experiments, including those planned for the upcoming Electron-Ion Collider. The new map, PLγ26, is now available for other scientists to use, offering a more precise tool for exploring the fundamental building blocks of light and matter.

Technical Summary: Particle-level parton densities and uncertainties for the resolved photon at NLO

Problem Statement
The study of resolved (hadronic) photon structure, which had produced a series of Leading Order (LO) and Next-to-Leading Order (NLO) Parton Distribution Function (PDF) sets, effectively paused after the end of HERA operations in 2007. While recent interest has resurged with the anticipated Electron–Ion Collider (EIC), existing photon-PDF fits rely heavily on the structure function $F_2^\gamma$ . Although $F_2^\gamma$ provides a theoretically clean probe of the photon's quark content, it offers little constraint on the gluon content. Conversely, jet production measurements in photoproduction at HERA and $\gamma\gamma$ collisions at LEP are sensitive to both quark and gluon densities. However, these jet measurements typically occur at low energy scales where non-perturbative corrections (hadronisation, multi-parton interactions) are large. Traditional fitting methodologies require applying external correction factors derived from Monte Carlo (MC) generators to fixed-order partonic calculations to match experimental data. This approach limits the number of usable measurements and introduces model dependence through ad-hoc corrections. Furthermore, previous fits were often restricted to data from single colliders or specific observables.

Methodology
The authors present a novel approach to fitting photon PDFs directly to particle-level observables rather than corrected partonic cross-sections. This methodology leverages modern general-purpose event generators to include non-factorisable effects (hadronisation, multi-parton interactions (MPI), and decays) directly within the fit procedure.

Event Generation: Predictions are generated using SHERPA-3.1.0 at NLO accuracy matched to the CSSHOWER parton shower (MC@NLO matching). The setup includes:
- Processes: Photoproduction ( $\gamma p$ ) at HERA and $\gamma\gamma$ collisions at LEP.
- Components: Direct, single-resolved, and double-resolved components are simulated.
- MPI Modeling: The MPI model (AMISIC) is explicitly tuned to the data because the resolved photon behaves like a hadron, and un-tuned MPI effects could be incorrectly absorbed into the fitted PDFs. Separate tunes are performed for HERA ( $\gamma p$ ) and LEP ( $\gamma\gamma$ ).
- Evolution: The photon PDFs evolve using a modified APFEL++ library (denoted APFEL++') in the $\overline{\text{MS}}$ scheme, employing a 4-flavour scheme with dynamic heavy quark generation.
Fitting Strategy (Surrogate Optimization):
- To overcome the computational intractability of running millions of MC events for every step of a PDF optimization, the authors employ a surrogate-based approach (similar to the PROFESSOR toolkit).
- An ensemble of algebraic surrogates (polynomials) models the relationship between PDF parameters and observable bin values.
- Parameter Sampling: 3,000 random PDF parameter sets are generated based on the SAL (Słomiński, Abramowicz, Levy) parametrisation ansatz. These are propagated through SHERPA using on-the-fly event reweighting at NLO, allowing the generation of differential cross-sections for all 3,000 PDFs in a single MC run.
- Optimization: The surrogates are trained on these reweighted datasets. The fit minimizes a $\chi^2$ function comparing surrogate predictions to experimental data (from H1, ZEUS, L3, and OPAL).
- Uncertainty Estimation: Experimental uncertainties are estimated using a replica method. 100 replica datasets are created by smearing the experimental data with Gaussian noise. The fit is repeated for each replica to generate a set of 100 PDF replicas, providing an asymmetric uncertainty band.
Data Selection: The fit utilizes a wide range of jet measurements, including dijet, inclusive-jet, and multi-jet (3- and 4-jet) final states from HERA and LEP. The analysis focuses on resolved-enriched regions (defined by $x_\gamma^{obs}$ ) but includes bins straddling the direct/resolved boundary.

Key Contributions

PL $\gamma$ 26: The production of a new set of NLO resolved-photon PDFs, PL $\gamma$ 26, which is the first to be fitted to a wide range of jet measurements from multiple experiments (H1, ZEUS, L3, OPAL) simultaneously.
Particle-Level Fitting: The demonstration of a viable technical framework for fitting PDFs directly to particle-level data using NLO+PS event generators, bypassing the need for external non-perturbative correction factors.
MPI Tunes: The derivation of specific MPI tunes for HERA and LEP photoproduction, which are necessary to prevent MPI effects from biasing the extracted photon PDFs.
Uncertainty Quantification: The provision of a full error set (100 replicas) for the resolved photon, allowing for quantitative uncertainty propagation in future phenomenological studies.

Results

Fit Quality: The PL $\gamma$ 26 set significantly improves the description of HERA dijet and inclusive-jet data compared to previous sets (GS96, ACFGP) and the MPI-tuned baseline using the older SaS 1M PDF. For example, the $\chi^2$ /bin for ZEUS dijet data drops from ~3.9 to ~0.8. However, the fit struggles with certain LEP OPAL dijet distributions and ZEUS 3-jet data, which contribute significantly to the total $\chi^2$ .
Parton Densities:
- Quarks: The up-quark density is the largest, as expected. The strange quark is suppressed by a fixed factor ( $r_s=0.3$ ). The fitted up- and strange-quark densities are 40–120% higher than those in the ACFGP and VALO 1.0 sets at intermediate $x$ .
- Gluon: The gluon distribution is smaller than in previous MS-scheme sets (ACFGP, VALO 1.0), particularly at low $x$ where it rises less steeply. The authors attribute this difference to the compensation between quark and gluon densities: since jet data constrain the sum of quark and gluon effects, and $F_2^\gamma$ (used in other fits) constrains quarks but not gluons, the PL $\gamma$ 26 fit compensates for a smaller gluon with larger quark densities.
- Charm: The charm quark is generated radiatively; its uncertainty is negligible in the plots as it is driven by evolution rather than the fit parameters.
Comparison: At $Q^2 = 5 \text{ GeV}^2$ , PL $\gamma$ 26 shows distinct behavior compared to the SAL (DIS $\gamma$ scheme) and VALO 1.0 sets, particularly in the high- $x$ region where the $\overline{\text{MS}}$ scheme allows quarks to rise before falling, unlike the DIS $\gamma$ scheme.

Significance and Claims
The paper claims that this work serves as a practical demonstration of the viability of particle-level PDF fitting. It highlights that:

Technical Feasibility: Modern MC generators (SHERPA) and reweighting techniques allow for the inclusion of non-perturbative effects directly in the fit, expanding the usable dataset to include low-scale jet measurements previously difficult to utilize.
Robustness: By tuning the MPI model separately, the authors avoid the risk of "absorbing" non-perturbative effects into the PDFs, a common issue in traditional fits.
Future Utility: The resulting PL $\gamma$ 26 set and its replicas provide a necessary tool for upcoming phenomenological studies, particularly for the Electron-Ion Collider (EIC) and ultraperipheral collisions at the LHC, where low-scale physics and non-perturbative effects are dominant.
Limitations: The authors are modest about the current state, noting that the parametrisation (fixed high- $x$ exponents) limits the flexibility of the fit and that the separation of quark and gluon densities remains ambiguous without combining jet data with $F_2^\gamma$ measurements. They propose that future combined fits and more flexible parametrisations are required to resolve tensions between different data types.

The work does not claim to replace global PDF fits but rather to establish a new, robust methodology for defining PDFs in regimes where fixed-order calculations and external corrections are insufficient.

Technical Summary: Particle-level parton densities and uncertainties for the resolved photon at NLO

More like this