  It is widely known that the $ZH$ production channel provides a promising
probe to the $H \rightarrow b\bar{b}$ decay at the LHC, when the Higgs and the
$Z$ bosons are highly boosted along the transverse direction. We show how
information on the $Z$ boson polarization -- that is disregarded in the current
LHC analyses -- can relevantly improve the signal from background
discrimination, helping us to observe and achieve a larger precision for the $H
\rightarrow b\bar{b}$ measurement in the $Z(\ell\ell)H$ channel.
