Determination of the parton distribution functions of the proton using diverse ATLAS data from $pp$ collisions at $\sqrt{s} = 7$, 8 and 13 TeV

TL;DR

ATLASpdf21 provides a NNLO QCD PDF determination by merging diverse ATLAS pp data at 7–13 TeV with final HERA DIS data, explicitly accounting for correlations among systematic uncertainties. The fit uses a 21-parameter PDF parameterization evolved via DGLAP from Q0^2 = 1.9 GeV^2, and incorporates a careful treatment of theoretical uncertainties, K-factors, and scale variations. The results show strong constraining power from W/Z data on light-quark seas, substantial gluon constraints from jets and ttbar data, and broad compatibility with global PDFs, while highlighting the importance of inter-dataset correlations for precise high-x behavior. The ATLASpdf21 set, available with both T=1 and T=3 tolerances, aligns with modern PDFs and demonstrates the value of ATLAS data in precision proton structure studies. Overall, this work advances proton structure knowledge by delivering a comprehensive, correlation-aware NNLO PDF set consistent with global fits and suitable for high-precision LHC predictions.

Abstract

This paper presents an analysis at next-to-next-to-leading order in the theory of quantum chromodynamics for the determination of a new set of proton parton distribution functions using diverse measurements in $pp$ collisions at $\sqrt{s} = 7$, 8 and 13 TeV, performed by the ATLAS experiment at the Large Hadron Collider, together with deep inelastic scattering data from $ep$ collisions at the HERA collider. The ATLAS data sets considered are differential cross-section measurements of inclusive $W^{\pm}$ and $Z/γ^*$ boson production, $W^{\pm}$ and $Z$ boson production in association with jets, $t\bar{t}$ production, inclusive jet production and direct photon production. In the analysis, particular attention is paid to the correlation of systematic uncertainties within and between the various ATLAS data sets and to the impact of model, theoretical and parameterisation uncertainties. The resulting set of parton distribution functions is called ATLASpdf21

Figures (41)

• Figure 1: ATLASpdf21 PDFs comparing those extracted from a fit in which correlations of systematic uncertainties between data sets are applied, with those extracted from a fit in which only the luminosity uncertainties for each centre-of-mass energy are correlated between data sets. Only experimental uncertainties are shown, evaluated with tolerance $T=1$. Top left: $xu_v$. Top right: $xd_v$. Bottom left: $x\bar{u}$. Bottom right: $x\bar{d}$. The lower panels show the comparison as a ratio to the default ATLASpdf21 PDF.
• Figure 2: ATLASpdf21 PDFs comparing those extracted from a fit in which correlations of systematic uncertainties between data sets are applied, with those extracted from a fit in which only the luminosity uncertainties for each centre-of-mass energy are correlated between data sets. Only experimental uncertainties are shown, evaluated with tolerance $T=1$. Top left: $x\bar{s}$. Top right: $xg$. Bottom left: $x(\bar{d}-\bar{u})$. Bottom right: $R_s$. For the $x\bar{s}$ and $xg$ plots, the lower panels show the comparison as a ratio to the default ATLASpdf21 PDF.
• Figure 3: Ratios of ATLASpdf21 PDFs extracted from a fit including correlations of systematic uncertainties between data sets to those extracted from a fit in which only the luminosity uncertainties for each centre-of-mass energy are correlated between data sets, at scale $Q^2 = 10000.0$$\text{Ge V}$$^2$. Only experimental uncertainties are shown, evaluated with tolerance $T=1$. Top left: $xu_v$. Top right: $xd_v$. Bottom left: $x\bar{u}$. Bottom right: $x\bar{d}$.
• Figure 4: Ratios of ATLASpdf21 PDFs extracted from a fit including correlations of systematic uncertainties between data sets to those extracted from a fit in which only the luminosity uncertainties for each centre-of-mass energy are correlated between data sets, at scale $Q^2 = 10000.0$$\text{Ge V}$$^2$. Only experimental uncertainties are shown, evaluated with tolerance $T=1$. Left: $xs$. Right: $xg$.
• Figure 5: The PDF ratio $R_s=x(s+\bar{s})/x(\bar{u}+\bar{d})$ from ATLASpdf21 compared with $R_s$ for fits not including some of the $W,Z$ data sets. Only experimental uncertainties are shown, evaluated with tolerance $T=1$. Left: not including $W,Z$ data at both 7 and 8 $\text{Te V}$. Right: not including $W,Z$ data at 8 $\text{Te V}$.