Drell-Yan processes in the high-energy limit

TL;DR

This work develops analytic high-energy (small-x) resummation for Drell-Yan and vector boson production using $k_T$-factorization within the ABF framework, delivering the Mellin-space coefficient function $D_{qg}(N, abla_s)$ and a color relation to $D_{qq}$, with the first two terms consistent with fixed-order NLO/NNLO and higher terms newly computed. It demonstrates that resummed results, when matched to fixed-order calculations, yield modest corrections to NNLO predictions for $Q<100$ GeV, while larger effects appear relative to NLO. The findings support the controlled inclusion of small-x resummation in LHC phenomenology, though certain channels like the gluon-gluon NNLO piece remain non-resummed. Overall, the paper provides a framework and quantitative assessments for incorporating high-energy logarithms into Drell-Yan and vector boson cross-section predictions at the LHC.

Abstract

We present the analytic computation of leading high-energy logarithms of the inclusive Drell-Yan and vector boson production cross-section. We also study the phenomenological relevance of the high-energy corrections for Drell-Yan processes at the LHC. We find that the resummation corrects the NNLO result by no more than a few percent, for values of the invariant mass of the lepton pair below 100 GeV.

Figures (3)

• Figure 1: Feynman diagrams for the process $g^*(k) \; q(p_1) \to \gamma^* (q) \;q(p_2)$. The quarks are on-shell and massless, while the initial state gluon and the final state photon are off-shell.
• Figure 2: In this plot from top to bottom we have: the NLO $K$-factor as defined in Eq. (\ref{['nlokfact']}) and the two NNLO $K$-factors of Eq. (\ref{['nnlokfact']}), $K^{NNLO}_1$ and $K^{NNLO}_2$ respectively.
• Figure 3: In this plot we have the NLO (top curves) and NNLO (bottom curves) resummed cross-section, normalised to NLO.