Complete electroweak O(alpha) corrections to charged-current e+e- --> 4fermion processes

TL;DR

This work delivers the first complete $O(\alpha)$ electroweak corrections for charged-current $e^+e^- \to 4f$ processes by employing a gauge-invariant complex-mass scheme and novel techniques to reduce 5- and 6-point one-loop tensor integrals. The authors integrate full virtual corrections with real-photon emissions and ISR, benchmarked against the RacoonWW DPA, and perform extensive cross-checks for UV/IR finiteness and gauge-invariance. They find that, at $\sqrt{s} \approx 170$–$300$ GeV, full corrections agree with the DPA within $\sim 0.3$–$0.6\%$, while at $\sqrt{s} \approx 1$–$2$ TeV the difference grows to $0.7$–$1.6\%$, and near threshold the full result improves the IBA by about $2\%$. The residual theoretical uncertainty is reduced to a few $\times 10^{-3}$ up to ~500 GeV, with higher-energy predictions requiring inclusion of Sudakov logarithms and improved QCD treatment for hadronic final states. Overall, the work provides a robust, gauge-invariant framework for precision predictions of $4f$ CC processes, essential for accurate $W$-mass determinations and future collider phenomenology, while outlining necessary directions for incorporating higher-order EW and QCD effects.

Abstract

The complete electroweak O(alpha) corrections are calculated for the charged-current four-fermion production processes e+e- --> nu_tau tau+ mu- anti-nu_mu, u anti-d mu- anti-nu_mu, and u anti-d s anti-c. The calculation is performed using complex gauge-boson masses, supplemented by complex couplings to restore gauge invariance. The evaluation of the occurring one-loop tensor integrals, which include 5- and 6-point functions, requires new techniques. Explicit numerical results are presented for total cross sections in the energy range from the W-pair-production threshold region up to a scattering energy of 2TeV. A comparison with the predictions based on the "double-pole approximation" (DPA) provided by the generator RacoonWW reveals corrections beyond DPA of < 0.5% in the energy range 170-300GeV, in agreement with previous estimates for the intrinsic DPA uncertainty. The difference to the DPA increases to 1-2% for sqrt{s} = 1-2TeV. At threshold, where the DPA becomes unreliable, the full O(alpha) calculation corrects an improved Born approximation (IBA) by about 1.6%, also consistent with an error estimate of the IBA.

Figures (2)

• Figure 1: Ten 6-point diagrams contributing to ${\rm e^+}$ e^+${\rm e^-}$ e^-$\to f_1 \bar{f}_2 f_3 \bar{f}_4$. The remaining 30 6-point diagrams are obtained by reversing the fermion flow in one or both of the fermion chains corresponding to the outgoing fermions.
• Figure 2: Absolute cross section $\sigma$ (upper plots) and relative corrections $\delta$ (lower plots), as defined in the text, to the total cross section without cuts for ${\rm e^+}$ e^+${\rm e^-}$ e^-$\to\nu_\tau\tau^+\mu^-\bar{\nu}_\mu$ obtained from the IBA, DPA, and the full ${\cal O}(\alpha)$ calculation (${\rm ee4f}$). All predictions are improved by higher-order ISR.