Electroweak corrections to large transverse momentum production of W bosons at the LHC

TL;DR

This work computes the full electroweak ${\cal O}(\alpha)$ corrections to high-$p_T$ W boson production in association with a jet at the LHC, including both virtual and real photon contributions. It provides compact high-energy approximations capturing leading logarithms up to two loops, and validates these against full calculations. Numerically, EW corrections are negative and grow with $p_T$, reaching around -40% at 2 TeV for $pp\to Wj$, while two-loop NNLL terms partially offset this with +5–10% corrections. The study also analyzes ratios like $W^+/W^-$ and $W^+/Z$, finding substantial stability in the former but meaningful EW effects in the latter at high $p_T$. The results underscore the necessity of incorporating EW corrections for precision W-boson phenomenology at the LHC.

Abstract

To match the precision of present and future measurements of W-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 W bosons, with emphasis on large p_T. We evaluate the full electroweak O(α) corrections to the process pp -> Wj including virtual and real photonic contributions. We also provide compact approximate expressions which are valid in the high-energy region, where the electroweak corrections are strongly enhanced by logarithms of \hat{s}/M_W^2. These expressions include quadratic and single logarithms at one loop as well as quartic and triple logarithms at two loops. Numerical results are presented for proton-proton collisions at 14 TeV. The corrections are negative and their size increases with p_T. At the LHC, where transverse momenta of 2 TeV or more can be reached, the one- and two-loop corrections amount up to -40% and +10%, respectively.

Figures (3)

• Figure 1: Transverse momentum distributions for $W$-boson production at the LHC: LO predictions (a) and relative electroweak corrections for $W^+$ (b) and $W^-$ (c) production in NLO (dotted), one-loop NLL (thin solid) and NNLO (thick solid) approximation.
• Figure 2: Unpolarized integrated cross section as a function of $p_{\mathrm{T}}^{\mathrm{cut}}(W)$ for $W^+$ (a) and $W^-$ (b) production: estimated statistical error (shaded area) and relative electroweak corrections in NLO (dotted) and NNLO (solid) approximation.
• Figure 3: Ratio of the transverse momentum distributions for the processes (a) $p p{\rightarrow} W^+ j$ and $p p{\rightarrow} W^- j$ and (b) $p p{\rightarrow} W^+ j$ and $p p{\rightarrow} Z j$ at $\sqrt{s}=14 \,\mathrm{TeV}$: LO (thin solid), NLO (dotted) and NNLO (thick solid) predictions.