O(α_sα) corrections to Drell-Yan processes in the resonance region

TL;DR

The paper addresses mixed QCD–EW corrections at $O(\alpha_s \alpha)$ for Drell–Yan processes in the resonance region, a setting crucial for precision W mass and weak mixing angle measurements. It adopts a pole (resonance) approximation to systematically separate factorizable production/decay corrections from non-factorizable soft-photon exchanges, validating the approach against NLO results with typical accuracy at the 0.1% level. The authors present first (preliminary) results for the dominant factorizable $O(\alpha_s \alpha)$ corrections, showing significant deviations from simple product-factorization and revealing that non-factorizable contributions are negligible. These findings suggest a practical path to incorporating mixed QCD–EW effects in high-precision predictions, while highlighting observable-dependent nuances such as recoil effects in the lepton transverse momentum distribution.

Abstract

Drell-Yan-like W-boson and Z-boson production in the resonance region allows for some high-precision measurements that are crucial to carry experimental tests of the Standard Model to the extremes, such as the determinations of the W-boson mass and the effective weak mixing angle. We describe how the Standard Model prediction can be successfully performed in terms of a consistent expansion about the resonance pole, which classifies the corrections in terms of factorizable and non-factorizable contributions. The former can be attributed to the W/Z production and decay subprocesses individually, while the latter link production and decay by soft-photon exchange. At next-to-leading order we compare the full electroweak corrections with the pole-expanded approximations, confirming the validity of the approximation. At O(α_sα), we describe the concept of the expansion and report on results on the non-factorizable contributions, which turn out to be phenomenologically negligible. Moreover, we present first (preliminary) results on the dominant factorizable O(α_sα) corrections, which originate from the interplay of initial-state QCD and final-state electroweak corrections. Numerically those corrections significantly differ from a mere product of the two next-to-leading-order correction factors.

Figures (5)

• Figure 1: Generic diagrams for the lowest-order amplitude (a), for the EW virtual NLO factorizable corrections to production (b) and decay (c), as well as for virtual non-factorizable corrections (d), where the empty blobs stand for all relevant tree structures and the ones with "$\alpha$" inside for one-loop corrections of ${\@fontswitch\mathcal{O}}(\alpha)$.
• Figure 2: Distributions in the transverse mass (left) and transverse lepton momentum (right) for $\mathrm{W^+}$W^+$$ production at the LHC, with the upper plots showing the absolute distributions and the lower plots the relative NLO EW corrections in PA broken up into its factorizable and non-factorizable parts (taken from Ref. Dittmaier:2014qza).
• Figure 3: Generic diagrams for the non-factorizable corrections of ${\@fontswitch\mathcal{O}}(\alpha_{\mathrm{s}}\alpha)$.
• Figure 4: Generic diagrams for the ${\@fontswitch\mathcal{O}}(\alpha_{\mathrm{s}}\alpha)$ factorizable corrections of the "initial--final" type.
• Figure 5: Relative factorizable corrections (in red) of ${\@fontswitch\mathcal{O}}(\alpha_{\mathrm{s}}\alpha)$ induced by initial-state QCD and final-state EW contributions to the distributions in $M_{\mathrm{T},\nu l}$ (left) and $p_{\mathrm{T,l}}$ (right) for $\mathrm{W^+}$W^+$$ production at the LHC. The naive products of the NLO correction factors $\delta_{\alpha_{\mathrm{s}}}$ and $\delta_{\alpha}$ are shown for comparison (see text).