Center-of-mass energy dependence of intrinsic-$k_T$ distributions obtained from Drell-Yan production

The internal motion of partons has been studied through its impact on very low transverse momentum spectra of Drell-Yan pairs created in hadron-hadron collisions at next-to-leading order using the Parton Branching (PB) method which describes the evolution of transverse momentum dependent parton distributions. The main focus is on studying the dependence of the intrinsic transverse momentum of partons in the initial state (intrinsic-$k_T$ ) on collision center of mass energy, $\sqrt{s}$.While the collinear parton shower Monte Carlo event generators require parton intrinsic transverse momentum distributions strongly dependent on $\sqrt s$, which is not the case in the PB method.In this paper we do the detailed study of the impact of soft parton emission on this dependence and show that by requiring minimal transverse momentum of the radiated parton at a branching of the order of 1-2 GeV , the dependence on the intrinsic-$k_T$ in the PB method will be introduced and will be steeper by increasing the minimal value.