One-loop weak corrections to hadronic production of Z bosons at large transverse momenta

TL;DR

The paper addresses the impact of electroweak radiative corrections on Z-boson production at large transverse momentum in hadronic collisions. It computes the full one-loop weak corrections to the partonic process $q\bar q \to Z g$ and derives compact high-energy expansions controlled by $\log(\hat s/M_W^2)$. The authors present exact analytic results and high-energy approximations, with numerical predictions for Tevatron and LHC; the corrections are negative and grow with $p_T$, reaching up to roughly $-40\%$ at the LHC, and include dominant two-loop Sudakov terms. The work provides a robust framework for incorporating electroweak effects into collider predictions and clarifies scheme dependencies between $\overline{MS}$ and OS renormalization schemes.

Abstract

To match the precision of present and future measurements of Z-boson production at hadron colliders, electroweak radiative corrections must be included in the theory predictions. In this paper we consider their effect on the transverse momentum ($p_T$) distribution of Z bosons, with emphasis on large $p_T$. We evaluate, analytically and numerically, the full one-loop corrections for the parton scattering reaction $q\bar q \to Z g$ and its crossed variants. In addition we derive compact approximate expressions which are valid in the high-energy region, where the weak corrections are strongly enhanced by logarithms of $\hat s/M_W^2$. These expressions include quadratic and single logarithms as well as those terms that are not logarithmically enhanced. This approximation, which confirms and extends earlier results obtained to next-to-leading logarithmic accuracy, permits to reproduce the exact one-loop corrections with high precision. Numerical results are presented for proton-proton and proton-antiproton collisions. The corrections are negative and their size increases with $p_T$. For the Tevatron they amount up to -7% at 300 GeV. For the LHC, where transverse momenta of 2 TeV or more can be reached, corrections up to -40% are observed. We also include the dominant two-loop effects of up to 8% in our final LHC predictions.

Figures (10)

• Figure 1: Tree-level Feynman diagrams for the process $\bar{q} q \to Z g$.
• Figure 2: One-loop Feynman diagrams for the process $\bar{q} q \to Z g$. The diagrams v5, v6 and b3 involve only charged weak bosons, $W^\pm$, whereas the other diagrams receive contributions from neutral and charged weak bosons, $V=Z,W^\pm$.
• Figure 3: Counterterm diagrams for the process $\bar{q} q \to Z g$.
• Figure 4: Relative one-loop corrections to the partonic differential cross sections ${\mathrm{d}} \hat{\sigma}^{ij} / {\mathrm{d}} \cos \theta$ at $\cos \theta =0$ for (a) $\bar{u} u$ channel, (b) $\bar{d} d$ channel, (c) $g u$ channel, (d) $g d$ channel. The solid, dashed and dot-dashed lines denote the modulus of the $\hat{\cal R}$ ratios, as defined in the text, for the full NLO cross section, the NLL approximation and the NNLL approximation of the one-loop cross section, respectively.
• Figure 5: Transverse momentum distribution for $pp{\rightarrow} Z j$ at $\sqrt{s}=14 \,\mathrm{TeV}$. (a) LO (solid), NLO (dashed), NLL (dotted) and NNLL (dot-dashed) predictions. (b) Relative NLO (solid), NLL (dotted) and NNLL (dot-dashed) weak correction wrt. the LO distribution. (c) NLL (dotted) and NNLL (dot-dashed) approximations compared to the full NLO result.