W-boson pair production at lepton colliders in the Feynman-diagram gauge

TL;DR

This paper analytically calculates helicity amplitudes for W-boson pair production at lepton colliders in the Feynman-diagram gauge, revealing differences from the unitary gauge and clarifying the role of Goldstone bosons.

Contribution

It provides a detailed analytical derivation of helicity amplitudes in the FD gauge, highlighting the absence of energy growth in longitudinal W amplitudes and the explicit contribution of Goldstone bosons.

Findings

No energy growth of amplitudes for longitudinal W bosons in FD gauge

Goldstone boson contributions are explicit without high-energy limit

Physical distributions can be interpreted through individual amplitudes in FD gauge

Abstract

We calculate helicity amplitudes for $e^-e^+\to W^-W^+$ analytically in the Feynman-diagram (FD) gauge. We show that, unlike in the unitary gauge, there is no energy growth of the individual Feynman amplitudes for the longitudinally polarized W bosons, and the contributions from the associated Goldstone bosons are manifest even without taking the high-energy limit. We also find that the physical distributions can be interpreted by the individual amplitudes in the FD gauge.