Estimating the effect of NNLO contributions on global parton analyses

TL;DR

This study probes the impact of NNLO contributions on global parton analyses by constructing seven NNLO fits alongside LO and NLO baselines, using extreme NNLO splitting-function scenarios to bound uncertainties. It finds that NNLO generally improves the description of DIS data and slows evolution at small x, leading to a more suppressed gluon distribution in that region, potentially turning negative in MSbar at very small x and low Q^2. Observable predictions such as F_L exhibit slower perturbative convergence at small x, while W/Z hadroproduction cross sections remain relatively stable, indicating their utility as luminosity monitors. The work highlights the importance of complete NNLO splitting functions and refined heavy-flavor treatments for precise parton delineations and motivates future updates with new HERA data and full NNLO inputs.

Abstract

We use the recent estimates of NNLO splitting functions, made by van Neerven and Vogt, to perform exploratory fits to deep inelastic and related hard scattering data. We investigate the hierarchy of parton distributions obtained at LO, NLO and NNLO, and, more important, the stability of the resulting predictions for physical observables. We use the longitudinal structure function $F_L$ and the cross sections $σ_W, σ_Z$ for $W$ and $Z$ hadroproduction as examples. For $F_L$ we find relatively poor convergence, with increasing order, at small $x$; whereas $σ_{W,Z}$ are much more reliably predicted.

Figures (8)

• Figure 1: The description of data F2 for the $F_2$ structure function at a few representative $x$ values obtained in the LO, NLO and NNLO global parton analyses.
• Figure 2: The description of data F2 for the $F_2$ structure function at large $x$ obtained in the LO, NLO and NNLO global parton analyses.
• Figure 3: A comparison of partons obtained in the ' central' NNLO analysis with those obtained in the NLO fit, first at $Q^2 = 10$ GeV$^2$ and then at $Q^2 = 10^4$ GeV$^2$. We show the NNLO/NLO ratios for the gluon and the up and down quark distributions.
• Figure 4: The evolution of the gluon obtained in the LO, NLO and NNLO global analyses. The gluons obtained using the extreme forms, $A$ and $B$, of the NNLO splitting functions are shown (dot-dashed curves), together with that from the average (continuous curves).
• Figure 5: The behaviour of the NNLO contributions to the coefficient function $xC^{(3)}_{L,g}(x)$ for $F_L$ taking $n_f=3$. The average of the two extreme behaviours is shown.