⚛️ phenomenology

QED Effects in PDFs -- A Les Houches Comparison Study

This paper compares QCD+QED and QCD-only parton distribution functions (PDFs) across various global fitting groups, with a detailed focus on the NNPDF4.0 set, to analyze how peripheral effects influence the magnitude and shape of QED corrections as precision in proton structure studies increases.

Original authors: Thomas Cridge, Juan Cruz Martinez, Joey Huston

Published 2026-02-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Thomas Cridge, Juan Cruz Martinez, Joey Huston

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 the proton as a tiny, bustling city inside an atom. For decades, physicists have been trying to map out exactly who lives there and how much "space" (or momentum) each resident takes up. The main residents are called quarks and gluons.

For a long time, scientists only counted these two groups. But recently, they realized there's a third, very shy resident: the photon (a particle of light). Even though photons are rare inside a proton, they are starting to matter because our maps (called PDFs or Parton Distribution Functions) have become so incredibly detailed that we can no longer ignore them.

This paper is like a "compare-and-contrast" study between different cartographers (scientific groups like MSHT, CT, and NNPDF) who are all trying to draw this map with the new photon resident included.

Here is the breakdown of their findings using simple analogies:

1. The "Zero-Sum" Game

Think of the proton's total momentum as a pizza with a fixed size. If you add a new slice for the photon, you have to take a tiny bit of crust away from the quarks and gluons to keep the pizza the same size.

The Finding: When the groups added the photon slice, they all agreed that the quarks and gluons had to shrink slightly. However, they didn't all agree on how much to shrink or which part of the pizza to take the crust from.

2. The "Different Recipes" Problem

The paper investigates why the maps look slightly different. It turns out the groups use different "recipes" for adding the photon:

The "Hand-Adjustment" Method (CT18): Some groups manually decided, "Okay, we'll take the extra space directly from the sea of quarks." This is like a chef deciding to shave off a specific layer of the crust by hand.
The "Fit-It-Yourself" Method (MSHT & NNPDF): Other groups let the math figure it out. They said, "We have a new photon; let the computer re-balance the whole pizza automatically."
The Result: The "hand-adjustment" method resulted in almost no change to the gluons (the main crust), while the "automatic" method took a bigger bite out of the gluons. This explained why the maps looked different at first.

3. The "Software Update" Glitch (NNPDF)

One group, NNPDF, had a particularly interesting situation. They released a new version of their map (Version 4.0).

The Issue: When they added the photon, they also secretly changed the "engine" that runs the map (the evolution settings). It was like comparing a car with a new engine to a car with an old engine, then blaming the difference on the new driver (the photon).
The Fix: When the authors of this paper fixed the engine so both maps used the same settings, the difference caused by the photon became much smaller and more consistent with the other groups.
The Lesson: Sometimes, what looks like a big new effect is actually just a change in the tools used to measure it.

4. The "Data Diet" Experiment

The paper also tested what happens if you feed the groups less data.

The Experiment: They took the massive dataset used by the newest map (NNPDF 4.0) and reduced it to look like the older, smaller dataset (NNPDF 3.1).
The Result: When the data was smaller, the "photon effect" looked smaller too. This suggests that the size of the dataset influences how much the photon seems to change the map.

5. Why Does This Matter? (The Higgs Connection)

The main reason they care about these tiny changes is the Higgs boson.

The Analogy: Producing a Higgs boson is like trying to bake a cake that requires two specific ingredients (gluons) to collide. If the "gluon map" says there is slightly less gluon available because a photon is hogging space, the predicted number of cakes (Higgs particles) we should see changes.
The Impact: The paper found that including the photon reduces the predicted number of Higgs particles by about 1% to 2%. While this seems small, in the world of high-energy physics, where we are trying to find tiny cracks in our theories, a 1% shift is huge.

The Bottom Line

The authors conclude that:

We are getting better: The differences between the groups are shrinking as they fix their "recipes" and "engines."
It's not just the photon: Even after fixing the methods, tiny differences remain. These might be due to inherent differences in how the groups interpret the data, not just the photon itself.
We need a standard: To get the most accurate picture of the proton, these groups need to keep comparing notes and standardizing how they include these tiny photon effects.

In short, the paper is a "quality control" check, ensuring that when we add the new "photon" ingredient to our proton recipe, everyone is measuring the same thing and not just changing the recipe by accident.

