Rising Bosonic Electroweak Virtual Effects at High Energy e+e- Colliders

TL;DR

The paper develops a gauge-invariant, $Z$-peak subtracted framework to compute bosonic electroweak virtual effects in $e^+e^- \to f\bar{f}$ up to 1 TeV, decomposing corrections into four quantities $\widetilde{\Delta}_{\alpha,ef}$, $R_{ef}$, $V^{\gamma Z}_{ef}$, and $V^{Z\gamma}_{ef}$. It explicitly evaluates charged- and neutral-boson contributions, including $WW$ and $ZZ$ box diagrams, and implements the results in the PALM program, with cross-checks against TOPAZ0 showing good agreement. The study finds that bosonic effects grow with energy, reaching about 10% in hadronic cross sections at 1 TeV, and highlights the critical role of initial-state radiation (ISR) with a QED Structure Function approach, especially when $Z$ radiative return is included. These findings underscore the necessity of including full bosonic virtual corrections and ISR for precise high-energy collider predictions, and open avenues for exploring SUSY-like extensions in similar frameworks.

Abstract

The virtual massive gauge boson effects on several observables in the process of charged fermion pairs production at $e^+e^-$ colliders are computed up to the TeV energy range in the Standard Model, working in the ``$Z$-peak subtracted'' representation. It is shown that these effects increase regularly with energy, approaching the typical ten percent relative size. A careful numerical evaluation is proposed, where the conditions dictated by gauge invariance are consistently implemented.

Figures (11)

• Figure 1: Feynman diagrams for self-energy $WW$ components. $\Phi^{\pm}$ and $C^{\pm}$ are the would-be Goldstone bosons and ghosts, respectively.
• Figure 2: Feynman diagrams for $WW$ vertex component (Fig. 2a), for single $W$ vertex (Fig. 2b) and for fermion self-energy diagrams (Fig. 2c).
• Figure 3: Feynman diagrams for $WW$ box contribution; $I_{3f}=-{1\over2}$ (Fig. 3a), $I_{3f}=+{1\over2}$ (Fig. 3b).
• Figure 4:
• Figure 5: Feynman diagram for $Z$ vertex insertion.