  We carry out the first detailed calculations of jet production associated
with $W$ gauge bosons in Pb+Pb collisions at the Large Hadron Collider (LHC).
In our calculations, the production of $W$+jet in p+p collisions as a reference
is obtained by Sherpa, which performs next-to-leading-order matrix element
calculations matched to the resummation of parton shower simulations, while jet
propagation and medium response in the quark-gluon plasma are simulated with
the Linear Boltzmann Transport (LBT) model. We provide numerical predictions on
seven observables of $W$+jet production with jet quenching in Pb+Pb collisions:
the medium modification factor for the tagged jet cross sections $I_{AA}$, the
distribution in invariant mass between the two leading jets in $N_{jets}\ge 2$
events $m_{jj}$, the missing $p_T$ or the vector sum of the lepton and jet
transverse momentum $|\vec{p}_T^{Miss}|$, the summed scalar $p_T$ of all the
jets in an event $S_T$, transverse momentum imbalance $x_{jW}$, average number
of jets per $W$ boson $R_{jW}$, and azimuthal angle between the $W$ boson and
jets $\Delta \phi_{jW}$. The distinct nuclear modifications of these seven
observables in Pb+Pb relative to that in p+p collisions are presented with
detailed discussions.
