QED Effects in PDFs -- A Les Houches Comparison Study

In the last decade, and even more so in the last few years, our knowledge of the internal structure of the proton has become more accurate and precise thanks to the large amount of data available and developments in theory and methodology. The reduction of the uncertainties associated to these developments has brought previously neglected effects into focus as their typical magnitude are competitive with the size of the uncertainties. One such effect is the inclusion of QED into PDF fits. Typically this is a percent effect, and thus while theoretically important, it has had a relatively limited impact on phenomenological studies up to this point. In this proceeding we study some of the effects which, while peripheral to the inclusion of QED in the proton, can considerably change the relative size and shape of the QCD+QED fit with respect to the QCD only determination. These may become important in the future as precision continues to increase. After a comparison of the QCD+QED PDFs with the QCD only PDFs of various global PDF fitting groups, we focus largely upon NNPDF4.0, which shows the biggest effect when including QED. Focusing largely on a single set of PDFs also enables more subtle effects to be analysed, making it an ideal candidate for this study.

💡 Research Summary

In the past decade the precision of parton distribution functions (PDFs) has reached the sub‑percent level thanks to the wealth of LHC and deep‑inelastic‑scattering data combined with NNLO and approximate N³LO QCD calculations. At this level of accuracy effects that were previously negligible become comparable to the remaining uncertainties, and one of the most important of these is the inclusion of quantum electrodynamics (QED) in PDF fits.

The paper presents a systematic comparison of QCD‑only PDFs with QCD+QED PDFs from the four major global fitting groups: CT18, MSHT20, NNPDF3.1 and NNPDF4.0. All groups now provide photon PDFs derived from the LUXQED formalism, which yields a photon momentum fraction of about 0.4 % at the Higgs mass scale (μ = 125 GeV). However, the way this photon momentum is taken from the other partons differs markedly among the groups, leading to distinct patterns in the redistribution of momentum among gluons and quarks.

CT18 offers three QED variants. The “CT18 QED proton” set subtracts the photon momentum by hand from the sea‑quark sector only, leaving the gluon distribution essentially unchanged. The “CT18 LUX” set adds the LUXQED photon on top of the original CT18 PDFs without enforcing the momentum sum rule, resulting in a negligible impact on the gluon–gluon (gg) luminosity. The “CT18 QED fit” determines the momentum balance during the fit itself, producing a modest reduction of the gg luminosity by about –1.1 %.

MSHT20 and the NNPDF families instead let the fit determine the full momentum redistribution. Consequently, the gluon momentum is reduced by 0.6 %–0.8 % and the quark singlet by 0.1 %–0.4 % at μ = 125 GeV. This reduction translates directly into a decrease of the gg luminosity, which is the dominant production channel for the Higgs boson. The paper quantifies the gg luminosity change at √s = 14 TeV: MSHT20 shows –0.60 %, NNPDF3.1 –1.36 %, and NNPDF4.0 –1.37 % when compared with their respective QCD‑only baselines.

A key technical issue investigated is the choice of the initial scale Qγ at which the LUXQED photon is extracted. CT and MSHT use low scales (≈ 1 GeV), while NNPDF adopts a high scale (100 GeV). By re‑extracting the photon in NNPDF4.0 at Qγ = 10 GeV the authors find essentially no change in the gg luminosity, confirming that the full QCD⊗QED evolution compensates for the different starting scales. Therefore, the remaining differences are attributed to intrinsic aspects of each fit: the data sets included, the treatment of electroweak corrections, and the baseline QCD methodology.

The authors also explore the impact of the evolution solution method. NNPDF4.0’s QCD‑only baseline was obtained with a truncated solution of the DGLAP equations, whereas the QED‑augmented set uses the exact solution implemented in the EKO library. A dedicated test where both the QCD‑only and QCD+QED fits are evolved with the exact solution shows that the gg luminosity changes by less than 0.1 %, indicating that at current precision the choice between truncated and exact evolution is subdominant to the QED implementation itself.

When moving from NNLO to approximate N³LO, the pattern of QED‑induced reductions persists, with MSHT20 and NNPDF showing gluon momentum losses of up to 1.5 % at the higher order. This demonstrates that QED effects do not disappear at higher perturbative orders and must be consistently included in future PDF releases.

Phenomenologically, the reduction of the gluon momentum directly affects Higgs boson production via gluon fusion, Drell–Yan processes, and high‑pT jet cross sections. The authors note that the PDF4LHC21 recommendation already averages the QED‑induced shifts from the three groups, but as experimental uncertainties shrink further, a more refined benchmarking of QED effects will become essential.

In summary, the paper provides a detailed benchmark of QED contributions to PDFs, identifies the sources of inter‑group differences (photon momentum allocation, LUXQED scale choice, baseline QCD fit), and quantifies their impact on key LHC observables. The work underscores that, in the era of sub‑percent PDF uncertainties, QED‑augmented PDFs are no longer optional but a necessary component of precision collider phenomenology.