  The production of vector boson tagged heavy quark jets potentially provides
new tools to probe the jet quenching effect. In this paper, we present the
first theoretical study on the angular correlations ($\Delta\phi_{bZ}$),
transverse momentum imbalance ($x_{bZ}$), and nuclear modification factor
($I_{AA}$) of $Z^0$ boson tagged b-jets in heavy-ion collisions, which was
performed using a Monte Carlo transport model. We find that the medium
modification of the $\Delta\phi_{bZ}$ for $Z^0\,+\,$b-jet has a weaker
dependence on $\Delta\phi_{bZ}$ than that for $Z^0\,+\,$jet, and the
modification patterns are sensitive to the initial jet $p_T$ distribution.
Additionally, with the high purity of the quark jet in $Z^0\,+\,$(b-)jet
production, we calculate the momentum imbalance $x_{bZ}$ and the nuclear
modification factor $I_{AA}$ of $Z^0\,+\,$b-jet in Pb+Pb collisions. We observe
a smaller $\Delta \left\langle x_{jZ} \right\rangle$ and larger $I_{AA}$ of
$Z^0\,+\,$b-jet in Pb+Pb collisions relative to those of $Z^0\,+\,$jet, which
may be an indication of the mass effect of jet quenching and can be tested in
future measurements.
