Can we trust small x resummation?

TL;DR

The paper assesses small-x resummation for parton evolution and DIS coefficient functions, addressing the stability and practical impact of resummation in the HERA and LHC kinematic regimes. It identifies three key ingredients—double-leading expansion, exchange symmetry, and running-coupling resummation—that together control the leading small-x behavior, ensuring momentum conservation and smooth matching to GLAP. The authors present a detailed ABF-based framework, extend it to quarks, and derive a resummed splitting-function matrix and resummed coefficient functions, with careful treatment of scheme issues (MSbar vs Q0MSbar). They show that, once all relevant terms are included and matched, resummed predictions are perturbatively stable and yield moderate corrections in line with NNLO, suppressing small-x structure functions and improving the reliability of PDFs and LHC predictions. The work highlights the importance of proper matching and scheme consistency, suggesting substantial practical benefits for high-energy phenomenology.

Abstract

We review the current status of small x resummation of evolution of parton distributions and of deep-inelastic coefficient functions. We show that the resummed perturbative expansion is stable, robust upon different treatments of subleading terms, and that it matches smoothly to the unresummed perturbative expansions, with corrections which are of the same order as the typical NNLO ones in the HERA kinematic region. We discuss different approaches to small x resummation: we show that the ambiguities in the resummation procedure are small, provided all parametrically enhanced terms are included in the resummation and properly matched.

Figures (12)

• Figure 1: Comparison of the HERA and LHC kinematical regions (from Ref. dittmar).
• Figure 2: Comparison of the LO, NLO and NNLO gluon distributions in the MSTW08 parton fit (from Ref. thorne).
• Figure 3: Double leading expansion of the GLAP anomalous dimension $\gamma$ (left) and the BFKL kernel $\chi$ (right).
• Figure 4: The BFKL kernel and its dual GLAP anomalous dimension computed at LO and NLO in the BFKL expansion, the GLAP expansion and the double--leading expansion.
• Figure 5: The LO and NLO resummed symmetrized double--leading kernels compared to the LO and NLO kernels in the BFKL expansion and the NLO GLAP kernel. CCSS denotes the corresponding result of Ref. ciafresb (from Ref. dittmar)