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

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.