The equivalent vector boson approximation at threshold energies

TL;DR

This paper derives the distributions of equivalent electroweak vector bosons in leptons and quarks, demonstrating the approximation's validity near threshold energies and discussing its implications for gauge boson emission processes.

Contribution

It provides a simple derivation of vector boson distributions and shows how threshold corrections naturally arise, extending the applicability of the approximation to lower energies.

Findings

The approximation is valid near $W$ and $Z$ boson thresholds.

Threshold corrections to distribution functions are naturally incorporated.

Implications for gauge boson emission processes are discussed.

Abstract

A simple derivation of the distributions of the equivalent electroweak vector bosons in leptons and quarks is presented. The applicability of the equivalent vector boson approximation at relatively low energies close to the $W$ and $Z$ boson thresholds is demonstrated. It is shown that the threshold correction to the distribution functions emerges naturally in the theory. Implications of the results for processes with the emission of the gauge bosons are discussed.