Technical Summary: QED Effects in PDFs – A Les Houches Comparison Study

Problem Statement
Over the last decade, the precision of Parton Distribution Function (PDF) determinations has improved significantly, driven by high-order QCD theoretical inputs (NNLO and approximate N3LO) and extensive LHC data. As PDF uncertainties have reduced to the few-percent level, previously neglected effects, such as Quantum Electrodynamics (QED) contributions, have become competitive with the size of these uncertainties. While the inclusion of QED in PDF fits is theoretically necessary and generates a photon PDF, there has been a lack of systematic benchmarking across global fitting groups regarding the specific impact of these QED effects on partonic distributions. Previous work [23] noted that while the total photon momentum is consistently determined, subtle differences exist in how the inclusion of the photon PDF affects the momentum distributions of other partons (quarks and gluons), particularly impacting the gluon-gluon luminosity relevant for Higgs production. This study aims to elucidate the sources of discrepancies observed between different global PDF groups (MSHT, CT, and NNPDF) when comparing QCD-only baselines against QCD+QED fits.

Methodology
The authors perform a comparative analysis of gluon-gluon luminosities and Higgs production cross-sections at $\sqrt{s} = 14$ TeV and $m_H = 125$ GeV. The study utilizes PDF sets from MSHT20, CT18, and NNPDF (versions 3.1 and 4.0) at both NNLO and approximate N3LO (aN3LO) orders.

Key methodological steps include:

Baseline Isolation: To distinguish between intrinsic QED effects and artifacts of fitting methodologies, the authors compare QCD+QED PDFs against QCD-only baselines that share identical settings (dataset, evolution schemes, and theoretical prescriptions). This involves constructing specific baseline sets for NNPDF4.0 and MSHT20 that match the QCD+QED configurations, rather than relying solely on public default sets which may differ in evolution settings or dataset composition.
Implementation Variations: The study investigates specific implementation choices, such as:
- Momentum Sum Rule: How the photon momentum is reallocated (e.g., subtracted from sea quarks only vs. determined by the fit).
- Evolution Schemes: The impact of using truncated solutions (TRN) versus exact solutions (EXA) for DGLAP evolution.
- Extraction Scale: The scale at which the photon PDF is extracted via the LUXQED formalism.
- Dataset Composition: The effect of reducing the NNPDF4.0 dataset to resemble the NNPDF3.1 selection.
Cross-Section Calculation: Gluon fusion Higgs production cross-sections are computed using the n3loxs code to translate luminosity changes into phenomenological impacts.

Key Results

Discrepancies in Public Sets: Initial comparisons of public PDF sets (Table 1) revealed varying reductions in gluon-gluon luminosity upon including QED, ranging from $-0.19\%$ (CT18+QED proton) to $-1.64\%$ (NNPDF4.0+QED).
Role of Implementation Choices:
- CT18: The small impact in the standard CT18+QED proton set is attributed to the "by-hand" subtraction of photon momentum from sea quarks only. When using the CT18+QED fit (where momentum balance is determined by the fit), the impact increases to $-1.09\%$ , aligning more closely with other groups.
- NNPDF4.0 Evolution: A significant portion of the difference between NNPDF3.1 and 4.0 arises from the change in evolution settings. NNPDF4.0 QCD fits use a truncated solution, while the QCD+QED fit uses an exact solution. When comparing NNPDF4.0 QCD+QED against a QCD-only baseline using the same exact evolution, the shape difference (slope) largely disappears, though a magnitude difference of $\approx -1.43\%$ remains.
- Dataset Size: Reducing the NNPDF4.0 dataset to mimic NNPDF3.1 further reduces the QED impact on luminosity to $-1.25\%$ , bringing it closer to the results of CT and MSHT.
Order Dependence: At aN3LO, the QED impact is slightly larger than at NNLO for default sets ( $-0.99\%$ for MSHT, $-1.88\%$ for NNPDF). However, when comparing against identical QCD baselines, these impacts reduce to $-0.86\%$ (MSHT) and $-1.57\%$ (NNPDF).
Cross-Section Impact: The variations in gluon-gluon luminosity translate directly to Higgs production cross-sections. For instance, the NNPDF4.0+QED set shows a reduction of $-1.63\%$ relative to its specific QCD baseline, compared to $-1.23\%$ for NNPDF3.1.

Significance and Conclusions
The paper concludes that a significant portion of the observed discrepancies in QED effects across global fitting groups can be attributed to differences in implementation choices (momentum reallocation strategies, evolution schemes) and inconsistencies in the QCD-only baselines used for comparison.

Even after harmonizing these technical settings, sub-percent level discrepancies persist between the groups. The authors suggest these remaining differences likely stem from inherent variations in the PDFs themselves (present even in QCD-only fits) which may be exacerbated by the inclusion of the photon. The study emphasizes that as precision requirements increase, these small differences become relevant. The authors propose that a full benchmarking of QED effects across groups is necessary to fully understand these sources and to properly account for the additional uncertainty arising from these inter-group differences in future phenomenological predictions, such as Higgs cross-sections. Currently, recommendations (e.g., in [23]) average these impacts, but a full combination of uncertainties would require a more detailed understanding of these residual differences.