Towards small x resummed DIS phenomenology

TL;DR

The paper investigates small-$x$ resummation in deep-inelastic scattering, introducing and computing small-$x$ resummed K-factors for $F_2$ and $F_L$ with fixed input PDFs and matching to fixed-order results. It shows that resummation tends to suppress DIS structure functions at small $x$ by a few percent—comparable to NNLO corrections but with opposite sign—implying a non-negligible effect for global PDF fits in the HERA region. By applying these K-factors to HERA kinematics, the work illustrates potential shifts in PDFs and observables that could be disentangled with high-precision data, highlighting the need for a fully resummed global PDF analysis. The results argue that percent-level precision at the LHC and future colliders like the LHeC will require incorporating small-$x$ resummation into PDFs to reliably propagate these effects into collider phenomenology and ultra-high-energy neutrino processes.

Abstract

We report on recent progress towards quantitative phenomenology of small x resummation of deep-inelastic structure functions. We compute small x resummed K-factors with realistic PDFs and estimate their impact in the HERA kinematical region. These K-factors, which match smoothly to the fixed order NLO results, approximately reproduce the effect of a small x resummed PDF analysis. Typical corrections are found to be of the same order as the NNLO ones, that is, a few percent, but with opposite sign. These results imply that resummation corrections could be relevant for a global PDF analysis, especially with the very precise combined HERA dataset.

Figures (4)

• Figure 1: Upper left: the small $x$ resummed $K$--factors for $F_2(x,Q^2)$ for various values of $Q$. Upper right: analogous $K$--factors for the NNLO case. Lower left: the small $x$ resummed $K$--factors for $F_L(x,Q^2)$ for various values of $Q$. lower right: analogous $K$--factors for the NNLO case. In all cases, the matching scale has been taken to be $Q_0=3$ GeV and the input PDF set is NNPDF1.0.
• Figure 2: The impact of small $x$ resummation on the kinematics of published $F_2(x,Q^2)$ HERA data. The various contours show the relative percent difference between the NLO and the small $x$ resummed computations.
• Figure 3: Comparison between the H1 measurent of $F_{L}(x,Q^2)$h1fl and the NLO and small $x$ resummed predictions computed with the NNPDF1.0 parton set.
• Figure 4: A comparison of various approximations to linear low-$x$ QCD for $F_2$ at the LHeC: the NNPDF1.0 prediction which includes PDF uncertainties and the NNPDF1.0 result corrected with the NNLO and small $x$ resummed $K$--factors. The expected experimental precision at the LHeC is also shown for illustration. The upper plot corresponds to $Q^2=$ 20 GeV$^2$, while the lower plot to $Q^2=$ 50 GeV$^2$.