Electroweak corrections to $Z$-boson hadroproduction at finite transverse momentum

TL;DR

The paper addresses the precise prediction of inclusive Z hadroproduction at finite $p_T$ by incorporating electroweak corrections beyond pure QCD. It computes the full one-loop EW corrections at ${\cal O}(\alpha^2\alpha_s)$ and ${\cal O}(\alpha\alpha_s^2)$, including QED, purely weak, and interference contributions across $Z+j$ and $Z+\gamma$ channels, as well as LO photoproduction with direct and resolved photons, using dimensional regularization and a hybrid renormalization scheme. The key finding is that EW corrections generally reduce the NLO QCD cross sections, with the dominant effect from the purely weak ${\cal O}(\alpha^2\alpha_s)$ terms, while QED, interference, and photoproduction provide smaller contributions; the new analytic results extend prior work and enable more precise SM benchmarks. This work improves the theoretical precision for Z-boson production at the Tevatron and LHC and informs PDF studies, including photon content, by supplying complete EW corrections and their interplay with QCD.

Abstract

We calculate the full one-loop electroweak radiative corrections, of ${\cal O}(α^2α_s)$, to the cross section of single $Z$-boson inclusive hadroproduction at finite transverse momentum ($p_T$). This includes the ${\cal O}(α)$ corrections to $Z+j$ production, the ${\cal O}(α_s)$ corrections to $Z+γ$ production, and certain QCD-electroweak interference contributions involving a single quark trace. We recover the QCD and purely weak corrections and study the QED corrections and the QCD-electroweak interference contributions for the first time. We also consider direct and resolved photoproduction in elastic and inelastic scattering. We present $p_T$ and rapidity distributions for the experimental conditions at the Fermilab Tevatron and the CERN LHC and assess the significance of the various contributions.

Figures (5)

• Figure 1: % $\mathcal{O}(\alpha^{1/2}\alpha_s)$ and $\mathcal{O}(\alpha^{3/2})$ tree-level diagrams interfering to yield $\mathcal{O}(\alpha^2\alpha_s)$ contributions to subprocesses $q+\bar{q}\to Z+q+\bar{q}$ and $q+q\to Z+q+q$.
• Figure 2: % Cross section distributions in (a) $p_T$ and (b) $y$ for $p_T>10$ GeV of $p\bar{p}\to Z+X$ at $\sqrt S=1.96$ TeV (Tevatron run II). In each frame, the NLO QCD result Gonsalves:1989ar, i.e. the sum of the $\mathcal{O}(\alpha\alpha_s)$ and $\mathcal{O}(\alpha\alpha_s^2)$ results (thin solid lines), the $\mathcal{O}(\alpha^2)$ Born result (thin dot-dashed lines), the purely weak $\mathcal{O}(\alpha^2\alpha_s)$ corrections to subprocesses (\ref{['qQ_Zg']}) and (\ref{['qg_Zq']}) Kuhn:2005az (thick dashed green lines), the residual electroweak $\mathcal{O}(\alpha^2\alpha_s)$ corrections (thin dashed blue lines), the $\mathcal{O}(\alpha^3)$ photoproduction contributions (thin dotted blue lines), and the total sum (thick solid red lines) are shown.
• Figure 3: % The residual electroweak $\mathcal{O}(\alpha^2\alpha_s)$ corrections in Fig. \ref{['fig:tevatron']} (thick solid red lines) are decomposed into the combination of the $\mathcal{O}(\alpha)$ QED corrections to subprocesses (\ref{['qQ_Zg']}) and (\ref{['qg_Zq']}) and the $\mathcal{O}(\alpha_s)$ QCD corrections to subprocess (\ref{['qQ_Zy']}) (thin solid lines), and the QCD-electroweak interference contributions from subprocesses (\ref{['qQ_ZqQ']}) (thin dot-dashed lines) and (\ref{['qq_Zqq']}) (thin dashed green lines).
• Figure 4: % Same as in Fig. \ref{['fig:tevatron']}, but for $pp\to Z+X$ at $\sqrt S=14$ TeV (LHC).
• Figure 5: % Same as in Fig. \ref{['fig:tevatron1']}, but for $pp\to Z+X$ at $\sqrt S=14$ TeV (LHC).