Electroweak Radiative Corrections to pp/ppbar -> W+/- -> l+/- nu Beyond the Pole Approximation

TL;DR

This paper delivers a complete calculation of electroweak O(alpha) corrections to pp/ppbar -> W -> l nu beyond the pole approximation, separating resonant and non-resonant contributions and including real photon emission and virtual corrections. Using a gauge-invariant decomposition and Monte Carlo phase-space slicing, the authors quantify how non-resonant, Sudakov-like logarithms affect the transverse-mass distribution, W width extraction, and W/Z cross-section ratios at the Tevatron and LHC. They find non-resonant corrections are small near the W pole but grow rapidly with MT, shifting the W width extraction and becoming comparable to QCD corrections at high MT, implying the need for resummation in extreme kinematic regimes. Updated electroweak K-factors for W/Z ratios and MT-based measurements are provided, along with a detailed comparison to previous pole-approximation results and clear guidance for incorporating these corrections into Run II and LHC analyses.

Abstract

We present a calculation of the complete electroweak O(alpha) corrections to pp/ppbar -> W+/- -> l+/- nu (l=e, mu) in the Standard Model of electroweak interactions, focusing on those corrections which do not contribute in the pole approximation. We study in detail the effect of these corrections on the transverse mass distribution, the W-width measurement, and the transverse mass ratio and cross section ratio of W and Z bosons.

Figures (8)

• Figure 1: The Feynman diagrams contributing to $W$ boson production at ${\cal O}(\alpha^3)$ in the Feynman - 't Hooft gauge ($\Phi^+$: Higgs -- ghost field, $u^+,u^{\gamma}$: Faddeev-Popov-ghost fields; the non-photonic contribution to the $W$ self energy insertion is symbolized by the shaded loop). An explicit representation of the non-photonic contribution to the $W$ self energy insertion can be found in Ref. [\ref{['Hollik']}].
• Figure 2: Feynman diagrams for the $W,Z$ box diagrams.
• Figure 3: The relative size (in percent) of the non-resonant ${\cal O}(\alpha)$ corrections to the Born $u \bar{d} \to W^+ \to \ell^+\nu$ parton-level total cross section as a function of the parton center-of-mass energy, $\sqrt{\hat{s}}$. The parameters used are listed in Eqs. (\ref{['eq:pars']}) -- (\ref{['eq:mhiggs']}).
• Figure 4: The ratio $[d\sigma^{{\cal O}(\alpha^3)}/dM_T]/[d\sigma^{ EBA}/dM_T]$ as a function of the transverse mass for a) $p\bar{p}\to e^+\nu_e(\gamma)$ and b) $p\bar{p}\to\mu^+\nu_\mu(\gamma)$ at $\sqrt{s}=2$ TeV. The solid lines show the ratio of the complete ${\cal O}(\alpha^3)$ electroweak and the EBA differential cross section. The dashed lines display the corresponding ratio for the case where only the resonant ${\cal O}(\alpha)$ EW corrections (see Eq. (\ref{['eq:res']})) are taken into account (pole approximation). The dotted lines show the ratio when the $p\bar{p}\to W^+(\to\ell\nu)Z(\to\bar{\nu}\nu)$ background is included in addition to the complete ${\cal O}(\alpha)$ EW corrections. The cuts and lepton identification requirements imposed are described in Sec. \ref{['sec:prelim']}.
• Figure 5: The ratio $[d\sigma^{{\cal O}(\alpha^3)}/dM_T]/[d\sigma^{ EBA}/dM_T]$ as a function of the transverse mass for a) $pp\to e^+\nu_e(\gamma)$ and b) $pp\to\mu^+\nu_\mu(\gamma)$ at $\sqrt{s}=14$ TeV. The solid lines show the ratio of the complete ${\cal O}(\alpha^3)$ electroweak and the EBA differential cross section. The dashed lines display the corresponding ratio for the case where only the resonant ${\cal O}(\alpha)$ EW corrections (see Eq. (\ref{['eq:res']})) are taken into account (pole approximation). The dotted lines show the ratio when the $pp\to W^+(\to\ell^+\nu)Z(\to\bar{\nu}\nu)$ background is included in addition to the complete ${\cal O}(\alpha^3)$ EW corrections. The cuts and lepton identification requirements imposed are described in Sec. \ref{['sec:prelim']}.