Parton distributions from deep-inelastic-scattering data

TL;DR

This work updates the extraction of parton distribution functions from deep-inelastic scattering data across LO, NLO, and NNLO QCD, jointly determining HT contributions and the strong coupling α_s. It employs updated HERA data, NNLO corrections, and a detailed treatment of experimental correlations to quantify uncertainties, finding α_s(M_Z)=0.1143±0.0014 (exp) with nonzero high-twist terms persisting at NNLO. The study demonstrates that experimental errors dominate PDF uncertainties, yet theoretical uncertainties are under control, and provides public access to the resulting PDFs with uncertainty bands and variant schemes. Comparisons with CTEQ/MRST highlight region-dependent differences driven by data choices and methodological treatment, underscoring the impact on collider cross sections and the universality of PDFs.

Abstract

We perform the analysis of existing light-targets deep-inelastic-scattering (DIS) data in the leading-order (LO), next-to-leading-order (NLO), and next-to-next-to-leading-order (NNLO) QCD approximations and extract PDFs simultaneously with the value of the strong coupling constant $α_s$ and the high-twist contribution to the structure functions. The main theoretical uncertainties and experimental uncertainties due to all sources of experimental errors in data are estimated, the latter generally dominate for the obtained PDFs. The uncertainty in Higgs boson production cross section due to errors in PDFs is $\sim 2$% for the LHC and varies from 2% to 10% for the Fermilab collider under variation of the Higgs boson mass from $100 {\rm GeV}$ to $300 {\rm GeV}$. For the $W$-boson production cross section the uncertainty is $\sim 2$% for the both colliders. The value of $α^{\rm NNLO}_{\rm s}(M_{\rm Z})=0.1143\pm 0.0014({\rm exp.})$ is obtained, while the high-twist terms do not vanish up to the NNLO as required by comparison to data.

Figures (15)

• Figure 1: The experimental (statistical and systematical) errors bands for the PDFs obtain in the LO (dots), NLO (dashes), and NNLO (full) fits.
• Figure 2: Impact of changes in the data set on the NLO PDFs and their errors. Full lines: relative experimental errors in our PDFs; dashes: the same for the PDFs of Ref. Alekhin:2001ch; dots: the same for the CTEQ6 PDFs.
• Figure 3: Ratios of the correlated systematic errors to the uncorrelated ones (upper panel) and of the normalization errors to the correlated ones (lower panel) for different PDFs (full curves: gluons; dashes: sea quarks; dots: $d$-quarks, dashed-dots: $u$-quarks).
• Figure 4: Relative increase of the experimental errors in our NLO PDFs due to rejection of different data sets from the fit (full curves: BCDMS data are rejected; dashes: HERA ones; dots: SLAC ones; dashed-dots: NMC ones).
• Figure 5: The experimental error bands for $F_2^p$ calculated using our NLO PDFs (full curves) compared to the H1 data used in the fit. Figures at the curves are values of $Q^2$ in units of GeV$^2$. For better view the factor of $x^{0.2}$ and vertical shifts are applied to the data points and curves. The same bands calculated using the A99 PDFs are also given for comparison (dashed curves).