# Polarisations of the $Z$ and $W$ bosons in the processes $pp \to ZH$ and $pp \to W^{\pm}_{}H$

## TL;DR

This paper presents a systematic method to analyze the polarization states of Z and W bosons in proton-proton collisions producing Higgs bosons, enabling detailed study of their interactions and potential new physics effects.

## Contribution

It introduces a comprehensive approach to relate polarization density matrices of Z and W bosons to measurable observables in proton-proton collisions, including effects of non-standard Higgs interactions.

## Key findings

- Complete polarization density matrices are linked to measurable observables.
- Method allows detailed analysis of Higgs boson interactions.
- Potential to identify deviations from Standard Model interactions.

## Abstract

The $Z$ boson in the process $pp \to ZH$ and the $W^+_{}$ and $W^-_{}$ in the process $pp \to W^{\pm}_{}H$ can be in polarised states. The polarisation density matrix of the $Z$ ($W$) boson contains the complete information about a state of polarisation of the $Z$ ($W$) boson, and $HZZ$, $HZ\gamma$ and $HWW$ interactions may be studied in detail from a careful analysis of these matrices. In this paper, a systematic approach to analyse these polarisation density matrices is presented. With the aim of making maximum use of the polarisation information, all of the elements of the polarisation density matrices are related with observables, which are measurable at the environment of $pp$ collisions. Consequences of non-standard $HZZ$, $HZ\gamma$ and $HWW$ interactions for these observables are discussed.