One-loop leading logarithms in electroweak radiative corrections, I. Results

TL;DR

The work presents a comprehensive framework for the complete one-loop electroweak logarithmic corrections in the high-energy, fixed-angle regime, separating contributions into symmetric-electroweak (sew) and pure electromagnetic (em) parts and expressing large logs through $L(s)$ and $l(s)$. It demonstrates that leading double logarithms arise from soft–collinear gauge-boson exchange while subleading single logs originate from collinear emissions and parameter renormalization, with all corrections factorizing into Born amplitudes for external states. The authors provide explicit results for four-fermion neutral-current processes and gauge-boson-pair production in $e^+e^-$ annihilation, including detailed treatments of longitudinal modes via the Goldstone-boson equivalence theorem and the mixing of neutral gauge bosons. They also show how ultraviolet-origin logs from running couplings and mixing angle renormalization enter as part of the renormalization procedure, and discuss cancellations between certain PR and collinear terms for transverse states. Overall, the paper supplies practical, analytic recipes to extract leading electroweak logarithms for general amplitudes, enabling precise predictions and informing resummation strategies for future high-energy colliders.

Abstract

We present results for the complete one-loop electroweak logarithmic corrections for general processes at high energies and fixed angles. Our results are applicable to arbitrary matrix elements that are not mass-suppressed. We give explicit results for 4-fermion processes and gauge-boson-pair production in electron-positron annihilation.

Figures (8)

• Figure 1: Feynman diagrams leading to DL corrections
• Figure 2: Lowest-order diagrams for $\bar{l}^\kappa_\sigma l^\kappa_\sigma \to \bar{q}^\lambda_\rho q^\lambda_\rho$ and $\bar{q}^\lambda_\rho l^\kappa_\sigma \to \bar{q}^\lambda_\rho l^\kappa_\sigma$
• Figure 3: Dominant lowest-order diagrams for ${\rm e}$ e$^+{\rm e}$ e$^-\to\phi^+\phi^-$ and ${\rm e}$ e$^+{\rm e}$ e$^-\to {\rm W}$ W$^+_{{\rm T}} {\rm W}$ W$^-_{{\rm T}}$
• Figure 4: Dependence of the electroweak correction factor $\delta^{{{\rm ew}}}_{{\rm e}$ e$_\kappa^+{\rm e}$ e$_\kappa^-\rightarrow {\rm W}$ W$_\lambda^+{\rm W}$ W$_{-\lambda}^-}$ on the scattering angle $\theta$ at $\sqrt{s}=1\,{\rm TeV}$ for polarizations ${{\rm R}}{{\rm L}}$, ${{\rm L}}{{\rm L}}$, and ${{\rm L}}{{\rm T}}$
• Figure 5: Dependence of the electroweak correction factor $\delta^{{{\rm ew}}}_{{\rm e}$ e$_\kappa^+{\rm e}$ e$_\kappa^-\rightarrow {\rm W}$ W$_\lambda^+{\rm W}$ W$_{-\lambda}^-}$ on the energy $\sqrt{s}$ at $\theta=90^\circ$ for polarizations ${{\rm R}}{{\rm L}}$, ${{\rm L}}{{\rm L}}$, and ${{\rm L}}{{\rm T}}$