Exploring non-perturbative Sudakov factor via $Z^0$-boson production in $pp$ collisions

$Z^0$-boson production at low transverse momentum offers an unique opportunity to explore the non-perturbative Sudakov factor. In this paper, we employ three parameterizations of the non-perturbative Sudakov factor to calculate the $\phi^*$-distribution and compare our results with the ultra precise experimental data. We extract the free parameters in each parameterization with a $\chi^2$ analysis. The parton-momentum-fraction dependence of these free parameters is also studied by comparing the values extracted at different collision energies and different rapidity ranges.