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

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