Electroweak Radiative Corrections for Collider Physics

TL;DR

The paper addresses the precision frontier of electroweak radiative corrections in collider physics, detailing the SM structure, renormalization schemes, and modern computational tools for one-loop EW predictions. It integrates virtual and real-emission techniques, IR subtraction/slicing methods, and SMEFT extensions to quantify deviations from the SM at high energies. By outlining on-shell and background-field formalisms, tensor-integral reduction, and automated EW-NLO pipelines (e.g., Recola/OpenLoops/MadGraph), it provides a unified framework for accurate predictions across multi-particle final states. The work further discusses PDF/QED factorization, photon-induced processes, and high-energy Sudakov logarithms, highlighting practical implications for LHC phenomenology and future colliders. These elements collectively enable robust, gauge-invariant, and systematically improvable EW calculations essential for precision tests of the SM and constraints on new physics.

Abstract

Current particle phenomenology is characterized by the spectacular agreement of the predictions of the Standard Model of particle physics (SM) with all results from collider experiments and by the absence of significant signals of non-standard physics, despite the fact that we know that the SM cannot be the ultimate theory of nature. In this situation, confronting theory and experiment with high precision is a promising direction to look for potential traces of physics beyond the SM. On the theory side, the calculation of radiative corrections of the strong and electroweak interactions is at the heart of this task, a field that has seen tremendous conceptual and technical progress in the last decades. This review aims at a coherent introduction to the field of electroweak corrections and tries to fill gaps in the literature between standard textbook knowledge and the current state of the art. The SM and the machinery for its perturbative evaluation are reviewed in detail, putting particular emphasis on renormalization, on one-loop techniques, on modern amplitude methods and tools, on the separation of infrared singularities in real-emission corrections, on electroweak issues connected with hadronic initial or final states in collisions, and on the issue of unstable particles in quantum field theory together with corresponding practical solutions.

Figures (16)

• Figure 1: Structural diagrams illustrating the various fermion--photon splittings leading to collinear singularities in scattering processes.
• Figure 2: Diagrams illustrating the EW dipole terms with emitters and spectators in the final state (FS) or initial state (IS).
• Figure 3: Left: breakup of the $(x,Q^2)$ plane in terms of the $F_2(x,Q^2)$ and $F_\text{L}\xspace(x,Q^2)$ data used in Equation (\ref{['eq:gammaPDF']}). Right: ratio of photon PDFs from some common PDF sets (with uncertainty bands) to the LUXqed photon PDF (uncertainty band in red). (Taken from Reference Manohar:2016nzj.)
• Figure 4: Resonance distortion due to ISR (left) and FSR (right). Left: Cross-section prediction for $\text{e}\xspace^+\xspace\text{e}\xspace^-\xspace\to\gamma^*/\text{Z}\xspace\to\mathrm{hadrons}$ as function of the CM energy $\sqrt{s}$ from TOPAZ0Montagna:1993aiMontagna:1995ja, in which "with QED" refers to photonic ISR (taken from Reference Montagna:1998sp). Right: Differential cross section for $\text{e}\xspace^+\xspace\text{e}\xspace^-\xspace\to\text{Z}\xspace\text{Z}\xspace\to\text{e}\xspace^+\xspace\text{e}\xspace^-\xspace\nu_\tau\bar{\nu}_\tau$ in the invariant mass $M_{\text{e}\xspace^+\xspace\text{e}\xspace^-\xspace}$ of the final-state $\text{e}\xspace^+\xspace\text{e}\xspace^-\xspace$ pair for $M_{\nu_\tau\bar{\nu}_\tau}=M_\text{Z}\xspace\xspace$, in which "${\cal O}(\alpha)$ corrected" refers to photonic FSR and "resummed" to the corresponding effect of soft-photon resummation (taken from Reference Beenakker:1998cu).
• Figure 5: Structure of vector-boson scattering at hadron colliders (left) and an example for a loop diagram for $q\xspace q\xspace\to q\xspace q\xspace l\xspace\bar{l\xspace}\bar{l\xspace}l\xspace$ (right).