QED Effects in PDFs -- A Les Houches Comparison Study

TL;DR

The paper addresses how including $QED$ in PDFs via the $LUXQED$ formalism affects parton luminosities and collider observables, focusing on the gluon–gluon channel. It benchmarks QCD+QED PDFs against QCD-only baselines at NNLO and approximate N3LO across CT18, MSHT20, and NNPDF4.0/3.1, highlighting how differences largely arise from $QED$ implementation and baseline choices. The main finding is that $gg$ luminosity shifts due to $QED$ are sub-percent, typically ranging from about $-0.6\%$ to $-1.6\%$ at NNLO and up to around $-1.9\%$ at aN3LO for some sets, with NNPDF4.0 often exhibiting the largest effects. Even after standardizing baselines and evolution settings, small residual differences remain, suggesting intrinsic PDF differences and reinforcing the case for cross-group benchmarking to faithfully propagate $QED$ uncertainties into precision Higgs cross sections.

Abstract

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.

Figures (7)

• Figure 1: Comparison of the gluon-gluon luminosities at $\sqrt{s}=14~\rm{TeV}$ for the QCD+QED and QCD only default PDFs of CT18, MSHT20, NNPDF3.1 and NNPDF4.0 at NNLO.
• Figure 2: Comparison of the gluon-gluon luminosities at $\sqrt{s}=14~\rm{TeV}$ with NNLO PDFs. (Upper Left) CT18 in the QED proton, LUX and QED fit PDF sets relative to the QCD only CT18 baseline. (Upper Right) MSHT20 QED relative to QCD only. (Lower Left) NNPDF3.1 QED relative to a QCD only baseline. (Lower Right) NNPDF4.0 QED relative to a QCD only baseline. Note the MSHT and NNPDF3.1 plots are repeated from Figure \ref{['fig:gglumis_defaultNNLOQEDPDFs']} as there are no changes to their QCD or QED comparison sets.
• Figure 3: Comparison of the gluon-gluon luminosities at $\sqrt{s}=14~\rm{TeV}$ obtained when the photon is extracted at a starting scale of $Q_{\gamma} = 10 \rm{GeV}$ compared to the default $Q_{\gamma} = 100 \rm{GeV}$ in NNPDF4.0 QED.
• Figure 4: Comparison of the gluon-gluon luminosities at $\sqrt{s}=14~\rm{TeV}$ for a range of NNPDF NNLO fits. In the upper left figure, the QCD baseline corresponds to the baseline used in NNPDF:2024djq, in this paper the QCD fit is evolved using the truncated solution while the QED variant uses an exact solution as implemented in EKO Candido:2022tld. In the upper right figure, the same QCD only fit (4.0-like) is performed once with the exact solution (EXA) and once with truncated (TRN). In the lower left figure we therefore present a QCD/QED comparison in which both fits are evolved using the exact solution. While the effect of the QED corrections at the Higgs mass is almost unchanged, the difference in slope has almost completely disappeared. Finally, the lower right figure corresponds to the same pair of fits using instead a reduced dataset, closer to the dataset of NNPDF3.1.
• Figure 5: Comparison of the gluon-gluon luminosities at $\sqrt{s}=14~\rm{TeV}$ for the QCD+QED and QCD only PDFs of (left) MSHT20 and (right) NNPDF4.0 at aN3LO using the PDFs available in LHAPDF.