Different polarization definitions in same-sign $WW$ scattering at the LHC

TL;DR

This paper investigates how different definitions of polarization frames affect the measurement of W boson polarization in same-sign WW scattering at the LHC, highlighting the importance of reference frame choices.

Contribution

It introduces a method to analyze W polarization in a gauge-invariant way and compares the effects of different polarization reference frames on experimental observables.

Findings

Polarization fractions vary with the choice of reference frame.

Kinematic distributions are sensitive to polarization definitions.

The gauge-invariant separation aids in more accurate polarization measurements.

Abstract

We study the polarization of positively charged $W$'s in the scattering of massive electroweak bosons at hadron colliders. We rely on the separation of weak boson polarizations in the gauge-invariant, doubly-resonant part of the amplitude in Monte Carlo simulations. Polarizations depend on the reference frame in which they are defined. We discuss the change in polarization fractions and in kinematic distributions arising from defining polarization vectors in two different reference frames which have been employed in recent experimental analyses.