Radiative corrections to pair production of unstable particles: results for e^+e^- --> 4 fermions

TL;DR

This work develops and applies a gauge-invariant double-pole approximation (DPA) within a pole-scheme framework to compute the complete ${\cal O}(\alpha)$ electroweak radiative corrections to $e^{+}e^{-} \to W^{+}W^{-} \to 4f$ with unstable $W$ bosons. It cleanly separates factorizable corrections (production and decay of on-shell $W$'s) from non-factorizable, soft/semisoft photon exchanges that couple different stages, and treats real-photon radiation across hard, semi-soft, and soft regimes with carefully defined phase-space mappings. The results show sizable corrections near the $W$-pair threshold driven predominantly by initial-state radiation, along with observable distortions in invariant-mass and angular distributions; non-factorizable corrections are generally small, while the formalism remains gauge-invariant and implementable for LEP2-era phenomenology and beyond. The study provides a practical, quantitative framework for incorporating RC into four-fermion final states via a DPA-based event-generation-compatible approach, enabling precise tests of the Standard Model and robust comparisons to anomalous triple gauge-boson couplings.

Abstract

Radiative corrections to processes that involve the production and subsequent decay of unstable particles are complex due to various theoretical and practical problems. The so-called double-pole approximation offers a way out of these problems. This method is applied to the reaction $e^{+}e^{-} \to W^{+}W^{-} \to 4 $fermions, which allows us to address all the key issues of dealing with unstable particles, like gauge invariance, interactions between different stages of the reaction, and overlapping resonances. Within the double-pole approximation the complete $\OO(α)$ electroweak corrections are evaluated for this off-shell $W$-pair production process. Examples of the effect of these corrections on a number of distributions are presented. These comprise mass and angular distributions as well as the photon-energy spectrum.

Figures (19)

• Figure 1: The generic structure of the factorizable $W$-pair contributions. The shaded circles indicate the Breit--Wigner resonances, whereas the open circles denote the Green functions for the production and decay subprocesses up to ${\cal O}(\alpha)$ precision.
• Figure 2: Examples for virtual (top) and real (bottom) non-factorizable corrections to $W$-pair production. The black circles denote the lowest-order Green functions for the production of the virtual $W$-boson pair.
• Figure 3: Comparison of different Born approximations for the total cross-section $\sigma_{\hbox{\scriptsize tot}}$ as a function of the accelerator energy. The four curves correspond to the cases i) -- iv) introduced in the text.
• Figure 4: The same curves as in the previous plot, this time for the lowest-order production-angle distribution $\,d\sigma/d\cos\theta\,$ at $\,2E=184\,\mathrm{GeV}$.
• Figure 5: Examples of one-loop diagrams that contribute to both factorizable and non-factorizable corrections.