The production of vector boson tagged heavy quark jets provides potentially new tools to study jet quenching, especially the mass hierarchy of parton energy loss. In this work, we present the first theoretical study on $Z^0,+,$b-jet in heavy-ion collisions. Firstly utilizing a Monte Carlo transport model, our simulations give nice descriptions of the azimuthal angle correlation $Deltaphi_{jZ}$, transverse momentum imbalance $x_{jZ}$ for $Z^0,+,$jet as well as the nuclear modification factor $R_{AA}$ of inclusive b-jet in Pb+Pb collisions. Then we calculate the azimuthal angular correlation $Deltaphi_{bZ}$ of $Z^0,+,$b-jet and $Deltaphi_{bb}$ of $Z^0,+,2,$b-jets in central Pb+Pb collisions at $sqrt{s_{NN}}=$~5.02 TeV. We find that the medium modification of the azimuthal angular correlation for $Z^0,+,$b-jet has a weaker dependence on $Deltaphi_{bZ}$, as compared to that for $Z^0,+,$jet. With the high purity of quark jet in $Z^0,+,$(b-)jet production, we calculate the momentum imbalance distribution of $x_{bZ}$ of $Z^0,+,$b-jet in Pb+Pb collisions. We observe a smaller shifting of the mean value of momentum imbalance for $Z^0,+,$b-jet in Pb+Pb collisions $Deltaleftlangle x_{bZ} rightrangle$, as compared to that for $Z^0,+,$jet. In addition, we investigate the nuclear modification factors of tagged jet cross sections $I_{AA}$, and show a much stronger suppression of $I_{AA}$ in $Z^0,+,$jet than that of $Z^0,+,$b-jet in central Pb+Pb collisions.
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