Improved effective vector boson approximation revisited

TL;DR

This paper revisits the improved effective vector boson approximation, calculating polarization-dependent luminosities in different gauges and assessing its accuracy for specific high-energy collision processes.

Contribution

It provides detailed calculations of vector boson luminosities for all polarization combinations in both unitary and axial gauges, and evaluates the approximation's quality for key collision reactions.

Findings

Luminosities calculated for nine polarization combinations.

Assessment of approximation accuracy in different gauges.

Application to $e^-e^+ o W^- W^+ u_e {ar u}_e$ and $e^-e^+ o t {ar t} u_e {ar u}_e$.

Abstract

We reexamine the improved effective vector boson approximation which is based on two-vector-boson luminosities $\mathrm{\mathbf{L}}_{\rm pol}$ for the computation of weak gauge-boson hard scattering subprocesses $V_1 V_2\to {\cal W}$ in high-energy hadron-hadron or $e^-e^+$ collisions. We calculate these luminosities for the nine combinations of the transverse and longitudinal polarizations of $V_1$ and $V_2$ in the unitary and axial gauge. For these two gauge choices the quality of this approach is investigated for the reactions $e^-e^+ \to W^- W^+ \nu_e {\bar\nu}_e$ and $e^-e^+ \to t {\bar t} \nu_e {\bar\nu}_e$ using appropriate phase-space cuts.