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Combining NNPDF3.0 and NNPDF2.3QED through the APFEL evolution code

V. Bertone, S. Carrazza

TL;DR

The paper presents NNPDF3.0QED, a PDF set that combines the NNPDF3.0 QCD partons with the photon PDF from NNPDF2.3QED, evolved using APFEL with a unified QCD⊗QED DGLAP approach. It demonstrates that including QED corrections yields only modest changes to the QCD PDFs and parton luminosities, while the photon PDF remains small in momentum fraction but compatible with other QED-corrected determinations. The study verifies momentum sum rule conservation and provides comparisons to CT14QED and MRST2004QED, highlighting the practical viability of unified QCD⊗QED evolution. It also outlines future improvements, such as incorporating NLO QED evolution and additional data to further constrain the photon PDF.

Abstract

We present sets of parton distribution functions (PDFs), based on the NNPDF3.0 family, which include the photon PDF from the NNPDF2.3QED sets, and leading-order QED contributions to the DGLAP evolution as implemented in the public code APFEL. The aim is to combine our state-of-the-art determination of quark and gluon PDFs with the so far only direct determination of the photon PDF from LHC data. In addition, the use of APFEL allowed us to employ a solution of the DGLAP equation that, differently from that used for the NNPDF2.3QED sets, includes QED corrections in a more accurate way. We briefly discuss how these sets are constructed and investigate the effect of the inclusion of the QED corrections on PDFs and parton luminosities. Finally, we compare the resulting sets, which we dubbed NNPDF3.0QED, to the older NNPDF2.3QED sets and to all presently available PDF sets that include QED corrections, namely CT14QED and MRST2004QED.

Combining NNPDF3.0 and NNPDF2.3QED through the APFEL evolution code

TL;DR

The paper presents NNPDF3.0QED, a PDF set that combines the NNPDF3.0 QCD partons with the photon PDF from NNPDF2.3QED, evolved using APFEL with a unified QCD⊗QED DGLAP approach. It demonstrates that including QED corrections yields only modest changes to the QCD PDFs and parton luminosities, while the photon PDF remains small in momentum fraction but compatible with other QED-corrected determinations. The study verifies momentum sum rule conservation and provides comparisons to CT14QED and MRST2004QED, highlighting the practical viability of unified QCD⊗QED evolution. It also outlines future improvements, such as incorporating NLO QED evolution and additional data to further constrain the photon PDF.

Abstract

We present sets of parton distribution functions (PDFs), based on the NNPDF3.0 family, which include the photon PDF from the NNPDF2.3QED sets, and leading-order QED contributions to the DGLAP evolution as implemented in the public code APFEL. The aim is to combine our state-of-the-art determination of quark and gluon PDFs with the so far only direct determination of the photon PDF from LHC data. In addition, the use of APFEL allowed us to employ a solution of the DGLAP equation that, differently from that used for the NNPDF2.3QED sets, includes QED corrections in a more accurate way. We briefly discuss how these sets are constructed and investigate the effect of the inclusion of the QED corrections on PDFs and parton luminosities. Finally, we compare the resulting sets, which we dubbed NNPDF3.0QED, to the older NNPDF2.3QED sets and to all presently available PDF sets that include QED corrections, namely CT14QED and MRST2004QED.

Paper Structure

This paper contains 3 sections, 2 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. The NNPDF3.0QED set
  3. Acknowledgements

Figures (3)

  • Figure 1: nameref-fig:pdfcomparison fith LAB: fig:pdfcomparison Comparison between NNPDF3.0 NNLO and NNPDF3.0QED NNLO for the $g$, $u$, $d$, and $s$ distributions at $Q=100$ GeV. Plots generated with APFEL WebCarrazza:2014gfa.
  • Figure 2: nameref-fig:luminosities fith LAB: fig:luminosities Comparison between NNPDF3.0 NNLO and NNPDF3.0QED NNLO for the $gg$ and $q\bar{q}$ parton luminosities at $\sqrt{s} = 13$ TeV as functions of the final state in variant mass $M_x$.
  • Figure 3: nameref-fig:photon fith LAB: fig:photon Comparison of the photon PDF at $Q=1.414$ GeV (left) and $Q=100$ GeV (right) between NNPDF3.0QED, NNPDF2.3QED, MRST2004QED with "current" (mem=0) and "constituent" (mem=1) quark masses, and CT14QED with photon momentum fractions $p_0^{\gamma} = 0$% and $p_0^{\gamma} = 0.14$%. Uncertainties for NNPDF3.0QED and NNPDF2.3QED are given as 68% CL level symmetric around the central value.