  Quit recently, two sets of new experimental data from the $LHCb$ and the
$CMS$ collaborations have been published, concerning the production of the
$Z^0$ vector boson in hadron-hadron collisions with the center-of-mass energy
$E_{CM}= \sqrt{s}=13\;TeV$. On the other hand, in our recent work, we have
conducted a set of $NLO$ calculations for the production of the electroweak
gauge vector bosons, utilizing the unintegrated parton distribution functions
($UPDF$) in the frameworks of $Kimber$-$Martin$-$Ryskin$ ($KMR$) or
$Martin$-$Ryskin$-$Watt$ ($MRW$) and the $k_t$-factorization formalism,
concluding that the results of the $KMR$ scheme are arguably better in
describing the existing experimental data, coming from $D0$, $CDF$, $CMS$ and
$ATLAS$ collaborations. In the present work, we intend to follow the same $NLO$
formalism and calculate the rate of the production of the $Z^0$ vector boson,
utilizing the $UPDF$ of $KMR$ within the dynamics of the recent data. It will
be shown that our results are in good agreement with the new measurements of
the $LHCb$ and the $CMS$ collaborations.
